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VSEPR theory and hybridization in determining the shape of a molecule
Our chemistry teacher told us that both VSEPR theory (which says that the electron pairs in the valence shell of an atom arrange themselves in such a way that repulsions among them are minimized and this arrangement of the electron pairs determines the shape of a particular molecule)  and hybridization (which is the intermixing of a particular number of atomic orbitals to form equal number of new orbitals which have same shape and energy)  can be used to determine the shape of a molecule and that they are independent of each other. I understand how the shape of a molecule can be predicted using the VSEPR theory but i cannot understand how hybridization helps in determining or rather predicting the shape of a particular molecule. I have searched the net but could not find any useful resource.
How does hybridization help in determining the shape of a molecule?

Classical hybridisation theory does not predict geometry but instead rationalises it. It's not Here I have some atoms connected by these bonds, hence the hybridisation is X, and from this geometry Y follows. It is more like Here I have some atoms connected by these bonds, they are arranged in geometry Y , and therefore the hybridisation is X. (Geometry here is found either by experiment, some semiquantitative theory or via computations.) $$$$ Things are likely different for modern hybridisation theory. You could also ask why hybridisation X mathematically rationalises geometry Y.

If you are in general Chemistry, I wouldn't worry about going about determining the geometry in this way. It is much simpler to work from a VSEPR approach. Determining the geometry entirely from hybridization requires understanding how to write linear combinations of wave functions.

The VSEPR theory can indeed be used to predict geometry a priori. You would count the number of substituents around a central atom, counting any lone pairs as substituents also, and then find an arrangement that maximises the distance between all substituents. This theory works well for elements of the first period and compounds in which the central element is in the highest oxidation state, but tends to fail very rapidly for all others, most notably because it cannot account for anything outside of the traditional 2-electron-2-centre bond and because it considers all lone pairs equal even though they are typically not.
The hybridisation theory can only be used to predict geometry in a very limited number of cases that involve carbon atoms, and it only works because carbon is extremely regular. However, using hybridisation to predict carbon geometry is basically circling back onto VSEPR: you check how many atoms are bound to a certain carbon and thereby deduce whether this carbon atom will be $\mathrm{sp,sp^2}$ or $\mathrm{sp^3}$. Carbocations and carbanions can also be accomodated for (by either counting the anionic lone pair or ignoring it — as in VSEPR).
In general, however, it is not possible to predict the geometry following a certain hybridisation. Rather, one determines the geometry by an independent mean (e.g. quantum chemical calculations, gas phase diffraction), deduces the bond angles (and bond lengths) from the geometry and then derives a hybridisation. In short: hybridisation follows geometry, not the other way around.

Then what is the purpose of hybridization? It provides no answers, makes no predictions. Is it utterly useless?

@JuanPerez It simplifies things, especially for beginning learners. It is a good tool for a number of simple molecules often encountered and can be partially generalised in a way that is useful in most cases. Finally, it allows electronic predictions based on the geometry; this last one is probably the most powerful but also the one learners need the least.


text:
How to determine the correct InChI for a certain compound?
Let's say I have a compound L-xylulose 1-phosphate and I want to know its correct InChI, how to do this? The reason I ask is because when I go to different databases I get different results:
ChEBI:
$\ce{C5H11O8P}$
InChI=1S/C5H11O8P/c6-1-3(7)5(9)4(8)2-13-14(10,11)12/h3,5-7,9H,1-2H2,(H2,10,11,12)/t3-,5+/m0/s1

NIKKAJI; link taken from KEGG:
$\ce{C5H11O8P}$
InChI=1S/C5H11O8P/c6-3-1-12-5(8,4(3)7)2-13-14(9,10)11/h3-4,6-8H,1-2H2,(H2,9,10,11)/t3-,4+,5?/m0/s1

ModelSeed:
$\ce{C5H10O8P}$
InChI=1S/C5H11O8P/c6-3-1-12-5(8,4(3)7)2-13-14(9,10)11/h3-4,6-8H,1-2H2,(H2,9,10,11)/t3-,4+,5?/m0/s1

So, ChEBI and NIKKAJI do show the same chemical formula but different InChI expressions, while NIKKAJI and ModelSeed differ regarding their chemical formula but have the same InChI (which seems wrong, as ModelSeed's InChI suggests that it also als 11 Hs). But this would still not explain the differences for the first two...
That all looks quite fishy to me; how can I now decide which of the databases show me the correct information? Is it possible that one gets the same InChI for compounds that differ in their chemical formula (I thought this wouldn't be possible)?

One of the goals of the InChI project was to ensure uniqueness: [1]

Strict uniqueness of identifier
The same label always means the same substance, and the same substance always receives the same label (under the same labelling conditions). This is achieved through a well-defined procedure of obtaining canonical numbering of atoms.

Whilst this is often the case for InChI strings, there are some (complex) examples where the above goal has not been met, for example in the natural product Spongistatin (below) where two isomers incidentally have the same InChI key: [2]

InChI=1S/C63H95ClO21/c1-33(19-42(67)18-17-35(3)64)20-53-55(72)57-39(7)58(79-53)59(73)63(75)31-51(70)37(5)52(85-63)16-14-12-13-15-44-22-43(68)27-61(81-44)29-47(76-11)23-45(82-61)25-50(69)38(6)56(78-41(9)66)36(4)34(2)21-49-28-60(10,74)32-62(84-49)30-48(77-40(8)65)24-46(83-62)26-54(71)80-57/h13,15,17-18,36-39,42-49,51-53,55-59,67-68,70,72-75H,1-3,12,14,16,19-32H2,4-11H3/b15-13-,18-17+/t36-,37+,38+,39+,42+,43+,44+,45-,46+,47+,48-,49+,51-,52-,53-,55+,56+,57-,58+,59+,60+,61+,62+,63-/m0/s1
Although InChI can sometimes break (as per above) most of the issues with InChI strings are with implementation (how the structure is parsed to the thing generating the string in the first place). Several (common) features are at present un-supported by the InChI implementation:

Polymers
Complex organometallics
Markush structures
Mixtures
Conformers
Excited state and spin isomers
Local stereochemistry/chirality
Topological isomers
Cluster molecules
Polymorphs
Unspecific isotopic enrichment
Reactions

Generation of InChI strings
InChI is, by nature, an algorithm designed to be ran by a computer. Whilst strings can be parsed by humans (with ennough effort), the complexity of the strings is such that it is challenging to ensure they're correct. The InChI FAQ specifically deals with this:

You should not do so (though you of course can). This may give apparently reasonable answers but it is error-prone and may break relations in the InChI.

The most recent implementation of InChI is provided by the InChI trust, open source and free of charge.[3]
As alluded to above, a common source of InChI errors is the way in which the structure of interest is passed to the algorithm rather than with a fundamental flaw with the process used to generate it. Sh*t in, sh*t out, so to speak.
To give a concrete example, consider the heterocyclic system below:

Clearly, the two tautomeric forms cannot be distinguished chemically, but depending on how the InChI string is generated, they may end up having the same or different strings. In this case, we need to specify to the InChI algorithm whether we want to fix the hydrogens (to show a single tautomer, each of which would have a unique InChI string), or not fix them (such that both tautomers have the same InChI string)
Validation
The real question you're possibly interested in isn't How to determine the correct InChI for a certain compound?, but rather How to validate an InChI string for a certain compound?.
Given the complexity of the InChI strings, this is a challenging thing, and to my knowledge there is no tool which allows a string to be provided and says whether it is valid or not (similarly you can't provide a proposed IUPAC name to any tool which will say whether it is the IUPAC preferred name).
One thing you can do is use the InChI string to generate a structure (ChemDraw does this). Using your strings from the question, it's evident that they actually refer to different forms of the molecule (cyclic vs acyclic, just imagine the terminal primary alcohol attacking the ketone).

Chemically, it may be that the cyclic and acyclic forms are in equilibrium- in this case there is no way for InChI to represent the mixture (and hence which structure used to generate the string is ambiguous). It could also be that they are separable chemically and not interconverting, in which case quite rightly they should have different InChI strings.

[1]: Journal of Cheminformatics, 2015, 7, 23
[2]: http://www-jmg.ch.cam.ac.uk/data/inchi/ Accessed 3-Sept-2017
[3]: http://www.inchi-trust.org/about-the-inchi-standard/
Accessed 3-Sept-2017

Thanks a lot for this detailed reply, that helped already. Could you comment on the example from above (ChEBI and NIKKAJI). I still fail to understand why their InChIs are different. Did they maybe use different tools to generate them?

They have different InChI strings because they represent different structures. I have no idea how those respective websites generated the strings, so can't comment further (sorry!)

Ok, then I guess that's as far as we can get here :) Thanks once more for the detailed explanation.

It's worth pointing out that InChIs and InChIKeys are different things (though related). In the spongistatin example, while they have the same InChiKey, the InChI strings themselves are different. While designed such that collisions are rare, absolute uniqueness was not a design goal for InChiKeys. (Or in other words, your first quote is about InChI proper, not InChiKeys, so the spongistatin example is not strictly a counterexample.)

Related: Structure that breaks InChI

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What is the correct regular expression for InChI?
When I look for a regular expression for InChI, I succeed on EBI's MIRIAM Registery website:
^InChI\=1S?\/[A-Za-z0-9]+(\+[0-9]+)?(\/[cnpqbtmsih][A-Za-z0-9\-\+\(\)\,\/]+)*$

And indeed it works for some examples (using Python's re module):
import re

pattern = '^InChI\=1S?\/[A-Za-z0-9]+(\+[0-9]+)?(\/[cnpqbtmsih][A-Za-z0-9\-\+\(\)\,\/]+)*$'

s = 'InChI=1S/C2H6O/c1-2-3/h3H,2H2,1H3'

re.findall(pattern, s)

will print
[('', '/c1-2-3/h3H,2H2,1H3')]

However, if I take other examples, as e.g. this one
s2 = 'InChI=1S/C6H12O6/c7-1-2-3(8)4(9)5(10)6(11)12-2/h2-11H,1H2/t2-,3-,4+,5+,6?/m1/s1'

it fails
re.findall(pattern, s2)

will return
[]

What is the correct and general regular expression for InChI?
EDIT
If I see this correctly, in the pattern from above, question marks are not taken into account which are used to mark both “unknown” and “undefined” chiral centres. If one adjusts the regex accordingly, it at least works for the example above; whether it then holds for all InChI is unclear, of course.
pattern = '^InChI\=1S?\/[A-Za-z0-9]+(\+[0-9]+)?(\/[cnpqbtmsih][A-Za-z0-9\-\+\(\)\,\/\?]+)*$'

s2 = 'InChI=1S/C6H12O6/c7-1-2-3(8)4(9)5(10)6(11)12-2/h2-11H,1H2/t2-,3-,4+,5+,6?/m1/s1'

re.findall(pattern, s2)

will return
[('', '/c7-1-2-3(8)4(9)5(10)6(11)12-2/h2-11H,1H2/t2-,3-,4+,5+,6?/m1/s1')]

Given the complexity of InChI, e.g. canonicalization, I doubt that there exists a regular expression that matches exactly the valid InChI strings.

@aventurin: What about this regular expression from the link above? There is also a github repository for this. I hardly know anything about InChI, but it feels that it might be possible to find such a regular expression but that the ones published do not cover all cases?!

If the InChI grammar would be on the same level of the Chomsky hierarchy as regular expressions (type-3) it would be possible to find such a regular expression. But as I've already said, I doubt this is the case. See the following mailing list post to get an idea about the complexity of the InChI grammar. https://sourceforge.net/p/inchi/mailman/message/1619718/

@aventurin: Thanks, will go through this! The example above one can get to work, by taking ? into account as well I just realized: pattern = '^InChI\=1S?\/[A-Za-z0-9]+(\+[0-9]+)?(\/[cnpqbtmsih][A-Za-z0-9\-\+\(\)\,\/\?]+)*$' Whether that then works for all InChIs I don't know, of course...

@aventurin: I added a regex below which seems to work all the InChIs I currently work with; could you take a look whether it looks ok and maybe you also know an example where it would fail?! Thanks!

Your regular expression matches strings that are not valid InChIs, e.g. InChI=1S/2z or InChI=1S/CH100. If that's OK for your application, you should probably clarify your requirements. You could restrict to valid atomic symbols in the main layer by using something like ^InChI\\=1S?\\/((H|He|Li|Be|...)([1-9][0-9]*)?)+....

@aventurin: Thanks for your reply. This would then indeed be a problem with the official regex. The examples you give, InChI=1S/2z and InChI=1S/CH100, however, wouldn't be matched, it returns [('', '')] for the pattern in my answer. But I see where the problems could arise, thanks for pointing this out! Might be worth checking how inchi-trust handles such examples....

I used the matches method with Java regular expressions. You might get different results with other regex implementations.

I have down-voted the question, because I fail to see the usefulness of this approach. You should add context for which it is helpful, otherwise this becomes a purely computational exercise and should be off-topic here. Right now you are parsing an InChI string without actually caring what it represents, you delimit it with ^$ so it would only match a complete match (you cannot search with this regex). Also: Which implementation (language) are you using?

@Martin-マーチン: Thanks for giving a reason for the downvote. I thought giving an example of an InChI that cannot be matched would be sufficient as context. If I want to check whether a provided string is a valid InChI representation, then one needs a regex and the one that was used in the MIRIAM registery apparently failed for many. I was under the impression that chemists should have a way to check this and therefore asked here. And yes, I don't want to search with this regex but analyze an entire string i.e. am only interested in a complete match. Language is Python.

As long as you are not looking for something very specific, and you are not performing a sanity check of what you are matching against, the provided regular expression will match more often wrong than falsely not matching. It will even match more nonsense InChI than total number of existing ones. It is therefore not much better than the trivial catch them all:
^InChI\=1S?\/[^\s]+(\s|$)

The space (and some few others) is a character that will not be part of a correct InChI. The above will therefore match all correct InChI strings (and many more), and certainly more correct ones than the one given in the question (or in your answer).
The principal problem with the whole approach is basically given in the technical FAQ in section 5. Depending on what we are looking at, not all the layers will be present. There is not even a guarantee that a sum formula is present, as represented by the proton: InChI=1S/p+1. This one (and its relatives) is basically responsible why regex is doomed from the start, and that there is no correct regex in the first place.
If we wanted to implement only a tiny fraction of sanity control to reduce the number of mismatches, we will soon see that the whole string becomes about a page long.
Let's examine the given regex a little more to actually understand what it and why it's attempt is futile.
^InChI\=1S?\/[A-Za-z0-9\.]+(\+[0-9]+)?(\/[cnpqbtmsih][A-Za-z0-9\-\+\(\)\,\/\?\;\.]+)*$

Beginning with
^

matches the start of the string, which is not really necessary
 InChI\=1S?

matches the prefix, while leaving it open if standard or not
           \/[A-Za-z0-9\.]+(\+[0-9]+)?

matches a sum formula (even the silly ones) or anything that doesn't have a main layer and goes straight to isotopes or charges, etc.. Better would here be to make the sum formula optional, i.e. (\/[A-Za-z0-9\.]+)?
                                      (\/[cnpqbtmsih][A-Za-z0-9\-\+\(\)\,\/\?\;\.]+)*$

this is pretty much a fancy way of saying match any kind of layer, as often as you want,( or not,) in what order is just convenient, with whatever content.
However, it does not match *, which it should: InChI=1S/2C2H5.Zn/c2*1-2;/h2*1H2,2H3; as given in the FAQ.
A much better approach would be to match the layers separately, to have a little control, because they have a predefined order. For example start with the connectivity 1.1 layer (\/c[0-9\-\*\;\(\)]+)?, move to the connectivity 1.2 or hydrogen layer (\/h[H0-9,\(\)\;]+)?. I am not too sure whether I caught all special characters that might be inserted. Then match on with charge (\/q(\+|\-)+[1-9]+[0-9]*)? and the proton balance \/p, the various stereochemistry layers, fixed layers, etc. There are plenty. I probably got the charge already halfway wrong, as I am not sure whether it needs ; or not.
Coming up with a correct and not too greedy regex for each layer is already a nice task, and if you can do something useful with it, good. For everything else, there is a reason that a software exists to create and parse those strings. For every other purpose the greedy match-it-all from the start should work perfectly fine. Now, InChIKeys are something very different ...

This might not be the final version but covers all cases I have encountered so far (if you find an InChI which cannot be matched with this expression, please post it in the comments along with a source, so that one can adapt the regex):
pattern = '^InChI\=1S?\/[A-Za-z0-9\.]+(\+[0-9]+)?(\/[cnpqbtmsih][A-Za-z0-9\-\+\(\)\,\/\?\;\.]+)*$'

The following changes were made compared to the one posted in the question:

One also accounts for . in the chemical formula; check inchi-trust for an example
One takes ? into account; check inchi-trust for a detailed explanation
One also checks for ; ; check inchi-trust for an example
One also has to take . into account later on, not only in the chemical formula. That is explained in "The IUPIC International Chemical identifier":

/m parity inverted to obtain relative stereo ( 1 = inverted, 0 = not inverted, . = inversion does not affect the parity)

I guess this post will be updated in the future but for my examples it works now and all changes can be backed up by trustworthy sources.
The regular expression is updated now to the one I proposed. Apparently, they are happy to change their expression, so if you find cases where a valid InChI cannot be mapped, please report it to them or add it here in the comments. Clearly, this regular expression might also match strings which are actually not chemicals but at least one should be able to identify each valid InChI as InChI.

@downvoter: Could you please explain why you downvoted? It clearly addresses the question and provides explanation + sources. If there is something wrong, it would be nice to know what so that it can be fixed.

Why all the fuzz? If you are not performing a complete sanity check of every layer, then why match it at all? For example complete garbage like InChI=1/A100/cAfoobar would be matched. therefore InChI\=1S?\/[A-Za-z0-9\.\+]+(\/.+) already matches all correct InChI (and extracts the relevant layers, but it also matches all incorrect garbage. Somehow I fail to see how this string could be helpful anywhere...

As for your answer (I am not a down-voter), this is not a programming subsite, so you need to explain (either in the question or in the answer) what the parts of the regex actually do, and why they do it, right now this is all rather confusing. (Also please do not use any edit statements, revise the complete answer as necessary and make it read consistently. If anyone needs to know what changed, there is an extensive edit history available.)

@Martin-マーチン: All I need is a regex that tells me whether a given string has the correct form of an InChI, so it should identify all InChIs as correct. Clearly, one will then also match a lot of things that are not chemically relevant as your example but it should at least work for each valid InChI which the former regex apparently did not do.

@Martin-マーチン: And of course, if there is a better way of doing it, I would be more than happy to know about it. I just took the one provided, noticed that it failed and modified it that it works. If there is a better way that also checks each layer it would be great to know about it!

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text:
Nonpolar vs Polar Covelant Bonding
So I'm having trouble understanding the difference between the two. Looking specifically at water and carbon dioxide, CO2 is non-polar, because it is symmetrical and carbon shares two electrons with each oxygen and vice versa. But doesn't oxygen also share 1 electron with each hydrogen and vice versa? I know water isn't symmetrical, but for a molecule which I haven't seen the shape before how would I figure it out?

You've muddled it completely for yourself so no wonder you're confused.

What do you mean by I muddles it? Am I overthinking it?

It would help to read about VSEPR, the theory that predicts the shape of molecules.  https://chem.libretexts.org/Textbook_Maps/General_Chemistry_Textbook_Maps/Map%3A_Chemistry%3A_The_Central_Science_(Brown_et_al.)/09._Molecular_Geometry_and_Bonding_Theories/9.2%3A_The_VSEPR_Model

Look at each bond separately. In $CO_2$, in each $C=O$ bond, electrons are shifted towards oxygen atom as is has more pulling tendency(electron affinity). Now there is a formation of $\delta+$ charge on carbon and $\delta-$ on oxygen. This forms a dipole and you write it vectorially. In carbon dioxide, the vectors are equal and at $180$ degrees, so they cancel out and net dipole moment is 0, thus nonpolar molecule. Similarly, for the 2 $O-H$ bonds you get a net nonzero dipole moment, leading to a polar molecule.

Oh. Thanks for help. I think I misinterpreted something that was written in the textbook


text:
Amine Inversion and Paramagnetism
In amine inversion, there is a planar $sp^2$ intermediate.

The electron pair transferred from the blue lobe to the red one during the inversion. It is natural to assume, for a layman like me, that in the planar intermediate the electron pair is present in both lobes- one electron in each. That would impart paramagnetic character to the molecule. Does this really happen? I couldn't find any such phenomenon on internet.
Picture: http://chemistryjee.blogspot.in/2015/02/amines.html

For somebody who is not well-versed in quantum mechanics, it might be natural to guess that this is the case. But if I were you, I wouldn't assume so.
Both electrons share the same p-orbital, and are therefore still paired. They both occupy the entire volume of the p-orbital. What they do not do, is to divide the p orbital up into two half-orbitals, with each electron taking one half.
There is a somewhat related question here, which might address some issues: How do Electrons Cross Nodes in Orbitals?


text:
Freundlich Equation's dimensions
So, we have the Freundlich's Isotherm equation as $\frac{x}{m} = kp^{\frac{1}n}$, where the LHS measures the extent of adsorption with the corresponding pressure $p$ in the RHS with the two constants, $k$ and $n > 1$. But, I got a little confused with the dimensions on both the sides. Since $\frac{x}{m}$ is dimensionless, so should be the RHS. Therefore, I reasoned that the constant $k$ having units should cancel out the units of $p^{\frac{1}n}$. But yet I'm confused, and I don't think its right. What is going on?

Technically speaking, one typically wouldn't write the left hand side unitless, as it is the ratio of the mass of two different components (usually mg of some chemical per gram of the surface).
But, otherwise your intuition is correct and $k$ just needs units that will cancel with $p^{\frac{1}{n}}$ to give the units on the left hand side. So $k$ could have units of $\left(\dfrac{\text{mg chemical}}{\text{g surface}}\right)\left(\mathrm{bar^{\frac{-1}{n}}}\right)$.
We could also reformulate Freundlich's equation in terms of concentration (since we are dealing with an isotherm) as: $$q=KC^{\frac{1}{n}}$$ where $q=m/x$, $C$ is concentration of the chemical and $K$ is a new constant with units of $\left(\dfrac{\text{mg chemical}}{\text{g surface}}\right)\left(\mathrm{{\dfrac{L}{\text{mg chemical}}}}\right)^{\frac{1}{n}}$.
Source

About the units of the constant K of the Freundlich equation in terms of concentration in the answer above. It seems that you have "double thought" it - applied the reciprocal twice - once by inverting mg chemical per L to give L per mg chemical, but then again by writing a negative sign before the 1/n. It seems to me that the units of K should be "(mg chemical/g surface)(L/mg chemical)^(1/n)

You are right, I must have been indecisive at the time about how I would show the reciprocal and accidentally did it twice. I will make that edit, thank you for spotting that. In the future, it would be better to suggest an edit/post a comment on the original answer rather than add a new one.

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Clarification of Kinetic Energy during Phase Change
This website states that:
During a change of phase the temperature does not change, but the internal energy does.  The internal energy is the sum of the kinetic energy of the molecules and the chemical potential energy of the molecules.  During a change of phase, the average kinetic energy of the molecules stays the same, but the average potential energy changes.
I'm confused as the two bolded statements seem to contradict each other.
My interpretation is that during a phase change, the temperature remains equal, but the kinetic energy of its particles increase/decrease.
Could this please be clarified and confirmed?

In thermodynamics, temperature is essentially a measure of the average kinetic energy of a sample. See, for example, Wikipedia, especially section 2.1.

As temperature reflects the average KE, wouldn't temperature still increase during phase change?

It requires energy to change the phase of a material. This energy (in most cases) is supplied through heat. When you heat the material, this will cause the temperature (or average kinetic energy) to increase. However, if you reach a certain temperature (at certain conditions), this added energy will cause the material to undergo a phase transition. Phase transitions cost energy. So for a while, the temperature will not change. The energy from the heat will be used to change the phase of the material.

Once all of the material has changed its phase, then the added heat will continue to increase the temperature. So to answer your question, the temperature does not change during phase change.

https://chemistry.stackexchange.com/questions/15852/during-a-phase-change-in-matter-why-doesnt-the-temperature-change

Well, the KE stays the same, so the temperature stays the same. Or the other way round, if you prefer to think of it that way.

In my view, temperature is just a number to describe how much a molecule is moving, i.e. its kinetic energy (KE).
I think of phase changes as a having-dinner analogy: when you eat, your KE is the same (i.e. you're not moving faster or slower like when you walk or run, so your KE isn't changing much), but your potential energy (PE) is changing since the food you're consuming can be thought of as potential energy to be stored and used up later.
Thus, when you're eating, your internal energy (which is the sum of PE and KE) is changing since the PE variable changes, but temperature as a number to describe your movement isn't since your movement (i.e. KE variable) isn't changing.

Couldn't we say that during the change the molecules absorb the heat as kinetic energy, move faster so they can overcome the attractions (potential energy)? But the attraction are still there. So after a little time the molecules would be in a greater distance (higher potential energy) with same kinetic (conservation of energy) so the temperature will remain the same.

The temperature is not the average kinetic energy.
This is a bad habit which most chemists and physicists pick up because for an ideal gas, and for most systems at normal parts of the phase diagram, this is true. In thermodynamics, however, temperature is defined in terms of the thermodyanic beta as,
$$
\frac{1}{k_b}\frac{\partial S}{\partial E}=\beta
$$
where $\beta=1/(k_bT)$.
That is to say that during a phase change, because the temperature is constant, the ratio of the change in entropy to the change in total energy (kinetic plus potential) is constant. This means that when the phase change just begins and just ends, the ratio of entropy and energy must be identical, and unless this is quite an unusual phase change, this means both need to have changed from their initial values. It wouldn't be a phase change if neither entropy nor energy changed. Because temperature is defined in this way and not as $T\propto\langle \text{KE}\rangle$, then it is perfectly reasonable for the kinetic energy to either increase or decrease during a phase change.
For instance, in normal systems one would expect that the entropy of the liquid would almost certainly be larger than the entropy of the solid. This means that the total energy must decrease by an amount $T_m\Delta S$, which makes sense as one would expect the potential energy (and perhaps the kinetic energy) to decrease when going to the liquid phase. In other words, the entropic gain allows the system to energetically relax. With this picture, it is not too surprising that the average kinetic energy can decrease during a phase change.


text:
dissolving gold
I tried to refine gold, and I had something very strange happen. I have a bar of mixed metals made up of gold plated material. There is copper mixed in it for sure, and I would assume other metals too like steel, aluminum, and solder.
I put this bar in muriatic acid mixed with $\ce{H2O2}$, the reaction is over and by now it is just muriatic acid again, just more diluted.
Then I put the bar in a solution of baking soda mixed with water with acid still on it and an acid/base reaction happened. What I don't get is that within seconds the gold on the surface of the bar went into solution.

What happened, how the gold was dissolved, and how do I get it out of the solution?

You put a gold-plated bar in a mixture of $\ce{HCl}$ and $\ce{H2O2}$ (what mixture and molarity?) to achieve what result?  And then you put the bar, presumably still gold-plated(?), in an aqueous solution of $\ce{NaHCO3}$ and observed what reaction?  And you determined the gold was dissolved how?


text:
Why carboxylic group gets protonated preferantially on carbonyl oxygen?
When carboxylic group gets protonated, by strong acid, proton binds rather to carbonyl oxygen, then to hydroxyl. Is that really true? Or maybe it's a case of kinetic vs thermodynamic stability?

Are you asking about carboxylic acid or hydroxyketone? There's a significant difference.

carboxylic acid

I thought so, edited it. Next time write properly, to not give us additional work.

https://chemistry.stackexchange.com/questions/20289/more-acidic-protonated-carbonyl-or-protonated-hydroxyl

A productive mechanism involving addition to the acid will require activation of the carbonyl group (consider, for example, acid catalyzed esterification). That happens via protonation of the carbonyl, not the hydroxyl. The latter is not productive (unless your mechanism proceeds via an acylium ion). Since proton transfers are fast, you are accessing all of the protonated specifies, and whichever one reacts most quickly is the one you should consider for the mechanism.


text:
Electronegativity difference value
What is the exact electronegativity differece value of determinig whether a compound is ionic or covalent? Is it 1.7 or 2.1?

The short answer is neither. A bond's degree of ionic behavior depends on the model used, the compound at hand, and the scale of electronegativity. If you define it through dipole moment (at least 50% of elementary charge on each 'atom'), and use Pauling's classical electronegativity, and restrict yourself to diatomic compounds, I believe a simplified derivation shows it is $1.7$. (continues)

There is nothing exact about it. Use any value you like. It is arbitrary anyway.

(continues) This does not mean it is accurate, or that the compound with $|EN| \ge 1.7$ will show properties you  would associate with a typical ionic compound. Part of the reason is that even the dipole moment is not an accurate measure of a bond's ionic degree; it is affected by other electrons at each constituent 'atom'. There are also other models, and like 20 something different scales (many of which are disguised as pseudo-Pauling for convenience), two-dimensional analysis (less error prone, predicts metallic bond), etc etc

If you wish to skip the literature overview, I suggest reading two papers by Sproul (J Chem Edu, 70, 7, 1993, p 531;  J Chem Edu, 78, 3, 2001, p 387) and one by Meek, Garner (J Chem Edu, 82, 2, 2005, p 325).

I'm voting to close this question as off-topic because it's based on false premise.


text:
How to explain (non-/anti-) aromaticity in fulvene with the help of resonance structures?
Can someone please explain why the resonance structures of fulvene 1 is non-aromatic and 2 is anti-aromatic?

Why is fulvene non-aromatic, even though it has $4\pi$-electrons and no $\mathrm{sp^3}$ carbons?

Well just apply the Huckel rules and see there's 4 electrons in conjugation in (2) while (1) is not fully conjugated.

Structure 1 has pendant pi bonding.  The Huckel rules require a cycle of conjugated electrons and that does not go with pendant pi bonds.

TL;DR: You cannot assign aromaticity based on a couple of resonance structures. Penta-fulvene has negligible (anti)aromatic character, which is supported by computational and experimental investigations.

Introduction
Aromaticity is a complex and still not fully understood phenomenon. Active investigations are experimentally and computationally challenging. Unfortunately in schools and university it is often taught as something quite simple to fathom, which can be explained by looking at Lewis structures and counting electrons. This maybe true for many common compounds, but when you dig deeper you'll very soon find the limitations. (See the notes below.) It is certainly not helpful in the case of fulvenes.
Penta-fulvene's resonance and (anti)aromaticity
The resonance structures you have drawn are correct, but the set is missing one member, coincidentally the more important one. (Please see the notes below on resonance.) There are more, but those are with more charge separation and likely have only little contribution.

In general you cannot judge one resonance structure on its own. In this case it is not helpful at all. In all resonance structures, the π-system is fully conjugated, and delocalised over the whole molecule.
Penta-fulvene has C2v symmetry, and we see deviations in the single and double bond lengths. The values are from a quite extensive study on substituted fulvenes: K. Najafian, P. von Rague Schleyer, and T. T. Tidwell, Org. Biomol. Chem. 2003, 1, 3410-3417 (DOI: 10.1039/B304718K). Unfortunately, they use the unsubstituted fulvenes as comparison. From the abstract:

The fulvenes (1a–4a) have modest aromatic or antiaromatic character, and are used as standards for comparison.

Another study basically comes to the same conclusion, see E. Kleinpeter, and A. Fettke, Tetrahedron Lett. 2008, 49 (17), 2776-2781 (DOI: 10.1016/j.tetlet.2008.02.137). Citing quite liberally from various parts and omitting any literature references:

Fulvenes 1–4 have previously been synthesized (triafulvene 1, pentafulvene 2, heptafulvene 3 and nonafulvene 4), and were studied with respect to their dipole moments and NMR spectra. The 1H and 13C NMR spectra of triafulvene 1 (both protons and carbon atoms of the 3-membered ring moiety display resonances in the region of aromatic compounds) evidence a significant contribution of the resonance form 1b [aromatic charge separation]; the corresponding NMR spectra of 2–4, however, display typical olefinic compounds with strongly alternating bond lengths and only a small extent of charge separation (corroborated by the relatively small dipole moments).
[...]
Dependent on the criterion employed, 1–4 were reported as partially aromatic, non- or even antiaromatic.
[...]
[...] However, the expected partial aromaticity of the 3-membered ring moiety of 1 was not observed (vide supra).
  Similar conclusions can be drawn for the presence of partial aromaticity in 2: even if the occupation of πC=C of the exocyclic double bond is lowest in the series (which can be realized with the participation of 2a, corroborated by the correct direction of the dipole moment), both ICSSs [iso-chemical-shielding surfaces] at ±0.1 ppm [2: ICSS = −0.1 ppm (5.0); ICSS = +0.1 ppm (6.2)] are far away from reference benzene 7 [7: ICSS = −0.1 ppm (7.2); ICSS = +0.1 ppm (8.9)] or even from cyclopropenylium cation 6 [6: ICSS = −0.1 ppm (5.9); ICSS = +0.1 ppm (7.2)]—pointing to 2π electron aromaticity. Again, if there is partial 6π electron aromaticity in 2, due to the contribution of 2a, then it is only very small.
[...]
Compared with the corresponding fulvalenes, studied previously, which are genuine push–pull olefins and exhibit partial (anti)aromaticity in the corresponding 3-, 5- and 7-membered ring moieties (in the latter if structurally planar), the 3-, 5- and 7-membered ring moieties in fulvenes 1–4 reveal very small, if not negligible (anti)aromaticity only.

From all of the above I hope I was able to make clear how complex the concept of aromaticity is. Only because of thoughtful investigation and interplay between experiment and theory, penta-fulvene can be described as having negligible (anto)aromatic character.

Notes on aromaticity
The original definition of aromatic (gold book) only states is very broad and may include any and no compounds:

In the traditional sense, 'having a chemistry typified by benzene'.
A cyclically conjugated molecular entity with a stability (due to delocalization ) significantly greater than that of a hypothetical localized structure (e.g. Kekulé structure ) is said to possess aromatic character. If the structure is of higher energy (less stable) than such a hypothetical classical structure, the molecular entity is 'antiaromatic'. The most widely used method for determining aromaticity is the observation of diatropicity in the 1HNMR spectrum.
  See also: Hückel (4n + 2) rule, Möbius aromaticity
The terms aromatic and antiaromatic have been extended to describe the stabilization or destabilization of transition states of pericyclic reactions The hypothetical reference structure is here less clearly defined, and use of the term is based on application of the Hückel (4n + 2) rule and on consideration of the topology of orbital overlap in the transition state. Reactions of molecules in the ground state involving antiaromatic transition states proceed, if at all, much less easily than those involving aromatic transition states.

Much more rigorous is Hückel's (4n + 2) rule and therefore includes much less compounds. The main problem here is, that its application is often taught carelessly or even wrong. When one considers whether a compound is aromatic or not, it is probably one of the worst rules to follow. For fulvenes it certainly leads to the wrong conclusions.
The main problem is that this rule often gets reduced to counting π-electrons, but that is only a small part of it. Even if we include more recent developments and extensions of the rule, there is a lot more to it. (Originally only valid for a couple of hydrocarbons from which it was derived.) I like to encourage you to read up on the full definition (and links within) in the gold book:

Monocyclic planar (or almost planar) systems of trigonally (or sometimes digonally) hybridized atoms that contain (4n + 2) π-electrons (where n is a non-negative integer) will exhibit aromatic character. The rule is generally limited to n = 0–5. This rule is derived from the Hückel MO calculation on planar monocyclic conjugated hydrocarbons (CH)m where m is an integer equal to or greater than 3 according to which (4n + 2) π-electrons are contained in a closed-shell system. [...]

There is a more updated version on aromaticity in the gold book, which allows a more rigorous approach to the whole subject. Unfortunately it is not as simple as what was there before. You will need to understand a lot more about quantum chemistry, especially how to construct molecular orbitals. While Hückel MO calculations (which you could probably still do with a pencil and a [few] paper[s]) still provide a good entry point and approximation, it is more convenient using modern electronic structure programs and density functional theory (or similar) to elucidate aromaticity.
For the sake of completeness, here is the newer definition:

The concept of spatial and electronic structure of cyclic molecular systems displaying the effects of cyclic electron delocalization which provide for their enhanced thermodynamic stability (relative to acyclic structural analogues) and tendency to retain the structural type in the course of chemical transformations. A quantitative assessment of the degree of aromaticity is given by the value of the resonance energy. It may also be evaluated by the energies of relevant isodesmic and homodesmotic reactions. Along with energetic criteria of aromaticity, important and complementary are also a structural criterion (the lesser the alternation of bond lengths in the rings, the greater is the aromaticity of the molecule) and a magnetic criterion (existence of the diamagnetic ring current induced in a conjugated cyclic molecule by an external magnetic field and manifested by an exaltation and anisotropy of magnetic susceptibility). Although originally introduced for characterization of peculiar properties of cyclic conjugated hydrocarbons and their ions, the concept of aromaticity has been extended to their homoderivatives (see homoaromaticity), conjugated heterocyclic compounds (heteroaromaticity), saturated cyclic compounds (σ-aromaticity) as well as to three-dimensional organic and organometallic compounds (three-dimensional aromaticity). A common feature of the electronic structure inherent in all aromatic molecules is the close nature of their valence electron shells, i.e., double electron occupation of all bonding MOs with all antibonding and delocalized nonbonding MOs unfilled. The notion of aromaticity is applied also to transition states.

Notes on resonance
I will not go into a lot of detail here, because bon did an excellent job explaining it in: What is resonance, and are resonance structures real? However, allow me to make one point very clear: You cannot treat resonance structures on their own. You always have to treat them as a set, a superposition. There is no such thing as a most stable resonance structure, as well as there is no such thing as one of these structures dictating the reactivity. From a pencil and paper approach you hardly ever can judge which structure is most important for the description of the total bonding. Also, from a simple Lewis-type drawing you can almost never judge the properties of the compound.


text:
Why are regular plastic bags not smell-proof?
Due to the wide use of plastic bags as containers for almost everything in everyday life, I naturally use them to wrap and hold dirty diapers as a temporary stop before getting to throw them in the garbage outside. However, these bags do not stop the smell from spreading around the bags at all.
I wonder why is that? These bags seem to be tight enough to hold liquids (when intact), but they do not hold smells at all. I guess the obvious answer is that the plastic\nylon polymers have wide enough gaps between them for the passage of small clusters of molecules in the micro- or nano-level, but I was wondering if there was some other explanation and if anyone could elaborate on the matter.

Well, you basically answered your own question nicely with your "obvious answer" discussion. On a molecular scale, smallish molecules, like the volatile compounds that evaporate and make way to your nose, are able to permeate the plastic. This happens in part for the reason you said; on such a small scale, the plastic that appears fully "solid" and impermeable on a macro scale is actually a mesh of molecules with paths large enough for these small, smelly, molecules to escape.
There are factors at play other than molecular size, like the chemical composition of the plastic and the escaping compounds. If the compounds have a strong affinity for the plastic, it will take less time for them to permeate as they will more quickly absorb through the plastic.
Regarding your observation that the plastic seems to hold liquids, but not smells; this is probably an illusion. I suspect that the liquids you've placed in the bag actually have little or no smell (i.e. water, food oils). For example, in an analytical laboratory setting, water samples or water-based standards stored in various plastic containers have a limited shelf life because the water slowly permeates the plastic, evaporating into it's surroundings. So the water is escaping the plastic just like a smelly compound might do, but of course water has no smell.

Another factor could be surface tension. Water in a plastic bag may not wet well, whereas urine may have enough organics to wet plastic better. And thin plastic bags almost certainly has pinholes, which may be a more certain exit for wetting liquids. Similarly, light duty aluminum foil has about one visible (but tiny) pinhole per square foot. The heavy duty foil is about 10 times less porous.


text:
What compounds are created by mixing Styrofoam and paint thinner?
Yesterday I watched several videos that make a waterproof coat by disolving Styrofoam with paint thinner (my guess is that they use acetone). Will this recipe work for an emergency? Is it toxic (I don't want my pets to fell sick)?

Polystyrene is simply dissolved...

Polystyrene will be dissolved in acetone. The long polymer molecules will dissociate from each other and float around in the acetone solvent; but the polymer chains will likely not be broken down into their small styrene monomer units. If you mix acetone and polystyrene ("styrofoam"), you will simply end up with polysterene in acetone. Not significant chemical reaction is expected to take place, only the physical process of dissolution/solvation/dissolving.
I would assume such a solution is toxic and keep it far away from animals, eyes and mouths.


text:
Why is an alkoxide released instead of hydroxide in the attack of trialkyloxyborane by hydroxide?
In the mechanism of a hydroboration-oxidation, the oxidation part includes a nucleophilic attack of a hydroxide on a trialkyloxyborane ( $\ce{B(OR)_3}$ where $\ce{R}$ is an alkyl group).
It creates a tetrahedral intermediate consisting of a negative center of boron with four groups attached to it (the hydroxide nucleophile and the three alkoxides). This step is followed by the loss of an alkoxide as the leaving group. However, to my understanding, the alkoxide is a stronger base than the hydroxide. Thus, why doesn't the nucleophilic attack fail?
Edit: Is it because of steric comparisons between the size of the alkoxide versus the hydroxide (since boron is a relatively small atom)?

Both hydroxide and alcoholate can be displaced from the tetracoordinated intermediate. The difference is that displacing the hydroxide is just the back reaction of the inital attack while displacing the alcoholate will move the reaction forward.
You cannot argue that $\ce{X}$ is a stronger base than $\ce{Y}$ and therefore $\ce{X}$ will always get displaced. At best, you can argue that $\ce{X}$ is ten times stronger so the probability of $\ce{X}$ begin displaced is higher than that of $\ce{Y}$. For all intents and purposes of the argument, the basicities of (primary) alcoholates and hydroxide are too similar to make a real difference.


text:
Can benzene damage rubber or other materials or adhesives used in tire production?
In this article, "Bridgestone/Firestone, Inc. and Ford Motor Company: How a Product Safety Crisis Ended a Hundred-Year Relationship" the article states, "Industry observers have speculated [that]... a disproportionate amount of Benzene was added to the rubber compound which affected the adhesion in the years to follow," and "Excessive use of benzene can damage the quality of the tire material."
Is it true that too much Benzene can damage tires, either the rubber, the adhesives, or other materials used in tire manufacturing?

In the days when benzene was a cheap lab solvent and its toxicity wasn't well known, chemists used it to shrink the rubber stoppers in bottles and flasks as it infiltrates and drastically changes the properties of rubber. So the answer is probably "yes".

Rubber cement used to be simply rubber dissolved in benzene... now, safer alipahtic solvents are used. Benzene is an excellent solvent for isoprene.


text:
why do we modelize an electronic double layer with a classic capacitor?
in an electronic double layer, there is a voltage drop between the metal and the solution but in the litterature, scientists always modelize EDL with a classic capacitor. My question is why ? because for me, the two electrodes have not the same potential (+/-), it is assymetric ...


text:
Why is o-fluorophenol a stronger acid than p-fluorophenol?
The $\mathrm{p}K_\mathrm{a}$ value of o-fluorophenol is $8.7$, while that of the p-fluorophenol is $9.9$. It's obvious that the inductive effect is more dominant at ortho-position, which results in a more acidic nature.
However, won't the $\ce{H}$ attached to $\ce{O}$ form a hydrogen bond with the $\ce{F}$ at ortho-position resulting in a less acidic nature than p-fluorophenol?

What you've described is a classic case of two competing factors. Having two competing factors doesn't mean that it is simultaneously more and less acidic - all it means is that one factor is more important than the other. From the pKa values it should be clear which one is more important, and you seem to have realised that too.

https://chemistry.stackexchange.com/questions/7683/ortho-effect-in-substituted-aromatic-acids-and-bases


text:
Can negative adsorption be considered equal to sorption?
In my book it was written sorption is basically when the substance gets uniformly distributed into the bulk of the solid but at the same time its concentration is higher at the surface then in the bulk. for negative adsorption a same type of defination was there so is there any difference between them?

There is no difference, except that one is positive and the other negative.


text:
How does one actually get the energy from the Kohn–Sham equations?
This might be a silly question, but how does one acquire the energy of the system from the Kohn–Sham equations?
$\left[ -\frac{1}{2}\nabla^2 + V_{eN}(\vec{r}) + V_{ee}(\vec{r}) + V_{xc}(\vec{r}) \right]\phi_i(\vec{r})=\epsilon_i\phi_i(\vec{r})$
Where $\nabla$ is the Laplacian operator, $V_{eN}(\vec{r})$ is the electron-nuclei attraction, $V_{ee}(\vec{r})$ is the electron-electron repulsion, $V_{xc}(\vec{r})$ is the exchange-correlation potential, $\phi_i(\vec{r})$ are the one-electron wave functions and $\epsilon_i$ are the orbital energies.
Assuming that we run through this set of equations for each electron, we get a set of orbital energies: $\epsilon_i \cdots \epsilon_N$. How is the overall total energy of the system then calculated?

Is your question how you write the total energy in equations? Because then I think wikipedia is a fine start.
Or is it how to get the total energy in practical? Like inside the programs.

A common mistake is the thought that the total energy is the sum of all orbital energies $\{\epsilon_i\}$.
From Step #6 of Daniel Crawford's SCF programming project (modified slightly in some places):

The SCF electronic energy may be computed using the density matrix as:
$$
E_{\text{elec}} = \sum_{\mu\nu}^{\text{AO}} D_{\mu\nu} (H_{\mu\nu}^{\text{core}} + F_{\mu\nu})
$$
The total energy is the sum of the electronic energy and the nuclear repulsion energy:
$$
E_{\text{total}} = E_{\text{elec}} + E_{\text{nuc}},
$$

where the density matrix is defined as (Step #8)

$$
D_{\mu\nu} = \sum_{m}^{\text{occ. MO}} C_{\mu m} C_{\nu m},
$$

the Fock matrix as (Step #7)

$$
\begin{align}
F_{\mu\nu} &= H_{\mu\nu}^{\text{core}} + \sum_{\lambda\sigma}^{\text{AO}} D_{\lambda\sigma} \left[ 2(\mu\nu|\lambda\sigma) - (\mu\lambda|\nu\sigma) \right] \\
&= H_{\mu\nu}^{\text{core}} + 2 J_{\mu\nu} - K_{\mu\nu}
,
\end{align}
$$

and the core Hamiltonian as (Step #2)

$$
H_{\mu\nu}^{\text{core}} = T_{\mu\nu} + V_{\mu\nu}.
$$

I've also introduced the definitions of the Coulomb matrix $J$ and the exchange matrix $K$:
$$
\begin{align}
J_{\mu\nu} &= \sum_{\lambda\sigma}^{\text{AO}} D_{\lambda\sigma} (\mu\nu|\lambda\sigma) \\
K_{\mu\nu} &= \sum_{\lambda\sigma}^{\text{AO}} D_{\lambda\sigma} (\mu\lambda|\nu\sigma) \\
\end{align}
$$

Now, identify each of the terms in the Kohn-Sham equations with the terms from above.
$$
\begin{align}
\hat{T}_{e} &= -\frac{1}{2} \nabla^2 \rightarrow T_{\mu\nu} = \left< \chi_{\mu} \left| \hat{T} \right| \chi_{\nu} \right> \\
\hat{V}_{eN}(\vec{r}) &= \sum_{A}^{\text{nuclei}} \frac{Z_A}{|\vec{r} - \vec{R}_{A}|} \rightarrow V_{\mu\nu} = \left< \chi_{\mu} \left| \hat{V}_{eN} \right| \chi_{\nu} \right> \\
\hat{V}_{ee}(\vec{r}) &\stackrel{?}{\rightarrow} 2 \hat{J} \\
\hat{V}_{\text{XC}}(\vec{r}) &\stackrel{?}{\rightarrow} - \hat{K}
\end{align}
$$
This last part isn't quite correct though. Usually, when looking at the Kohn-Sham equations, one replaces the full electron-electron interaction $\hat{V}_{ee}$ with the sum of the Hartree potential $\hat{V}_{H}$, which gives the Coulomb energy, and the exchange-correlation potential $\hat{V}_{\text{XC}}$, which replaces the exact exchange $\hat{K}$ with a (currently approximate) expression for both the exchange term and the true electron-electron (correlated) interaction.
In terms of how the energy is actually calculated, all quantities from above are the same as in Hartree-Fock theory, except the calculation of the exact exchange integrals during the Fock build is replaced with calculating the exchange-correlation matrix $F^{\text{XC}}$, leading to

$$
\begin{align}
F_{\mu\nu}^{\alpha} &= H_{\mu\nu}^{\text{core}} + J_{\mu\nu} + F_{\mu\nu}^{\text{XC}\alpha} \\
F_{\mu\nu}^{\beta} &= H_{\mu\nu}^{\text{core}} + J_{\mu\nu} + F_{\mu\nu}^{\text{XC}\beta}
\end{align}
$$

For a density functional approximation (DFA) based on the generalized gradient approximation (GGA), where the functional is dependent on both the density $\rho(\mathbf{r})$ and its gradient $\nabla \rho(\mathbf{r})$,

$$
\begin{align}
E_{\text{XC}} &= \int f_{GGA}^{\text{DFA}}(\rho_{\alpha},\rho_{\beta},\gamma_{\alpha\alpha},\gamma_{\alpha\beta},\gamma_{\beta\beta}) \, \mathrm{d}\mathbf{r} \\
\gamma_{\alpha\alpha} &= |\nabla \rho_{\alpha}|^{2} \\
\gamma_{\beta\beta} &= |\nabla \rho_{\beta}|^{2} \\
\gamma_{\alpha\beta} &= \nabla \rho_{\alpha} \cdot \nabla \rho_{\beta} \\
\end{align}
$$
The exchange-correlation parts of the Fock matrices are given by
$$
F_{\mu\nu}^{\text{XC}\alpha} = \int \left[ \frac{\partial f}{\partial \rho_{\alpha}} \chi_{\mu}\chi_{\nu} + \left( 2\frac{\partial f}{\partial \gamma_{\alpha\alpha}} \nabla\rho_{\alpha} + \frac{\partial f}{\partial \gamma_{\alpha\beta}} \nabla\rho_{\beta} \right) \cdot \nabla(\chi_{\mu}\chi_{\nu}) \right] \mathrm{d}\mathbf{r}
$$

$f^{\text{DFA}}$, $\frac{\partial f^{\text{DFA}}}{\partial \rho}$, and $\frac{f^{\text{DFA}}}{\partial \gamma}$ are unique closed-form expressions for each DFA, and are usually evaluated numerically on an atom-centered grid (ACG) such as a Lebedev grid. This generally requires mapping the set of AOs/basis functions $\{\chi\}$ onto this grid.
References

John A. Pople; Peter M. W. Gill; Benny G. Johnson; Kohn–Sham density-functional theory within a finite basis set. Chem. Phys. Lett. 1992, 199 557-560

$\tiny{\text{As usual, sorry if I'm lazy with notation, being consistent is so difficult...}}$


text:
Separation of alkylated 1,2,4-triazole in solution
I was looking into heterocyclic compounds and their alkylation (i.e. the regioselectivity of the alkylation of the compound).
People are able to give pretty exact numbers, for an experiment done in solution. Take, for example, 1,2,4-triazole, the alkylation can occur in one of two positions and papers state that the yield is about 9:1 in the 1 to 4 position.
How would one go about the separation of the solution to validate these claims? Or is there a method where this can be quantified in solution?

Joule and Mills Heterocyclic Chemistry [1] confirms that 1,2,4-triazoles alkylate with ~9:1 selectivity for N1 over N3, citing a paper in Tetrahedron Letters  from an industrial group at Merck as the source of the data[2].
The ratios reported were based on 1H-NMR of the crude product.[#] In this case, all of the compounds formed are known compounds, and as such it was easy to compare the data for 1-alkyl vs 3 alkyl. If the compounds formed were completely novel, it may be harder to tell which is which, though more complex NMR methods such as H-N or C-N correlation are often used in the pharmaceutical industry where this issue of regioselectivity often arises.
As an aside, the paper points out that the N1 and N3 alkylated products are easily separable, in this case by distillation, but in normal cases, silica gel chromatography (or HPLC if needed) can usually be used to separate the different regioisomers, with sufficient effort!

[1]: Mills, K.; Joule, J. A. Hetrocyclic Chemistry; Wiley:Chichester- Sussex, 2010
[2]: Bulger, P. G.; Cottrell, I. F.; Cowden, C. J.; Davies, A. J., Dolling, U-H. Tetrahrdron Lett., 2000, 41, 1297
[#]: The reaction was worked up, but not purified prior to working out the ratios. This is good practice, as it assures that you haven’t accidentally columned away some of the minor product, as is often the case

I can confirm from my own work that these regioisomers are readily separable by silica flash chromatography.

Is anyone aware if TLC will work?

@AS_1000 In all likelihood, yes. If it separates on a flash column using silica gel, then it will likely separate on a TLC place using the same eluent. You might be able to find this yourself if you look up the Rf values from the paper referenced (usually found in the Supporting Information section, and always available for free without subscription).


text:
pH-value of a multicomponent buffer
We are trying to predict the pH-value of a multicomponent buffer. It consists of:
\begin{array}{lcrr}
\# &\text{Component} &C,\,\pu{mol L-1} &\mathrm{p}K_\mathrm{a1} &\mathrm{p}K_\mathrm{a2} &\mathrm{p}K_\mathrm{a3}\\
\hline
1 &\text{Citric acid} &\pu{2.60e-5} &3.13 &4.76 &6.40 \\
2 &\ce{NaH2PO4} &\pu{5.65e-3} &7.21 & &\\
3 &\ce{(NH4)2SO4} &\pu{2.27e-3} &9.20 & &\\
4 &\ce{NaHCO3} &\pu{1.19e-3} &10.33 & &
\end{array}
Our problem is that we don't know how to combine several equilibria which exist in the solution. Since $\ce{NaHCO3}$, for example, is an ampholyte, it is difficult to tell if it reacts as an acid or a base.
Although this should be a somewhat common problem, we didn't find any formula or method to calculate the pH of such systems. We would be thankful for any idea!

Where did you get all this values? If it's real problem then just mix it and check pH. Still it may be homework and it seems it breaks our homework policy.

It is a real problem indeed. I already checked the pH, but I am curious though if there's a way to calculate it. We also had the idea to write an excel-sheet or a program which tells us the pH of multicomponent systems, which would be useful in the lab.

First suggestion, you are missing some pKa's, although I think the only important ones are those of H2CO3 (3.6) and H3PO4 (2.12). Then, clearly undissociated citric acid is not compatible with HCO3- or even H2PO4-. Just make then react and star from there.

Sorry, in my previous comment I made a mistake, the pKa of H2CO3 seems to be 6.35.

Let me guess: is the pH you measured about 6.3?

It should be at about 5.4. It's a buffer which simulates saliva called "Mondelli Buffer". You can find it by googling it. My task was to increase its pH to 6.3 without changing the concentrations of the single ions to much (it's accidentally the same as you calculated for the original buffer, I guess). So I decided to put in a smaller amount of $\ce{NaH2PO4}$ (it turned out to be $2.50\cdot 10^{-3}mol/L$).
But I would like to know, if there is also a way to calculate the pH of more complicated systems like this in advance...

@SimonPflug. I suggest you check the Medusa (or Spana, in its newest java version) software: https://www.kth.se/che/medusa/ and https://sites.google.com/site/chemdiagr/


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pH of an amino acid solution
I'm trying to help a friend of mine with this chemistry question:

What is the pH of a $1.0M$ solution of glycine?

They're given that the pKa of COOH is $2.4$ and the pKa of the amine group is 9.6. The solution they were given says the pH is just $\frac{2.4+9.6}{2} = 6.1$, but I don't see any reason why this should be true especially since this answer initially appears independent of the given concentration of glycine.
Now if I try to solve this the long way: If I initially just have a solution of glycine, I believe it would function like a weak acid, and hence the equation is:
$$Ka = \frac{[H^+][A-]}{[HA]}$$
or
$$10^{-9.6} = \frac{x^2}{1-x} \approx x^2$$
Thus pH = $4.8$
At the very least, I found this document: https://www.ch.ntu.edu.tw/~ccchan/course/genchem2003/Notes/final_ans.pdf
Which showed that the pH of a $0.05 M$ solution of glycine has a pH of $5.54$, so with a much higher concentration of glycine functioning like a weak acid, my pH should be less than $5.54$ (and hence definitely less than the $6.1$ the professor put as his solution). Am I missing something?

The mean value of pKas is not pH of solution in general, but an isoelectric point.

@andselisk Yea I'm familiar with that. That's why I didn't understand why the professor claimed that was the pH of a 1.0M solution

I think the professor is right. I would solve it like any other acid-base problem. Glycine (G, neutral as zwitterion) can either protonate to HG+; or deprototonate to G-. The mass balance and charge balance equations are:
C$_G$=1.0=[HG+]+[G]+[G-] (Mass balance for glycine)
[H+]+[HG+]=[OH-]+[G-]    (Charge balance)
Given these two equations, and the three for $K_{a1}$, $K_{a2}$ and $K_{w}$, I could solve exactly the system of five equations with five unknowns. But that would be overkill, since we can do some approximations:

Since G is both a (not so) weak acid and a weak base, we can assume that it doesn't dissociate that much to HG+ or G-. So, the predominant form would be G, which (given the $pK_a$'s) is predominant in the 3.5 to 8.5 pH range (aprox, it depends on the errors that we tolerate).
In this pH range, and given the high glycine concentration and $pK_a$ values, [HG+]>>[H+] and [G-]>>[OH-]; so that, from the charge balance:

[HG+]=[G-]
This equality solves the problem since, combining the equations for $K_{a1}$, $K_{a2}$, we get:
$K_{a1}K_{a2}=\frac{[G-][H+]^2}{[HG+]}=[H+]^2$ so $[H+]=\sqrt{K_{a1}K_{a2}}$
$pH=\frac{1}{2}log(pK_{a1}+pK_{a2})=6.0$
You can check that at this pH, [G]=1,[HG+]=$10^{-3.2}$,[G-]=$10^{-3.6}$, so that the approximations [HG+]>>[H+] and [G-]>>[OH-] are valid.
(For more details see 6.7.5 at https://chem.libretexts.org/Textbook_Maps/Analytical_Chemistry_Textbook_Maps/Map%3A_Analytical_Chemistry_2.0_(Harvey)/06_Equilibrium_Chemistry/6.07%3A_Solving_Equilibrium_Problems)

Maybe I missed it, but where in solving this problem did you use that the concentration is 1.0M? Because if that doesn't factor into solving this, then we're literally saying that the pH is 6.0 regardless of how much  glycine is used which seems problematic. The other question I would have then is exactly what is wrong with the way I solved it which gave 4.8

@Brenton .The concentration is there in the mass balance equation. But it does not appear in the solution due to approximations I made. Check the more exact equation in the link provided, and if you calculate the pH with it, you'll see that the aaproximation (pH=6) is veeeery good. Anyway, the fact that the pH is independent of total concentration (as long as C does not get too small) is not problematic, but expected. It is quite common: pH of a buffer, pH of amphoteric form (which is this case),...

@Brenton . About the way you solved it. You considered zwiterionic  glycine (+)H3N-CH-COO(-) as a weak acid (from the ammonium group); but it is also a weak base (from the carboxylate). You assumed (correctly) that it is an stronger acid than base (that is the reason the pH is below 7). But you did not considered that -COO(-) is a stronger base than water; so as soon as H+ is liberated, (+)H3N-CH-COOH starts forming. You just cannot ignore the other pKa. The overall reaction would be: 2HG -> H2G(+) + G-, which has K=10^(-7.2). So, at equilibrium [H2G+]=[G-]=10^(-3.6), which means [H+]=10^(-6)

I have another question. Why do we consider only the zwitterion $\ce{NH3+-CH-COO-}$ but not the neutral molecule $\ce{NH2-CH-COOH}$ so there would be altogether $4$ species? Is it that the zwitterion is much more abundant than the neutral molecule at any pH once amino acids dissolve in water?

@ZhuoranHe Both $\ce{NH2-CH-COO}$ and $\ce{NH3+-CH-COO-}$ are neutral, they are just different tautomeric isomers of the same species. From the point of view of acid-base equilibria, the zwitterion and non-zwitterion forms of neutral glycine are the same species, since both have lost a proton from the cationic $\ce{NH3+-CH-COOH}$.

I think the ability for $\ce{NH2-CH-COOH}$ and $\ce{NH3+-CH-COO-}$ to gain or lose a proton $\ce{H+}$ should be different because they have different charge distributions. Then the shift of the equilibrium $\ce{NH2-CH-COOH <=> NH3+-CH-COO-}$ can have an effect. But to my surprise, your calculation done here seems standard.


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How can I decide the most activated spot?
All of those are activated. And to me, those 2 that are most far from the $\ce{NO2}$ group are the major products. But, between those 2, which one will be the major? Because both of them are more separated in the same way:

(1) By "most activated", you mean "least deactivated", right? (2) Those two spots are exactly the same.

Yes, yes. So, if i put in any of those two, it will be the same result?

Yes, exactly. You shouldn't expect either position to react faster or slower than the other, because they're precisely the same.

Ortho, can you answer other thing to me? If you have a 1-nitro-3-hydroxy-benzene, which one will say what is the major product? -OH, or NO2?

The -OH obviously. Always the more activating group has a greater say in the outcome of the reaction.


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Why do α-amino acids have a C-H bond at the α-carbon?
I've just started studying biochemistry and I read that a general $\alpha$-amino acid looks like (ignore the ionisation for now):

My question is: why isn't the general $\alpha$-amino acid formula like $\ce{CRR'NH_2COOH}$ instead of $\ce{CHRNH_2COOH}$? Coming from a physics background, the latter feels more "natural" as it is more general.
Some possible reasons I've thought of (and disqualified):

Maybe the $\ce{C-H}$ bond dissociation energy is too high: I looked at a paper [1] but the bond energies seem to be not too high (relative to say $\ce{C-C}$ bonds.
Steric factors: I don't think this applies as having a small group, like say $\ce{CH_3}$, won't create a lot more steric repulsion relative to $\ce{H}$.

If the answer is along the lines of "it is defined this way because we actually see repeating units of these structures in proteins, so we naturally define the smallest subunit accordingly", then provide chemical grounds (if possible) to justify the fact that structures like $\ce{CRR'NH_2COOH}$ are not prevalent in proteins.
[1]: Moore, B. N., & Julian, R. R. (2012). Dissociation energies of X–H bonds in amino acids. Physical Chemistry Chemical Physics, 14(9), 3148-3154.

In the most general sense, the term α-amino acid does encompass doubly substituted structures like those you mention. After all, the name doesn't specify any particular substitution, or lack thereof, at the α-carbon. The name only really means that there is an amino group α to a carboxylic acid, i.e. one carbon away. Similar nomenclature is used to describe molecules where the amino group is 2, 3, ... carbons away from the carboxylic acid, also without any specification of substitution.

The disubstituted compounds you described, $\ce{H2N-C(R)(R')-COOH}$, can be synthesised in the laboratory. Pharmaceutical companies seem to have an interest in these compounds. Here is one example from a collaboration between Eli Lilly and IUPUI1 (there are many more - pharmaceutical companies like Pfizer2 even have some patents on these compounds):

Wikipedia actually has an example of a naturally occurring α-amino acid without a hydrogen at the α-carbon. Apparently, it is produced by some fungi:

However, the term α-amino acid is nearly always used to refer to the proteinogenic amino acids, which do happen to have a hydrogen at the α-carbon.
These proteinogenic amino acids were discovered many years ago. Generally, they are obtained by treatment of proteins with acid (which hydrolyses proteins into their constituent amino acids). Their chemical formulae were painstakingly identified by a series of decomposition reactions - back in the old days, there was no NMR. The history of the discovery of the proteinogenic amino acids is described in a review article3 from 1931(!) - which tells you how long ago these were discovered.
So, part of the reason why these aren't disubstituted is simply because we found them to not be so. However, I can understand if one complains of this conclusion being intellectually unsatisfying. So, here is some extra speculation.
One major step involved in the biosynthesis of amino acids is transamination. I don't have a list on me right now, but I think most amino acids go through such a step at one point in time.

The mechanism (described on Wikipedia, or in any biochemistry textbook) necessitates that one hydrogen is added to the α-carbon. [For the organic chemists out there, this is essentially an enzyme-mediated reductive amination.]
It turns out that, on top of this, it is also possible that such disubstituted amino acids are actually harmful. According to Weber and Miller, writing in the Journal of Molecular Evolution:4

Replacement of the α-hydrogen by a larger substituent, such as a methyl group, would also increase significantly steric hindrance around the amino and carboxyl groups. Steric difficulties have been encountered in the chemical synthesis of peptides with α-aminoisobutyric acid.
Also, the severely constrained stereochemical behavior of peptides of α-methyl-α-amino-n-butyric acid suggests that peptides composed of α-methyl substituted amino acids would not have the structural versatility of peptides derived from α-hydrogen substituted amino acids.
An additional factor involves the ribosomal peptidyl transferase, which would develop a specificity for either an α-hydrogen or an α-methyl of the amino acid. This would prevent the synthesis of proteins containing both types of amino acids.

References

Green, J. E.; Bender, D. M.; Jackson, S.; O'Donnell, M. J.; McCarthy, J. R. Mitsunobu Approach to the Synthesis of Optically Active α,α-Disubstituted Amino Acids. Org. Lett. 2009, 11 (4), 807–810. DOI: 10.1021/ol802325h.

Graham, S. R.; Mantell, S. J.; Rawson, D. J.; Schwarz, J. B. (Pfizer, Inc.) Amino acid derivatives. U.S. Patent 7612226 B2, Nov 3, 2009.

Vickery, H. B.; Schmidt, C. L. A. The History of the Discovery of the Amino Acids. Chem. Rev. 1931, 9 (2), 169–318. DOI: 10.1021/cr60033a001.

Weber, A. L.; Miller, S. L. Reasons for the occurrence of the twenty coded protein amino acids. J. Mol. Evol. 1981, 17 (5), 273–284. DOI: 10.1007/BF01795749.


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In the nonideal solution, why can't one of the solute be positive deviation and the other be negative deviation?
In the nonideal solution, why can't one of the solute be positive deviation and the other be negative deviation?
Let's say A and B makes a nonideal solution.
The moleculat force between A and B means A-B.
Let's say A-A > A-B > B-B.
Then A would evaporate more than in the pure state, and B would evaporate less than in the pure state.

Have you read that it's not possible..? Please refer to any text.. it will be helpful.

For multiple component systems we use activity coefficient $\gamma$ in modified Roult's law as:
$$K_i=\gamma \frac{P_i^\star}P $$
and $\gamma$ is defined in the terms of $f$ : fugacity or fictitious pressure for a real gas.
You should read further about "Vapour Liquid Equilibrium" for multiple components.
Maybe:  http://www.journalrepository.org/media/journals/BJAST_5/2012/Dec/1355741742-Olaleke312012BJAST1789.pdf. You can see there is no reason why it can't have deviation in multiple directions.

Please include the essential part of the reference in your answer. Unless the question is a [tag:reference-request], we strongly discourage replies that refer the OP to an external resource, short or long. Helpful links on their own are comments, and links should be archived if possible.


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What's the configuration of chromium(III) in aqueous medium according to crystal field theory?
It has $\mathrm{3d^3}$ configuration, but how will we decide if they enter $\mathrm{t_{2g}}$ or $\mathrm{e_g}$ orbitals since we don't know which complex will form?

The amount of ligands that can fit  around a cation is guarded by sterical factors. The exact shape and spin of the complex formed is guarded by energy: a configuration with lowest energy is formed. (actually it is a bit more complex, read about kinetic and thermodinamic control)

You nailed it, this is almost a chicken-and-egg problem. As long as we don’t know which complex will form, we cannot say which orbitals are populated. This is why it is often and regularly repeated that you need to know the geometry before you can make a call.
In an octahedral complex, the $\mathrm{t_{2g}}$ orbitals will always be populated first as they are lower in energy. (Look up any introduction on crystal field theory or check out the answers on this site.) In a tetrahedral complex, $\mathrm{e}$ — not $\mathrm{e_g}$, as there is no centre of symmetry, meaning the the $\mathrm{u/g}$ designators do not make sense, even though the orbitals are still often called $\mathrm{e_g}$ at introductory level — are the orbitals of choice to begin with. Again, just look at the scheme.
Thankfully, however, we can make an educated guess based on various factors.

octahedral complexes are more common especially at introductory levels and for the ‘top middle’ of the d block elements (roughly from titanium to nickel)
the LFSE (ligand field stabilisation enthalpy) can be calculated to $\pu{-12Dq}$ in the octahedral case and $\pu{-8Dq}$ in the tetrahedral case which twice prefers octahedral
there is no compelling reason (size or charge balance) to consider tetrahedral to be preferable to octahedral.

Thus, the complex you are looking at will most likely be octahedral — and so it is: it is hexaaquachromium(III) $\ce{[Cr(H2O)6]^3+}$, which is octahedral.

Btw, I think electronic spectra are good enough evidence that the complex is octahedral: since these have a centre of symmetry, the transitions are parity forbidden and tend to have extinction coefficients 1-2 orders of magnitude smaller than typical tetrahedral complexes. I'll see if I can find a spectrum

Yes, I didn’t even go into spectroscopic details. That requires an experiment that OP maybe cannot make being restricted to paper chemistry.


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Concentrations of gases at equilibrium

The equilibrium constant for the reaction:
  $$\ce{2NO(g) <=> N2(g) + O2(g)}$$
  is $2.60 \cdot 10^{-3}$ at $\pu{1000^\circ C}$. If $\pu{0.820 mol}$ of $\ce{NO}$ and $\pu{0.223 mol}$ each of $\ce{N2}$ and $\ce{O2}$ are mixed at $\pu{1100^\circ C}$, what are the concentrations of $\ce{NO}$, $\ce{N2}$ and $\ce{O2}$ at equilibrium?

I'm really stuck, because with these types of questions usually the concentration of at least one reactant or product at equilibrium is provided, so I know the direction of the equilibrium shift.
Usually I allow the variable $x$ to equal the change in concentration of each product/reactant, where I subtract or add different ratios of it from the initial concentrations of the reactants and products (depending on the direction of equilibrium shift).
However, since I do not know the direction of equilibrium shift, how am I supposed to know whether to subtract or add $x$ to the reactants/products?

That's not important. Throw a coin, make a guess, try it that way. If you're wrong, your $x$ will turn up negative, that's all.

In cases like this calculate the reaction quotient, Q (https://chem.libretexts.org/Core/Physical_and_Theoretical_Chemistry/Equilibria/Chemical_Equilibria/The_Reaction_Quotient) using the initial concentrations, and compare the value with the equilibrium constant, K:

Q=K implies that the system is at equilibrium
Q > K means that there is an excess of products so the system will evolve towards the equilibrium consuming products (which means that you should subtract x from the products)
Q < K just the other way around, the system will shift to the right to reach equilibrium (subtract x from the reactants)


text:
Why is the alkene a more stable species in this case?

How can we account for $\mathrm{S_N1}$ substitution in this case versus elimination in others?
When we dehydrate alcohols, we usually carry out the reaction in concentrated sulfuric acid and at high temperature. The hydrogen sulfate ($\ce{HSO4-}$) present after protonation of the acohol is a weak nucleophile, and at high temperature the highly reactive carbocation forms a more stable species by losing a proton and becoming an alkene. (Emphasis mine) Furthermore, the alkene is usually volatile and distills from the reaction mixture as it is formed, thus drawing the equilibrium toward alkene formation. The net result is an $\mathrm{E1}$ reaction.
 (Solomons, 11th edition page 511)

The author seems to imply that the formation of an alkene from a carbocation is energetically more favorable than the formation of an $\mathrm{S_N1}$ product. Why?
Once the carbocation is formed, the step leading to the $\mathrm{S_N1}$ product requires the formation of a sigma bond whereas the step leading to the $\mathrm{E1}$ product requires the formation of one pi bond.
It seems to me that the $\mathrm{S_N1}$ product should be more favorable (not by a lot though, since the rate limiting step for both reactions is the same).

related https://chemistry.stackexchange.com/questions/41836/reactions-of-alcohol-with-sulfuric-acid

I don’t think that your interpretation is what the author meant. I think that they are comparing the reactivity (or inverse stability) of the alkene to that of the carbocation. I think we can both agree that a carbocation is a much more reactive species than an alkene.
When it comes to comparing the products of a nucleophilic substitution to those of an elimination, I don’t think there’s an easy call that can be made. It depends far too much on variable factors such as the steric congestion around the reactivity site, the substitution pattern of the double bond, the size and shape of the nucleophile etc.
In the case of this specific reaction, however, we can make that call. The only mildly nucleophilic species is the hydrogen sulphate anion $\ce{HSO4-}$ deriving from deprotonated sulphuric acid. Hydrogen sulphate has three equivalent oxygens that each carry one third of the negative charge, and they are also practically symmetry-equivalent (not ideally, though, since the proton will angle off). The high oxidation state of the central sulphur atom reduces the electron density on the oxygens. Each of these oxygens is therefore a very bad nucleophile — compare to typical sulphonic acid residues such as tosylate or mesylate which are equally terrible nucleophiles. This should make a nucleophilic attack highly unlikely.
A second thing to remember is that sigma bond does not equal sigma bond. Usually when discussing sigma bonds, $\ce{C-C}$ or $\ce{C-H}$ bonds are meant which are very unpolar, have a bond dissociation energy of something around $\pu{400 kJ/mol}$ and are thus very hard to dissociate. Here, we would be making a $\ce{C-O}$ bond. But not any kind of $\ce{C-O}$ bond: the oxygen belongs to a sulphate residue. This makes the $\ce{C-O}$ bond very weak and very easily cleaved, especially since sulphate is a very good leaving group.
Therefore, in this specific case we can actually make the call and say that the elimination product is more stable than a product of a nucleophilic substitution.
One more thing: you do write cleavage of a sigma bond. But what is actually happening is akin to a deprotonation: a proton leaves leaving its electrons behind in a type of acid-base reaction. As you may know, these are typically very rapid as protons have an easy time ‘jumping’ from one molecule to another if the overall conditions for acid-base reactions are favourable.

Okay, I got it. Just one last question: you wrote in your edit that HSO4- is a poor nucleophile. Why wouldn't it be a poor base also?

@xasthor I can’t follow. $\ce{HSO4-}$ is a (very) poor base as it is the conjugate base of a strong acid.

You wrote: HSO4- is a very poor nucleophile. 'This should make a nucleophilic attack highly unlikely.'  Why would an attack on a hydrogen atom be any less likely?

@xasthor Because we have a very reactive carbocation and the full reaction is $\ce{R2CH-\overset{+}{C}R2 + HSO4- <=>> R2C=CR2 + H2SO4}$. The overall reaction is exergonic because the alkene is an even weaker base than hydrogen sulphate.


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How to predict the correct splitting pattern in a NMR spectrum
If I were to do a simulation and obtain all the chemical shifts and coupling constants between the different atoms, how would I then predict the NMR spectrum with coupling. Without coupling, I just use the chemical shifts and compare those to a base (TMS for example) and then I have all the peak locations and I'm pretty much done. But how do I incorporate all the splittings?
My guess would be to compare the chemical shift difference between two nuclei, $i$ and $j$ with their coupling constant and when $\Delta\sigma_{ij} > J_{ij}$ then I need to split the peaks corresponding to particle $i$ and $j$ but this would mean that coupling between nuclei that are very far apart with a very small $J$ would also be split, which is not really what you want.

Ah, coupling is a hard one to pin down. Sometimes it is just not visible …


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Is benzyl chloride or allyl chloride more reactive?
What compound is more reactive, benzyl chloride [(chloromethyl)benzene] or allyl chloride (3-chloroprop-1-ene)? I know that both have a higher reactivity than alkyl and aryl chlorides.

Not really, I was exercising SN1 and SN2 mechanisms and I was just wondering. I am thinking that Allyl Chloride is more reactive because the Benzyl Chloride is stabilized by conjugation. But I'm not sure about it.

@user50487 Could you please edit your question to include those thoughts (and the rationale behind them)?


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Derivation of formula used in calculating molecular mass from a mixture
In a solution to a problem, to calculate Molecular mass of unknown gas from a mixture containing $\ce{O2}$ in $80~\%$, the author used the formula :

$\frac{1}{\sqrt{M_\text{mix}}}=\frac{X_{\ce{O2}}}{\sqrt{M_{\ce{O2}}}}+\frac{X_\text{gas}}{\sqrt{M_\text{gas}}}$.

The exact problem is:

Pure $\ce{O_2}$ diffuses through an aperture in $224\mathrm{s}$, where as mixture of $\ce{O_2}$ and another gas containing $80~\%\ \ce{O_2}$ diffuses from the same in $234\mathrm{s}$. The molecular mass of gas will be?

Solution by author:

$$\begin{align}\frac{t_\text{mix}}{t_{\ce{O2}}} &= \frac{r_{\ce{O2}}}{r_\text{mix}} = \sqrt{\frac{M_\text{mix}}{32}}\\[1em]
\frac{234}{224} &= \sqrt{\frac{M_\text{mix}}{32}}\\[0.5em]
M_\text{mix} &= 34.92\\[1em]
\Longrightarrow \qquad \frac{1}{\sqrt{M_\text{mix}}} &= \frac{X_\text{gas}}{\sqrt{M_\text{gas}}} + \frac{X_{\ce{O2}}}{\sqrt{M_{\ce{O2}}}}\\[1em]
\Longrightarrow \qquad \frac{1}{\sqrt{34.92}} &= \frac{0.2}{\sqrt{M_\text{gas}}} + \frac{0.8}{\sqrt{32}}\\[0.5em]
M_\text{gas} &= 51.5\end{align}$$

I wish to know why this works here?

Hint: $$v_{rms}=\sqrt{\frac{3RT}M}$$
And weighted average of speeds for mixture.
EDIT:
$$ v_{mix} ^{rms}= x_1 v_1^{rms}+ x_2 v_2^{rms}$$
This will complete the derivation of the formula you gave.

This does not provide an answer to the question. To critique or request clarification from an author, leave a comment below their post. - From Review

Actually there is just one step to the derivation after you write down both the equations.. I guess OP can solve that on his own.  I think spoon feeding complete derivation won't do any good.

Hint answers aren't really well-received here. If you want to give a hint, it's better to do it as a comment.


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Why can unsymmetrical tert-butyl ethers be prepared by dehydration of the constituent alcohols?

Practice problem 11.11 what stops R-O-R from forming at the same rate as the desired product?

In order to understand why this is OK, you have to understand the mechanism by which this occurs. It is essentially an $\mathrm{S_N1}$ reaction that is most favoured by the conditions (acidic + polar protic solvent).
So, for the formation of an ether $\ce{^tBu-O-R}$ where $\ce{R}$ is a primary alkyl group:

competing formation of $\ce{R-O-R}$ is slow because primary carbocations are very unstable, and
competing formation of $\ce{^tBu-O-^tBu}$ is slow because $\ce{^tBuOH}$ is a poor nucleophile (tertiary alcohols are very bulky).

What stops an SN2 mechanism from operating to form  ROR?

@xasthor Water is a bad leaving group for an SN2 reaction – the tert-butyl cation is stable enough to promote loss of water (in an SN1 sense), then ROH can attack (tBuOH is a terrible nucleophile).. there really is only 1 favoured outcome in this reaction..

@NotEvans, H2O+ is not a bad leaving group. Besides, if it was a bad leaving group, it would not only affect the SN2 rate but also affect the SN1 rate

SN2 displacement of a primary alcohol (as in an SN2) without prior activation is not a favourable/well known reaction.  Look in any organic chemistry textbook (I suggest Clayden...)- it's well explained and it may help to clarify the basics for you :)

@xasthor I think what you are saying is that after protonation, it is possible for $\ce{ROH2+}$ to react in an SN2. Yes, it is possible - but then there is no good nucleophile (alcohols are really quite poor). Compared to the SN1 reaction which has everything going for it (very polar solvent + tertiary cation), I don't think it's likely that this SN2 can be competitive in terms of rate. Maybe, at most, you get some side product. If you compare to generic ROH + R'OH, which simply produces a hopeless mixture... this is much better.

A key info here is the room T vs the 100+Celsius to form primary ethers. Ether formation is probably an SN2 reaction on a protonated alcohol. Slow addition of t-butyl alcohol to an acidified primary alcohol should give good yields and minimize side reactions. The t-butyl cation should be immediately attacked by the alcohol molecules solvating the protonated alcohol. It would be interesting to react optically active 3-methyl hexan-3-ol and compare to a Williamson synthesis.


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Reducing damage from acid burns
Pretty simple: If you do not have access to water, what could reduce damage from getting acid on your skin?
I'm a total noob - I studied philosophy - but I know bases neutralize acids. I have a vague sort of idea coal does too? Are there other ways?

Coal does not. Bases do, but they can inflict even more severe damage by themselves. The other ways are worse yet. In short, if you do not have access to a lot of water, don't mess with acids and chemistry in general.

I'm not messing with anything. I'm thinking that from time to time - 700+ times a year in London for instance - you might be happily strolling about the park, when someone suddenly applies acid to your face.
I was thinking of options for emergency treatment, so that victims might wake up the next day with less scarring.

Wow, so that's a real problem. Well, then a bottle of water or a public drinking fountain is your best bet. Other ways are less reliable and less available.

That's a pretty real problem. I imagined maybe some sort of wet wipe, something cheap and disposable you could keep in a pocket or purse. An acid attack first aid kit.
As you can see, I don't know a lot about chemistry. But then that's why I ask someone wiser =)


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How did Joseph-Louis Proust know what gases weighed?
Proust's work led him to conclude that compounds always contain the same ratio, by weight, of their constituent elements. How did he know (or deduce?) what gases weighed?
Precise answers appreciated - I can find nothing on the net that explains how the weight of gases was measured at that time - all accounts of Proust & Dalton's work skip over this & other accounts just refer to modern tech.
I am not a chemist - I just want to know this.

Not that I feel this is off-topic here, but you may get a better answer over at  History of Science & Mathematics

I think this should be migrated to History of science.SE

He knew because he weighed them
This might seem ridiculously obvious but the early pioneers of modern atomic theory based the idea on actual results they got from weighing things before and after reactions.
It is perfect possible to weigh a container full of gas if you have an accurate enough balance (the buoyancy of the air cancels out if you use the same vessel for different gases). Note that the idea of a vacuum was developed in the 17th century so was well-known by the time of Proust and he could also have measured the empty weight.
The idea is simple: fill a vessel with some gas and weigh the vessel very accurately. A litre of oxygen weighs about 1.5g which is large enough to measure and with good equipment and technique large enough to measure accurately. A liter of hydrogen would be a little under .1g, a big difference.
A series of careful experiments like this with a range of gases would reveal something about the weight-ratios and carefully counting weights and volumes before and after reactions would tell you more (2 volumes of hydrogen react with one of oxygen, for example).
This is what people like Proust did, though with equipment we would now regard as primitive. The reason why it isn't mentioned a lot in modern descriptions is probably because it seems too basic and simple. Nowadays we just teach the theory not so much about the careful experiments that came first and actually led to the theory.

Disclaimer: I just remember this from my chemistry classes, when we talked a tiny bit about history. So I have no proper sources for when and with which gases these experiments were conducted.
First let's start with a very important chemical equation for your question.
In a more or less good approximation gases obey the following relationship:
$$pV=nRT$$
Or to put it in another way:
$$V \propto n$$
If you double the number of particles in a gas, you get double the volume. What they could find experimentally is, that they needed e.g. 2 L of hydrogen to react with 1 L of oxygen in the burning of hydrogen to water:
$$ 2 \ce{H2 + O2 -> H2O} $$
If 0.5 L of oxygen and 2 L were present, there were still 1 L of hydrogen remaining after the reaction.
If this experiment was repeated for various gases, it was possible to see this recurring pattern of integer multiples.
Now comes the most important part of science: From these experiments they did not know for sure that there are atoms etc. At least not with the security of today where we can see them in AFM, mass spectrometry...
BUT: The hypothesis of atoms and constant integer ratios in chemical reactions was in good agreement with the available experimental data of this time AND was short and elegant (Occam's razor).
And to answer your initial question. This does not require the knowledge about the molar mass. But starting from these findings, it was now possible to obtain the molar mass. On method was to vapourize known masses of a substance and apply the above relationship.


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Symantics of parts per (million, billion, etc)
I have always thought that parts per million meant that in a solution of one million particles, one of those particles is the particle that you are looking for its concentration in ppm. However looking at the formula ppm=(mass solute/mass solution)* 1 million, it seems like it may be meaning one part of mass per mass of solution?
Doing a example calculation for one atom of mercury in 999,999 molecules of water, I get about 11 parts per million and not the 1 ppm. It seems like the ppX changes with molar mass of the X. Am I missing some key concept here or do I have the right idea. Thanks
(1 atom Hg)(mol Hg/Avogardros#)(20.59g/mol Hg)= 3.3309E-22g Hg = variable A
(999,999 molecules H2O)(mole H2O/ Avogardros#)(18.015g/mol H2O)= 2.9915E-17g H2O=variable B
ppm=(moles solute/moles solution)*10^6
ppm=A/(A+B) *10^6 = 11.13ppm

The notation "parts per" is just a dimensionless unit to describe small amounts.
In chemistry it's used for concentrations of dilute liquids.. whereas in physics it can be used for defining change with respect to another quantity and in Six sigma it's used to define "defects per million opportunities".
In chemistry however, $ppm$ is mostly used as concentrations of dilute solutions in water and sometimes used interchangeable with $mg/l$. The notion of "one particle per million particles of solvent" can be used for solid-solid solutions or initial understanding of the term.

I am aware what it is and how it is used but I was looking for clarification because the definition and the idea presented seem incongruous based on my example


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How to safely change the color of a fire tornado?
So I've been watching a lot of fire tornado videos and I came across one that had a reasonable and safe setup (around the 3:23 mark):
Fire Tornado DIY
Is there a way to change the color of the fire tornado using the butane-powered base option?
The initial display of the tealight allows for either powdered/liquid chemicals to be added, but how would one safely add chemicals such as alcohol with the butane base setup?


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Why does p-dichlorobenzene have zero dipole moment while hydroquinone does not?
At first I thought that both the OH groups would cancel out their dipole moments in hydroquinone. On reading further, I realized that because of the two different planar structures possible, it has a non-zero dipole moment. My textbook says the dipole moment of para-dichlorobenzene is zero. But by the same logic we used for hydroquinone, shouldn't this have a non-zero dipole moment as well?

Cl isn't the same as an OH group. For one, there's an extra hydrogen atom that can rotate out of the plane.

Possible duplicate of Non-zero dipole moment of hydroquinone

Probably not a dupe although very related.

OP, please take a quick look at this meta question. There is no need to apply boldfaced type that much in such a short post.

There is exactly one possible conformation of p-dichlorobenzene. It is stiff as a board. The protons at the OH groups can move, largely independently.

To facilitate this discussion, here are the two structures.

You may remember from the beginning of organic chemistry classes that free rotation can occur around single bonds. This is mostly taught for $\ce{C-C}$ bonds but true for any σ symmetric bond. On the other hand, rotation is restricted around (partial) double bonds which rely on exactly one π system such as the phenyl ring.
This means that all $\ce{C-O, O-H}$ and $\ce{C-Cl}$ bonds in the above image are freely rotatable. Rotating either $\ce{C-O}$ bond of hydroquinone will move the corresponding hydrogen out of the phenyl ring plane. (In more scientific terms: the dihedric angle will no longer be $0^\circ$ or $180^\circ$.) Therefore, planarity may be lost. Also, if both hydrogens point to the same side, inversion symmetry is lost. In both cases, a nonzero dipole moment will be observed, as highlighted in this related question.
In para-dichlorobenzene’s case, you can also rotate the $\ce{C-Cl}$ bond. However, the result is entirely philosophic in nature, as only the positions of atomic nuclei are relevant for symmetry considerations and such. However you rotate that ball at the end of a stick, the end result will be the same. There is no way in which you could reduce symmetry. Hence the molecule has zero dipole moment.


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Stereochemistry: synthesis of an epoxide
This is a procedure to synthesize a propylene oxide.

I wonder if the inversion occurs or not after the reaction. That is, I want to know which product is correct in the diagram above.
I thought that this reaction is an SN2 reaction, so inversion occurs. However, I'm a little confused because the whole reaction is intramolecular.
Is it correct that this reaction is SN2, and the inversion occurs?

"Is it correct that this reaction is SN2, and the inversion occurs?" Yes, and yes, so the product is the one on the top.

"Inversion" in this context doesn't mean that every substituent has to be flipped. Maybe it's clearer if you take away the intramolecular aspect of it. This is a typical SN2 reaction as introduced in many textbooks:

Would you agree, here, that the stereochemistry at carbon has undergone inversion? It is nothing to do with the methyl group or the hydrogen, but rather it is because of the fact that the chloride (that was originally pointing down) was replaced with an oxygen (that is now pointing up).
Now to make it an intramolecular reaction, just replace the R with a single bond to the OH.

I see! Inversion is associated with two nucleophiles then.