text:
Chemicals additive resistant to acetone?
I am an ink developer. I'm am working on an ink to withstand chemical alteration after curing. I am having trouble defeating the acetone portion of my testing. Does anyone know of an additive that would help my alcohol based ink resistant to acetone ( and other) chemicals?

Just an idea. Have you tried using simple water ?

Actually, I have not

Making an ink resistant to wide spectrum of solvents isn't trivial. The only approach I can come with is to use something that reacts with air on drying or is otherwise altered after it is applied. The exact details depend on your use case, so if you can share ? Is it an ink for a printer, artistic purposes, permanent marker or something else?

In short form, permanent marking, indoors and out. A company I found sells a chemical resistant ink but it's $440 per gallon and I just can't justify that.  I was hoping to modify an existing ink to have these properties and so far I have made it resist isopropyl and denatured alcohol with pine rosin !

What is the ink applied to, and how it is cured? There are several (mostly pigment-based) inks used in pens like Uni-Ball Signo 207, Sakura Pigma Micron or Pentel EnerGel Permanent, which you might want to look into in case you are dealing with paper or similar material. The ink used in these pens can withstand acetone and the majority of other organic solvents.

Air cured, applied to painted drums, pallets, lumber,steel beams.

@DevCrew I see, you might want to [edit] this info into the question. In that case, laser engraving, chemical etching or laminated labels would be better than ink labeling, I would think.

This is most likely accurate but I'm so invested at this point, plus now I'm fixated on figuring it out. I was proud of the pine resin method

Look into reactive inks and dyes. Though some require fixation, e.g., an alkali, there are also single-bath reactive inks and dyes.
Since these inks directly change the chemical nature of cellulose, they cannot be removed without removing a layer of the substrate. This is analogous to skin stains careless chemists get when working with nitric acid, which, "stains human skin yellow due to its reaction with the keratin." The stain stays until the skin wears off.  [What, me?? Oh, hardly ever! That would be a blot on my escutcheon.]
That said, some might not resist attack from bleaches, leaving a clear ("leuco") dye. However, the mark might still be revealed by IR or UV photography, or by chemical reduction.

Good reads ! Thank you so much. I've been thinking of potassium permanganate as a stain but that stuff scares me with the alcohol base.

Permanganates might leave a permanent stain... however, the black MnO2 can be removed with bisulfites, possibly removing the coloring -- or not.

If at all, what could be something I could add, similar to Permanganate ( stain wise ) but without the harsh opposition to an alcohol base ?

nanocrystalline graphite, possibly a mix of aluminum lake dyes

We had a stain removal center in our lab Last resort was permanganate followed by bisulfite and detergent to remove the MnO2.  Our motto "If we could not remove the stain we fixed the hole"

That is awesome hahaha I love it. Thank you !


text:
Which methoxy- and nitro-substituted azulene has the lower ground state energy?
My contention is that the first azulene structure, with the nitro group on the aromatic cyclopentene ring has a lower ground state energy, as the negative charge can not only resonate into the nitro group, but also through the bridgehead carbon bond. In the second azulene derivate, the negative charge can resonate into the nitro group, but it cannot resonate across bridgehead carbon bond. As such, the first structure has a lower energy ground state because the energy is more delocalized. Is this correct?

If you consider the polarity of azulene itself and the effect of methoxy and nitro substituents on benzene, then you should have you answer.

We have a great question on resonance: https://chemistry.stackexchange.com/q/51632/4945 Please read it. Within the concept of resonance there is no resonating. Your viewpoint is somewhat classical, as if the charges are actually localised. They are not. Azulene is an aromatic compound. If you were to substitute it with a similar aromatic compound, would you expect a significant difference? I wouldn't, and I guess that is the case here, too. Btw. the methoxy groups are usually drawn with an angle.

@user55119 since azulene has more pi electrons on the 7 membered ring, it is more electronegative on that side, so having the nitro group there stabilizes the electron density, while having the electron donating methoxy group on the electron poor cyclopentene also stabilizes that side, which is electropositive, thus structure 2 is more stable?

Wrong! As Martin has said, ignore the double bonds. Azulene is aromatic. Consider cyclopentadienyl anion and cycloheptatrienyl cation.

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Is it possible to make a reversible "Solid State" Hydrogen fuel cell using Ammonia Borane and Iron Oxide?
Well, I saw this video about hydrogen reduction, in which pure hydrogen gas is exposed to iron oxide at high temperatures, producing water vapor and leaving pure iron behind.
And as such, I wondered if there was a way of instead of an hydrogen reduction, there was a "oxygen reduction" so to speak, in which a material "carrier" with a lot of hydrogen bonds reacts with oxygen, generating water and leaving a pure material carrier behind.
Unfortunately, I'm not quite knowledgeable in chemistry, so I asked a lot of questions to ChatGPT on the subject, and although it has a lot of limitations, I received answers that seemed to make sense.

But I'm asking here to know if what it suggested is actually true:
It suggested using either LiNH2-BH3 (Lithium Amidoborane-Borane), NaNH2-LiH (Sodium Amide-Lithium Hydride) or Ammonia Borane (NH3BH3).
And accordingly to ChatGPT, the Ammonia borane would have up to 20% of weight reacted with hydrogen, and once it reacted with the oxygen in the iron oxide, it would leave behind ammonia and boron nitride. The ammonia/nitrogen would be "stored" on a copper oxide metal ammine complex (again, accordingly to ChatGPT).
Then, in order to "charge" the cells by using a reversible hydrogen fuel cell, one would generate pure hydrogen and pure oxygen from water and react everything back to its original state. Just like a battery.
6kg of hydrogen + 16kg of ammonia + 13kg of boron nitride + 16kg of copper metal ammine complex  + 3kg of oxygen + 6kg of iron powder = 60kg in total.
And 6kg of hydrogen is more or less 720 megajoules or 200,000 watt-hours, but with inneficiencies, it would be quite lower value.
Of course, this is ChatGPT we are talking about, it is an AI model that makes statements and answers that sound true.
In one of question in particular, it suggested that Tuolene had a capacity of adsorption of 96% of hydrogen per kg of weight. Which is not true and once I pointed it out, the AI admited it was incorrect.
In any case, I seems interesting to make a solid hydrogen fuel cell, but if it was actually possible, I sure would have seen a lot of news on the subject already.

Safe storage and consumption of hydrogen is one of the key research areas of synthetic fuels. Since we're still burning the fossil stuff, it's a long way coming. I'm afraid your question doesn't fit our format. FWIW: LLM juggle with language, they don't make sense of what they write. As such you could have "corrected" a fact that would have been correct in the first place. Please don't waste valuable fossil fuels on asking a dumb machine things it cannot possibly comprehend.

@Martin-マーチン This is a question's website, I've made a question. How I'm going to know if what the ChatGPT said is incorrect if no one answers? :|

The answer to your original question is no. An iron oxide-ammonia borane fuel cell will not work because the reaction is endothermic. I'll go into a bit more detail though.
ChatGPT gave you its usual frothy mixture of truth, lies, and complete nonsense.
I'll help you tease it out, but in reality you should just reject the whole thing.

It suggested using either LiNH2-BH3 (Lithium Amidoborane-Borane), NaNH2-LiH (Sodium Amide-Lithium Hydride) or Ammonia Borane (NH3BH3).

These are all real compounds that have been considered for use in fuel cells. However, to the extent that ChatGPT suggests they will work, don't believe it. Let's say they're among the candidates for a hydrogen storage material.

accordingly to ChatGPT, the Ammonia borane would have up to 20% of weight reacted with hydrogen

Ammonia borane is 20% (actually 19.6%) hydrogen by weight. However, you can't access all that hydrogen efficiently and reversibly -- an important detail that GPT left out.

once it reacted with the oxygen in the iron oxide, it would leave behind ammonia and boron nitride

OK, here's where it goes totally off the rails.
One big problem with this whole idea is that hydrogen reduction of iron oxide to iron is endothermic. You have to put in energy to do that, rather than getting energy out. This is worth it when you're making steel, but obviously the opposite of what you want in a fuel cell. The same problem occurs with ammonia borane. According to my calculation for the reaction $\ce{NH3.BH3 + Fe2O3 -> BN + 2Fe + 3H2O}$, the change in enthalpy is +90 kJ/mol. That's the wrong direction. There are other problems too, though.
At the high temperatures where iron oxide is reduced by hydrogen, it would likely react with ammonia too, so that would not be the final product. In fact, ammonia reduction has been proposed as an alternative to hydrogen reduction for steel production. (This proposal makes no practical sense to me, but it shows that at temperatures where hydrogen reacts with iron oxide, ammonia probably isn't stable either.)
The stoichiometry of GPT's proposed reaction doesn't work.
Overall I rate this part as ranging between wrong and nonsense.

The ammonia/nitrogen would be "stored" on a copper oxide metal ammine complex (again, accordingly to ChatGPT).

Copper ammine complexes are a thing that exists, but there's no reason to believe they would be a good storage mechanism under fuel cell conditions. They also can't store nitrogen gas. This is just totally made up and useless.

Then, in order to "charge" the cells by using a reversible hydrogen fuel cell, one would generate pure hydrogen and pure oxygen from water and react everything back to its original state. Just like a battery.

This again is just totally made up. It's the fuel cell chemistry version of the "draw the rest of the damn owl" meme... "then just react everything back to the original state!" While it is relatively easy to re-oxidize your iron, getting the other side back to the original ammonia borane will be a real challenge.
The efficiency of water splitting is also pretty bad.
Conclusion
ChatGPT gave you very little of value here, and a lot of lies and incomplete information.
I'll give it credit for one thing -- it listed some hydrogen storage materials. Everything else it told you is wrong or devastatingly incomplete and misleading. And, most importantly, it completely failed to tell you the real problem with your idea.

Thanks for the answer :) (some mods say that I need to wait at least 24hours before checking an asnwer btw)

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Why the C4 in this 1,3,4,5-substituted Cyclohexanes has a R/S configuration?

(1S,3S,4S,5S)-3,5-dimethoxy-1-phenylcyclohexane-1,4-dithiol.
ChemDraw21 shows the C4 is S configuration. However I think C4 has two same function groups(C3 and C5 are both S configuration; C2-1-6 and C6-1-2 are also the same).
So why C4 is chiral? where did I go a mistake?

OK, I seem to find how to name this, link

If you got your answer, feel free to self answer it. Self answer is appreciated and it helps future readers.


text:
Methanol Ethanol butanol mixture assay via spectrophotometer
I have a mixture of Ethanol / Methanol and Butanol that I wanted to assay. Would it be possible to develop a spectrophotometeric method for this? (Currently a GC is being used)
The analysis does not have to be too accurate. 1% accuracy would be fine. However the interest is in a rapid analysis and hence something like spectrophotometric is of interest.
Any thoughts?

I doubt that you could avoid chromatography.

Alkohols have no absorption spectrum in the visible region. In the UV region, their spectra are quite similar. So they are difficult to detect separately by UV spectrophotometry.

And their chemistry is similar too, in case one would think about some more absorbing derivates. It would be slower with more effort and much less selectivity and accuracy than GC.

Thanks! A different question: any other sugesstions for a 3 component system that would be easy to analyse? This is for a distillation experiment so a non azeotropic system of miscible components is what I am looking for.

They have Significant differences in the C-H and C-O stretch areas that should resolve nicely at 2 or 1cm-1 resolution in a good FTIR. A multivariant analysis is necessary. I recommend a 3-bounce trough atr cell. This would give a constant pathlength and remain in the dynamic range of the instrument. Raman spectroscopy might also work same math; scan only the selected ranges.


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What exactly is meant by standard state in thermodynamics?
I was told that the standard enthalpy of a reaction is the enthalpy change when the reaction occurs with all reactants and products being in there standard states and under standard conditions(1 bar pressure for gases and 1molar concentration for solutions),but when we say 1 bar pressure for gases,do we mean that the partial pressure of each of the gaseous reactants and products is 1 bar,or that the total pressure of the reactants and products combined is 1 bar?

Comments have been moved to chat; please do not continue the discussion here. Before posting a comment below this one, please review the purposes of comments. Comments that do not request clarification or suggest improvements usually belong as an answer, on [meta], or in [chat]. Comments continuing discussion may be removed.


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Hückel's rule for FAD (isoalloxazine) electronic structure
Isoalloxazine is called aromatic in literature. It's a part of FAD cofactor. In some PDB structures it has flat geometry (3DK9) in some cases it has not (3GYJ).
I've applied Hückel's $4n+2$ rule for $\pi$ electrons to check aromaticity. I draw my current guess about $\pi$ electrons with red dots and lone pairs with blue clouds:

I've found a total of 20 $\pi$ electrons, which suggests non-aromaticity.
On the left ring, I've identified 6 $\pi$ electrons, indicative of aromaticity.
N10 is anticipated to be $sp^3$ hybridized disrupting aromatic system. If N10 is $sp^2$ hybridized it contributes 2 $\pi$ electrons.
N3 atoms are likely $sp^2$ hybridized due to the presence of 2 $\ce{C=O}$ groups.

Which part of isoalloxazine is aromatic?

This is a somewhat interesting and useful exercise, but ultimately doesn't give much result, as far as actual aromaticity is concerned. N10 is conjugated and you can draw an antracene-like mesomeric structure. This unfortunately doesn't prove anything - doesn't say how major a contributor it is.

Whoever instructs students to use the $4n+2$ rule on a molecule such as this deserves to be placed on a rack and pulled until he confesses that the rule does not really apply.
First off, technically the rule should be applied only to single conjugated rings. If we fudge our way past that minor detail by ignoring the internal carbon-carbon bond, there are those pendant carbonyl double bonds. Pendant pi bonding also means you don't have a ring, and so can't properly apply the $4n+2$ rule.
If we are really willing/forced to stretch things:
As described here, if polarizing carbonyl groups to eliminate pendant pi bonds involving them ($\ce{C=O->\overset{+}{C}–\overset{-}{O}}$) results in an aromatic structure, then the molecular structure will in fact favor such a polarization. If we do that here, and if we count the remaining conjugated pi electrons properly, we get not $20$ but $14$:

$6$ electrons in the left ring

$2$ additional electrons from the $\ce{N–R}$ nitrogen in the center ring but not from the other nitrogen, whose lone pair is outward-pointing

$4$ additional electrons fem the pi bonds drawn in the middle and right rings

$2$ additional electrons from the nitrogen on the right ring.

We can argue that a chain of three conjugated rings with $14$ pi electrons like anthracene would be expected to show aromatic character, but we had to pull several muscles to get there. Better to do a more sophisticated molecular orbital analysis, preferably backed by experimental measurements such as nmr chemical shifts of hydrogen atoms bonded to the ring system, to know for sure.


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Why 2-methyl-1-propene's halohydrin formation does not involve steric effect?
This concerns Marc Loudon's Organic Chemistry 6th Edition's 5.2 page 187.
Consider 2-methyl-1-propene and its halohydrin formation mechanism. Usually, there will be formation of bromonium, where I assume there is no way that solvent stabilization will create carboncation.
$Q:$ Why does not hydronium attack C1 from opposite side of bromide of bromonium ion to open the ring? Consider swapping methyl group at C2 position by t-butyl group. I would expect significant steric hindrance from 2 t-butyl groups and this would force ring opening attack at C1 position as attacking happens at opposite side of bromide. If I remember correctly from Sunderberg's Advanced Organic Chemistry reading on bromonium cation, there is possibility of steric hindrance happening.

There is a steric effect, but it cuts both ways - bromine is large and its symmetric coordination to both C atoms would also cause greater clash between methyl groups. Essentially, this thing is like t-butyl cation stabilised by neighbouring Br.


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How exactly does the Nernst equation account for temperature?
I am doing an experiment that involves changing the temperature of the electrolytes in a voltaic cell and seeing the effect on the initial voltage produced. I'm a bit confused because if I use the same concentration of solution for each electrolyte, then $Q = 1$ and $\ln Q = 0.$
Then, you are simply left with $E_\mathrm{cell} = E_0.$ I read another post where it says $E_0$ itself is a function of temperature but I don't full understand how that works. Is there any way I can account for this in a high school lab environment?

Se also: https://chemistry.stackexchange.com/questions/26405/why-does-temperature-affect-cell-potential

There are two temperature dependences involved in the Nernst equation. The explicit one
$$\frac{RT}{nF}\ln{a}\tag{1}$$
and the implicit one
$$\begin{align}
E^\circ(T) &= \frac{-\Delta_\mathrm rG^\circ(T)}{nF} \\
  &= \frac{-\Delta_\mathrm rH^\circ(T) + T\cdot \Delta_\mathrm rS^\circ(T)}{nF} \\
  &\simeq \frac{-\Delta_\mathrm rH^\circ + T\cdot\Delta_\mathrm rS^\circ}{nF}, \tag{2}
\end{align}$$
where the TD variables assume the reaction
$$\ce{Ox + $\frac n2$ H2 -> Red + n H+} \tag{R1}$$
and the respective $E^\circ$ is for the half-reaction
$$\ce{Ox + $n$ e- -> Red} \tag{R2}$$
Standard reduction potentials  for nonstandard temperature are not usually available but for exceptional cases. Its change with temperature can be determined experimentally after subtracting the change of the the activity term. Theoretically it could be calculated if there is known or measured the standard reaction enthalpy.
The Nernst equation contains terms dependent and independent on activity. It is similar as for calculation of pH with terms dependent and independent on concentrations.
With a single potential, we would have $E(T,a)$. It is advantageous to have the term  independent on activity, as it is the specific parameter for the reaction. The single potential would not be and we could easily compare two half reactions.

Thank you for your response! Is there any way to determine the standard E at a given temperature then (either experimentally or literature values)? Also if the standard E is already affected by temperature, why is there another E in the Nernst equation? Is that not "doubling" the effect of it?

See the updated answer.

You are trying to study the effect of changing temperature[T] on the voltage of a galvanic cell. There are several factors to consider: First: the molar concentrations change with T. Second: The activities of ions vary with concentration and T. Third: There is a linear effect of T on EMF E[0]nF =-RTlnKeq. Fourth: Keq is a logarithmic function of T depending on the heat of reaction.
The first can be compensated by using the volume expansion of water. The second by researching activity coefficients. The third and fourth are what you hope to measure. Why the temperature dependence? Part of the energy content of the reactants is the thermal energy or heat; this is proportional to the absolute T. The rest is in the chemical potential energy difference in the bonds of the reactants and products. This is measured by the difference between the actual condition and the equilibrium condition. Why does the equilibrium constant change with T? When heat is added to a system at equilibrium the system changes in the direction that removes heat resulting in a new T and a new Keq. This is an application of LeChatlier's Principle.
A suggestion: For the reaction think about using a pH electrode with matching reference electrode. Solutions of known activities over activity and temperature ranges are available. The second study could be the equilibrium of pure water as a function of temperature. You will need a pH meter that reads in tenths of millivolts  and a way to determine the activity of H3O+ in pure water using the Nernst Equation.

An instantaneous own vote! What is going on here?

Thank you for your response! How does the concentration change with temperature? For my experiment, I am recording the initial voltage produced, so I would imagine the reaction doesn't have time to reach equilibrium. I will also be using low temperatures (less than 50 degrees celsius so I don't think it would evaporate). I'm not sure if I have access to a pH electrode or a pH meter (at least with that precision)

The potentials must be measured at zero current Use a good volt meter. Design the apparatus with minimum head space, plastic cling wrap will top evaporation. The density of water at the various T will almost correct for concentration changes. For temperatures might I suggest an ice bath, Zero Celsius, [273 K] An accurately measured ambient room temperature [~295K] and a hot water bath about 40 C [~315 K]. The exact Ts are not important . They must be measured precisely. Ask your teacher about the pH possibility it will be a good thing to have in the lab. Also you can work with activities.


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Chemistry behind cleaning with vinegar vs citric acid; do they work differently? Should I prepare the same pH solutions to compare them?
I noticed a pack of "Mysterious Citric Acid" while out shopping so I picked it up to see what the big deal was. Several palates of the stuff had just arrived at a local outlet store. I figured that some chemical manufacturer had surplus so they quickly printed up some very promising looking packages.
Vinegar is often touted as a household cleaner, by it self at some dilution, or combined with various other household ingredients. I am wondering if the chemistry behind the use of a citric acid solution (when titrated properly, say for example to the same pH?) is the same as that of an acetic acid solution as far as household cleaning activities are concerned, or if they work differently or one is preferred over the other in some cases.

below: click for full size

Citrate chelates ionic calcium, accelerating dissolution of carbonate deposits.

Consider the more extreme case - should you compare cleaning properties at the same pH for acetic and hydrochloric acid ? E.g. at pH 2.5 ? The former would be much better, having much bigger neutralization capacity.  // Consider also citrate and acetate complexes with iron as rust removers on Wikipedia.

I like citric acid for household cleaning. I use it to descale my electric cattle the washing machine, the sink, the floors, the faucets, the everything. It smells a lot nicer than vinegar, and it usually does the job pretty well. Only thing left to wonder is: Whats so mysterious about it?!

Citric acid chelates  not only calcium, but many other metals, including manganese and iron found in some water supplies, which leave stains in kettles and on fixtures. It's also used in soil remediation: https://iopscience.iop.org/article/10.1088/1755-1315/896/1/012023/pdf . It might not be the most powerful chelating chemical, but it's comparatively safe and inexpensive.

@Martin-マーチン thanks, I'd never heard of it as a household product until I saw this for sale recently. By amazing coincidence have a bunch of hard yellow flakes of deposits I just collected from the inside of my electric hot water machine recently (it seems to have a non-stick coating inside) so I can compare vinegar and ctric acid solutions on them. Chelation of calcium ions sounds like something that happens to already-dissolved calcium; curious if and how either work to get them in to solution to begin with.

@BuckThorn ditto

I suppose I should have chosen my words more carefully. By dissolution I meant bringing a solid into solution. By accelerate I did not mean that the forward step of the reaction occurred faster, but rather that the product in solution is stabilized, inhibiting the reverse reaction (carbonate deposition).

Food grade citric acid is also a condiment: I purchased a bottle of it, with the name “sour salt”, at a local grocery store. I ended up using it for something else.


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Some advice on inorganic textbook
I'd like to have some advice on Inorganic textbooks.
I've already consulted some books (Kettle, Drago, Keiter, Cotton) and they are all very useful, but now I'm searching for a textbook which focuses deeper on the relationships between electronic configurations, periodic properties and reactivity.
I'd like to have a guideline which explain why some elements are more inert than others or their affinities but based on the description for example of the shielding properties and kind of valence electrons.


text:
"Probability flux": Imaginary part
I was confronted with this problem from "Mathematik für Chemiker", 8th edition (Ansgar Jüngel, Hans G. Zachmann):

$$ \begin{align}
\partial_t |\psi|^2
 &= \partial_t (\bar\psi\psi) \\
 &= \partial_t\bar\psi\cdot\psi+\bar\psi\cdot\partial_t \psi \\
 &= {-\frac{i\hbar}{2m}\Delta\bar\psi\psi+\frac{i\hbar}{2m}\bar\psi\Delta\psi} \\
 &= -\frac{i\hbar}{2m}\textrm{div}\big(\nabla\bar\psi\psi-\bar\psi\nabla\psi\big) \\
 &= \frac{\hbar}{m}\textrm{div}\big(\Im(\bar\psi\nabla\psi)\big) \quad\quad\quad (13.7)
\end{align} $$

I calculated it over and over, but eventually got the same sign error:
$-\frac\hbar m\mathrm{div}\big(\Im(\bar\psi\nabla\psi)\big)$ instead of $\frac\hbar m\mathrm{div}\big(\Im(\bar\psi\nabla\psi)\big)$

Here is my working:
$$ \begin{align}
\partial_t|\psi|^2
 &= \partial _t(\psi\bar\psi) \\
 &= (\partial_t\psi)\bar\psi + \psi\partial_t\bar\psi \\
 &= \psi\partial_t\bar\psi + (\partial_t\psi)\bar\psi \\
 &= \Big(-\frac{i\hbar}{2m}\Delta\bar\psi\Big)\psi + \Big(\frac{i\hbar}{2m}\Delta\psi\Big)\bar\psi \\
 &= -\frac{i\hbar}{2m}\big((\Delta\bar\psi)\psi - (\Delta\psi)\bar\psi\big) \\
 &= -\frac{i\hbar}{2m}\Big( \frac{\partial^2\bar\psi}{\partial x^2}\cdot\psi - \frac{\partial^2\psi}{\partial x^2}\cdot\bar\psi \Big) \\
 &= -\frac{i\hbar}{2m}\frac{\partial}{\partial x}\Big( \frac{\partial\bar\psi}{\partial x}\cdot\psi - \frac{\partial\psi}{\partial x}\cdot\bar\psi \Big) \\
 &= -\frac{i\hbar}{2m} \textrm{div}\big((\nabla\bar\psi)\psi - (\nabla\psi)\bar\psi\big)\\
 &= -\frac{i\hbar}{2m}\mathrm{div}\Big(-2i\Im\big((\nabla\psi)\bar\psi\big)\Big)\\
 &= -\frac\hbar m\mathrm{div}\Big(\Im\big((\nabla\psi)\bar\psi)\big)\Big)\\
 &= -\frac\hbar m\mathrm{div}\big(\Im(\bar\psi\nabla\psi)\big)
\end{align} $$
I used the $\bar{z}-z = -2ib = -2i\Im(z)$ approach. In my understanding this should result in the cancellation of $-2$ and $-\frac12$, leaving us with $\frac{i\hbar}m\textrm{div}\big(i\Im(\bar\psi\nabla\psi)\big)$.
Using $i^2= -1$ $\implies$ ${-\frac{\hbar}{m}\textrm{div}\big(\Im(\bar{ψ}\nablaψ)\big)}$.

Physically is it possible for $\partial |\psi|^2/\partial t $ to be negative, and  certainly $(-i)(-i)=-1$.

Your result and calculation are correct, and you reproduce properly the well known continuity equation for a free particle,
$
\partial_t \rho = - \vec \nabla \cdot \vec j
$
with $\rho = |\psi|^2$ and $\vec j= \frac{\hbar }{m} \ \Im \{\bar \psi\nabla \psi \}$
such that,
$
\partial_t|\psi|^2 = - \nabla \cdot  \frac{\hbar}{m}\Im \{ \bar \psi\nabla \psi \}
$
There is a sign error in the last expression of equation 13.7, which should contain a minus sign.


text:
What is the difference between using an oven or an IR lamp to dry the coatings of fuel cells?
I wondered how the morphology of the catalyst coating for fuel cells changes if it is dried either in a conventional oven (40 °C, 60°C, 80°C) or under an IR lamp.
I am pretty certain that it changes, as Liu states:

"If the formulation and preparation processes of the catalyst ink, as well as the coating process are fixed, the drying process of the ink film deposited on the substrate will determine the morphology and structure of the CL. There are several influencing factors that should be considered, e.g., the drying techniques, evaporation conditions, solvent physical properties, or solid concentration in the ink." [1]

However, this paper does not mention IR lamp drying explicitly.
[1] H. Liu, L. Ney, N. Zamel, X. Li, Applied Sciences 2022, 12, 3776.

IR lamp has less defined and less homogenous maintenance of the increased temperature of target.

The mechanisms of heating differ. An Oven heats by conduction from the collisions of higher temperature gas molecules colliding with the substrate and from black body radiation. Volumes of low specific heats will heat faster than volumes with high specific heat. Infrared or microwave heating involves quantum changes in molecular levels. The original absorption of energy causes a population inversion in vibrational-rotational levels and no increase in temperature. The excited molecules relax losing energy by emission or collisional deactivation. The areas that heat first are the absorbers and the molecules in their vicinity. In both cases equilibration takes time [This is why it is a good idea to let microwaved liquids rest a while before disturbing them].
The difference among heating techniques are empirical. Different methods can give different results. The best comparison I can give is the difference in cooking results among an induction stove, gas range, electric stove, deep frying, hot air oven and a microwave oven. Each does things differently and has its place.
Infrared heating is the mechanism behind atmospheric warming. The Earth is the infrared heater. Gas molecules that absorb specific ir frequencies are the energy absorbers. The absorbed energy eventually becomes heat and is distributed about the Earth.


text:
Mechanism of formation of nile blue dyes
Hello I was thinking about the formation mechanism of the double condensation to form nile blue. However, I am stuck, as I can't explain why the condensation of the hydroxyl moiety happens.

In this example, I suppose the nitroso group gets protonated, and the electrophilic nitrogen atom is attacked, and condensation happens, as well as the reformation of the aromatic ring. But why does the hydroxy group also get condensated and thus forming a fused ring?

You are correct that the first step of the mechanism involves protonation of the nitroso group. Be aware that protons are being exchanged on the amines during the course of the condensation. There are a number of subtleties in the mechanistic pathway that may be invoked but I have selected what, in my experience, is a likely route. Be forewarned, there is a surprise in store.
Condensation of aryl nitroso compound 1 and β-naphthol 2 affords intermediate 3, which rearomatizes to oxime 4. Dehydration of the oxime may well be stepwise but, in order to save space, I have shown it as a concerted process to form quinoid structure 5. The dehydration of 4 could lead to the double bond stereoisomer of 5 but that product would be sterically hindered. Addition of the phenolic oxygen to the quinoid moiety provides 6 that rearomatizes to tetracycle 7. Here is the surprise! The leuco-form of the dye is formed, not the dye itself. continued

Let's presume that the reaction is not conducted under an inert atmosphere. Then oxygen is a likely suspect. The ground state of oxygen is a triplet, which can abstract an electron from the amino group of 7 to form radical cation 8 and the radical anion of oxygen 9. The latter species is protonated by acid to afford the hydroperoxy radical that abstracts a hydrogen atom from radical cation 8 to produce the tautomeric forms, 10 and 11, of the dye.

I am upvoting this answer for reasons of shock and awe. Wow!

It would be good to add reference to info or pictures. Unless it is knowledge gathered during the time with source lost in the abyss of the past, what is often my case.

This looks entirely reasonable and convincing

@Poutnik: I was taking the OP's reaction at face value. I've been "pushing arrows" for 65 years; no need for references.


text:
What does the circle mean in this picture?
So I found this picture on wikipedia and I was wondering what this big circle (which all of the substituents were attached to) meant.

source: https://en.wikipedia.org/wiki/Apamin

Well, that's a ring. It would be pretty hard to draw such polypeptide with accurate geometry, making it still readable.

BTW you should link directly to where you found it.

External addresses and links may change and become defunct.  In case of an illustration like the one from wikipedia, just provide the illustration itself including a proper note of the source of origin.

You might be interested: Cyclic polymer https://www.researchgate.net/figure/Mechanism-of-formation-of-cyclic-polymer-with-controlled-molecular-weight_fig9_256830670

Departing from amino acids, peptides are formed by the reaction of an amine and a carboxylic acid via an amide bond.  This may yield linear peptides, or cyclic peptides, and apamin is only one example of them.
Sketchers often attempt a representation which is easy to read on expense on a depiction identical to the 3D structure of a molecule; which differs from the purpose of a structure viewer.  To illustrate this, below is the 3D structure of the entry on ChemSpider the Wikipedia page you quote cross links.  For an increased clarity of the representation, I removed all hydrogen atoms from the model.

simplified model based on ChemSpider entry 23975893


text:
Data sheet for the dynamic viscosity of salt-water-glycerol solutions
Does anyone know where I can get data for the dynamic viscosity of salt-water-glycerol solutions? Specifically 80% glycerol and 20% salt water by mass at 19.2 degrees celsius. Salt concentrations vary between 0 and ~1 mol dm^-3. Anything close is also appreciated. If this is too specific for data sheets and textbooks, are there simple equations or simpler data sheets that I could use to approximate the values I need? If you're wondering, I need results of papers to back up my lab results. Thanks.

As a start in the CRC handbook of Chemistry & Physics, at 25 C and 80% mass percent glycerol the viscosity of glycerol water is given as 45.9 cp.

Effect of the salt on viscosity is hard to predict.


text:
Explanation/calculation for the pH of a solution of 2.0 M Sulfuric Acid reacting with Zinc?
For school, I am doing a small study on a chemical reaction involving 2 M Sulfuric Acid (H₂SO₄) and Zinc (Zn). I have done some background research on the process to calculate the pH of a solution, but the expected value doesn't seem to match either the initial pH of the H₂SO₄, or the change in pH over time.
For reference, we calibrated our pH probe multiple times to an accuracy within ± 0.1 of the expected values of the calibration solutions (pH 4 and pH 7). Water displayed a pH of 7.06.
According to the probe, the pH of 2 molar H₂SO₄ is ≈ -0.25 ± 0.03, which I do not understand. Research indicates that the pH of a solution can be calculated using $-log_{10}(\ce{H^+})$. When completely dissociated in water, 2 molar sulfuric acid should have a H⁺ value of 4, so the pH should be equal to $-log_{10}(4)$, which is ≈ -0.602, over 0.35 off from the measured value of -0.25.
Also, as the reaction between Zinc and Sulfuric Acid progressed, the pH of the solution decreased (from ≈ -0.25 to ≈ -0.30). This also makes no sense to me, as my intuition would tell me that the pH would increase, not decrease. This is the main result I am seeking answers for.
If anyone could explain this to me, it would be incredibly helpful for my study.

HSO4^- is not strong acid. pH is given by H+ activity, not concentration. At such ionic strength I, activity coefficients  raise with I. Dissolving Zn raises ionic strength, which may cause stronger activity coefficient raise than is the decrease of H+ concentration. Note that generally, calculations at these concentrations may be very misleading.

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Why you'd expect it to work well below 0 pH? You shouldn't even put glass electrodes in extreme solutions. If it was a base, you could even damage it.

I agree with Mithoron, I forgot to mention that.

@Poutnik I would not have thought that 2 molar H_2SO_4 would be an "extreme solution". Also, I have not learned about "ionic strength" yet, so how can I calculate the theoretical pH change? Are calculations infeasable for this reaction?

@Matt The meaning of the "Extreme solution" is very much context dependent. For theoretical prediction of pH it IS an extreme solution as it is extremely difficult to calculate it. One has to use quite complicated models of thermodynamic activity of H+(aq).

Thankyou all for your help with this question, it helped Matt and I with our investigation greatly. It is submitted and I am happy with what I submitted, and you guys gave us heaps of help!

The first consideration is the equipment, a calibration variance of 0.1 is unacceptable. The reference electrode should be a flowing double junction electrode, the outer chamber fill solution might need some research. Calibrate at pH7; set the slope at pH4; record all mv values. The difference between7 and 4 should be almost 180 mv. pH 2 buffer is available get some and check for linearity.
Accurately prepare 2M, 1M and 0.5M sulfuric acid and measure the mv readings and the pH of each. Find the Ka for bisulfate and try to calculate the possible [H3O+]. Make calibration curves for both concentrations. Then add an amount of Zn to give a calculated molarity change to each solution. Hopefully to change each solution into the lower one in sulfuric acid. If the values fit one of the calibration curves the activity coefficients are reasonably constant; if not they must be researched. Good luck the results should be very interesting. Please report back

Unfortunately, our pH probe only supports two point calibration to my knowlege. Not only that, but we have no time left to collect any further results. Does this mean that our results, particularly the negative pH, are wrong and due to the pH probe measuring incorrectly?

The negatve is right  you do not know how negative. pH meters are calibrated  at only ONE point  usually the isoelectric point near pH 7. The pH 4 point sets the slope done with the temperature control not the  calibration control. Find the time and try to do the experiment properly.

I am also working with Matt on this experiment, we are unable to gain any further results, due to time constraints. As a school experiment, our teachers provided us with the option of using 2M Sulfuric acid and Zinc. From what I gathered from your responses, is that these reactants are not ideal at all. We are using the SparkVUE app paired with the PASCO pH probe. We calibrated the probe with two points, under the careful supervision of our teacher, and Lab Technicians at our school who confirmed that it is the correct way to calibrate. The results that we gathered are negative and decrease after the zinc is put into the sulfuric acid. What we are trying to find out is why the zinc is causing the pH to decrease, and what the trend of the data means. Thankyou for your helpful responses Poutnik, Mithoron, and jimchmst.

This is the graph of the change in pH over time for reference.

@Menton, could you check the pH range in which your electrode is reliable? The pH value you are trying to measure seems too high. Can you try your experiment with a lower pH? For example, using a 0.1 M $\ce{H2SO4}$ solution.

no, we are unable to do anymore tests. and we were not given an option for a lower concentration. A different group asked for 0.5M but were not given it.

@Menton, I don't usually work with pH meters but I'm not sure that if you work very far out of the calibration range of the electrode, the pH meter readings can be very reliable.  Maybe you need different calibration points to be able to measure such low pHs.

You may find this document helpful. A guide to pH measurement (Metler-Toledo) : https://www.mt.com/mt_ext_files/Editorial/Generic/1/Guides_to_Electrochemical_Analysis_0x000248ff00025c9a00093c4a_files/guideph.pdf

I understand you might not be able to do so, but the right way to proceed would be a negative control: perform the exact same measurement but without adding the zinc powder. The pH decreasing during the reaction is clearly anomalous, and so most likely an experimental artefact. As several people have pointed out, regular pH electrodes were not designed for highly acidic solutions like this, so its' very possible that the membrane's properties slowly change, becoming more sensitive to protons over time. If so, you'd see the same in the blanco experiment, except more so as no hydrogen is evolved


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Determining whether precipitation will occur or not and finding the concentration of a specific ion in a solution

The Ksp value of AY2 = 9.148 x 10^-2. I am having problem with calculating the concentration of ions. And without the correct concentration I can't find the Qsp/Kip so I'm stuck without them I can't determine whether the new solution will precipitate or not. How to calculate the concentration of ions in this type of scenario?

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1/ Enumerate initial concentrations 2/ Involve variable of amount of precipitated salt 3/ express ion concentrations as function of this variable. 4/ Formulate and resolve equation involving Ksp and ion concentrations.

whoami - determine separate ions concentrations in the starting solutions, then use the dilution equation: $$\ce{m_1 * V_1 = m_2 * V_2}$$ to get concentrations in the mixed solution.


text:
Enthalpy change of a solution of 1-pentanol in 1-butanol
I came across a question asking to indicate the enthalpy of solution for a solution of 1-pentanol in 1-butanol.

The options were the following:

$\Delta H < 0$
$\Delta H \approx 0$
$\Delta H > 0$

I chose 3, which was wrong, as I thought that the $\Delta H_\text{solution}$ would be positive since the intermolecular forces in 1-pentanol would be slightly greater due to the extra methyl group, and as such, it would require more energy to break the IMFs between the 1-pentanol molecules than the energy released from the forming of IMFs between the 1-pentanol and 1-butanol. Which one should be the correct answer?

Your reasoning is good whether wrong or right , it might depend on the relative amounts. read my comment  below

Dissolving a "big" molecule like 1-pentanol in 1-butanol is equivalent to suppressing a small proportion of the hydrogen bridges between neighboring ROH. The changes in van der Wals effects due to alkyl groups are negligible. So, because of the small changes in hydrogen bridges, the mixture should be a little endothermic. But I agree with Poutnik, the heat effect must be tiny, and near zero.

There most likely is a positive entropy of mixing, at equilibrium H =TS so both have the same sign. The reaction is endothermic whether one can measure it accurately is their problem not the test takers. A poor test question.

It is more about careful reading of the task info than about knowledge of chemistry.
Both molecules are almost identical, it may be hard to guess the enthalpy sign. But whatever sign the mixing enthalpy has, it will be close to zero.
Therefore. the right answer is $\Delta H \approx 0$, regardless of if it is positive, negative or if its difference from zero is statistically insignificant.

This is another question that if one actually knows the answer one is doomed to get it wrong Either 1 or 3 MUST be correct but the answer is two because the test writer is ignorant.

Option 2 will be correct in any case too

No option 2 is politically correct The question is just inappropriate.

If the confidence interval of Delta H covers 0......


text:
How to quench and get rid of P2S5?
I am using $\ce{P2S5}$ as a thionating agent on ketones and amides. The reaction works very well, however there is little to no information on how to safely quench and get rid of the unreacted $\ce{P2S5}$. The procedures I use simply rotavap the crude product and recrystallize the desired product, which works great, but some unreacted $\ce{P2S5}$ is always left at the bottom of the flask. I read about people adding a dilute solution of $\ce{K2CO3}$ in order to hydrolyse the remaining $\ce{P2S5}$ into phosphoric acid and $\ce{H2S}$ but I'm not sure how safe this is. I'm working on less than $\pu{10 g}$ scale.

People underestimate how toxic H2S is. A quench into aqueous oxidant e.g. Oxone will prevent H2S formation and hydrolyse the P2S5

Which product is obtained instead of H2S?

Depends on exactly which oxidant is used. Sulfite anion would be the most likely.

Did you see Bergmann's approach to use the adduct of pyridine and $\ce{P2S5}$? The reagent obtained by a brief reflux (crystalline, less smelly than $\ce{P2S5}$) is used in e.g.  MeCN.  The eventual addition of water decomposes the excess into a water soluble pyridinium phosphorothioate. 2011JOC1546 (introduction) and Kingi and Bergman in 2016JOC7711 (an application by them) though so far at scale of about $\pu{1 mmol}$.  It could be still more efficient that Lawesson's reagent.


text:
Can we add specific conductivities at any concentration?
Suppose we have specific conductivities of $\pu{0.1 M}$ $\ce{K+}$ and $\pu{0.1 M}$ $\ce{Cl-}$. Can we add their specific conductivities to get specific conductivity of $\pu{0.1 M}$ $\ce{KCl}$?

We can, but the problem is usually the other way around. Specifically, KCl  of various molarity is used as conductivity standard to calibrate conductometers.

Conductivity is not necessarily a linear function, particularly at high concentrations. See https://chemistry.stackexchange.com/questions/26781/conductivity-as-a-function-of-acid-concentration For example, there's a reduction at high NaCl concentrations, though KCl is more linear over that range.

No, you can add molar conductivities of ions only in a dilute regime. This is also known as Kohlrausch's law of independent migration.


text:
How does an organic acid change the structure of chrysotile asbestos?
This patent (https://patents.google.com/patent/US5041277A/en) describes how dilute acids such as lactic acid and acetic acid can change the fibrous structure of chrysotile asbestos with up to 98% efficiency. The inventor goes on to say how the end result is no more dangerous than sand, but I don't understand why. What is the new structure after it reacts with the acid?

Mmm, wording in this patent it pretty lame. Essentially, this is simple acid-base reaction, with stronger acid displacing weaker.


text:
Is tropylium cyclopentadienide possible?
Has this ever been tried? The respective aromatic ions are readily accessible, e. g., in the form of sodium cyclopentadienide and tropylium bromide. It shouldn't be hard to just combine these two salts. People have went down much more intricate ways to obtain exotic aromatics. Especially considering the prospect of a pure hydrocarbon ionic compound (maybe even an ionic liquid?), formally derived from benzene by intermolecular exchange of a CH⁺ charged ring segment. Or call it, with some hand-waving, a heterolytic cleavage of azulene.
I've done some superficial peek into literature (tricky, since there are tons of sources discussing the two aromatic ions separately); best I cold find was https://doi.org/10.1248/cpb.11.126 with their compound VII:

(with some bulky substituents on the cyclopentadienide ion), that “easily formed red crystals” from aqueous solution. Apparently, though, learning about the pure C₇H₇C₅H₅ was none of their priority. But the fact that this is isolatable, and doesn't fall apart/rearrange immediately, sounds promising to me.

https://chemistry.stackexchange.com/questions/9212/can-a-organic-compounds-such-as-hydrocarbons-contain-an-ionic-bond

It's not a matter of bulkiness - you need powerful withdrawing groups on cyclopentadienyl and donating ones on tropylium. Otherwise charge density is so high you get covalent bond.

While I can't give a definitive disproof, my intuition is that an unsubstituted cyclopentadienide anion would be far too nucleophilic and react with the tropylium cation at non-cryogenic temperatures (or alternatively, there could be direct charge transfer forming radicals which would then react in various ways). Note that the presence of opposing charges vastly increases the kinetic and thermodynamic propensity towards reaction in the absence of other inert screening charges. All those cyano substituents in the successfully isolated compound you show are really pulling a lot of weight, delocalising and stabilising that negative charge to tame it.
But it is also possible to delocalize the charges in the absence of assisting heteroatoms using larger and larger pi-conjugated systems to eventually stabilize them. The excess charges essentially have to be "diluted" over enough atoms and spaced far enough apart to stop them from mutually reacting. Have a look at these first examples of hydrocarbon salts to get a feel for what's necessary to keep the charges separate. Typically both the cation and the anion have to be extensively overbuilt. Anion 1 and cation 5 can be viewed as a derivative of the cyclopentadienide and tropylium cation, respectively, and their combination does result in an isolable salt (actually the least stable salt of the combinations tried in the study).

Interestingly, this paper also mentions that tropylium acetate is a covalent compound, and the acetate anion is substantially less basic/nucleophilic than unsubstituted cyclopentadiene, so once again the odds of your desired salt existing in reasonable conditions are likely quite low.


text:
How do I calculate the masses of compounds in a mixture from a GC?
I'm supposed to analyse the two GC graphs in the attached picture (I quickly drew them instead of taking a picture). The question states ths "A mixture contains 3-Methylhexane. To determine the mass of 3-Methylhexane in the Mixture, a 1:1 - Mixture of pure 3-Methylhexane with the comparative substance Hexane was produced and analysed by GC (first graph). The second graph shows a GC of the same mixture after adding 1g of Hexane. Question: Find the mass of 3-Methylhexane in the mixture."
Now, first thing I'm confused about is the area of the hexane peaks. How could the area be the same if there is more ($\pu{1 g}$ more) hexane in the second graph?
The areas of the peaks are:
|----------+--------+----------------|
| analysis | hexane | 3-methylhexane |
|----------+--------+----------------|
| run 1    |  0.675 |           1.02 |
| run 2    |  0.675 |           0.90 |
|----------+--------+----------------|

Could someone give me a hint of how to proceed?
As depicted in the scheme (not drawn accurately) I calculated an area ratio about the data of run 1 (left hand side) as: 0.675 / 1.02 = 0.66. But how do I determine masses now?

Don't worry about the absolute areas. Work with the ratios to set up the initial equations. You have two equations in two unknowns: x/y = r1 and (x+1g)/y = r2. Solve for x and y.

Something seems seriously confused in the task.

Poutnik is right. First difficulty : the area of $3$-methylhexane cannot be $1.02$ and $0.9$ as given. Visually, the first area looks about $1.3$ or $1.4$ and not $1.02$. Second difficulty :  The area of the two peaks of hexane are exactly the same (to less than $0.1$ %), although the second graph is made with more hexane. This is difficult to understand. The whole problem looks as if both graphs have been interchanged, and some more $3$-methylhexane has been added in the first graph, with the same amount of hexane in both graphs.

Did you perform the GC with a FID/TIC?  Especially with compounds as volatile as hexane, the absolute numbers and peak shapes can vary depending on temperature gradient, column type, column length, use of an automatic sampler vs. a manual injection, etc.  Then, the raw data collected, same protocol on both for background correction and integration criteria?  For an analysis of added standards, the ratio of your additional $\pu{1 g}$ to the total ($\pu{10 g}$ vs $\pu{100 g}$, for example) equally is a detail to keep track. (It can be less relevant for the specific question here, though.)

@Maurice Sorry for confusing you. I just quickly drew these graphs in MS Paint because otherwise I would have had to take a picture. The values are as close to the correct ones as I could calculate from the (low res) image I received. I would totally agree with your conclusion that 3-methylhexane would have to have been added, but the task doesn't say that for some reason.

@Buttonwood I didn't perform the GC, but just received the data from a task in my book

@BuckThorn the thing is, I don't have any mass measurements to use. So I'm not sure what you mean by (x+1g), since x could only be an area. I might be totally misunderstanding though, would you mind elaborating?

You are afaiu not trying to determine the molecular mass, you are trying to determine how much (x or y) of each compound is present in your mixture. Spiking with a known quantity is one way to figure it out but assumes the areas are proportional to amount (mass in mixture) of substance.

The homework question is ill-posed, i.e., there are too many incorrect assumptions and in reality nobody will ever try this. It is better to ask the instructor what are they trying to ask.


text:
Why do we call STO-nG a basis set?
Why do we call the Hartree Fock basis-set for an atom a "basis set?" In linear algebra, a basis must be linearly independent. Looking at the STO-3G "basis set", the basis functions in this set are not linearly independent.
Let me define the basis set and show why I say they are not linearly independent:
For Hartree Fock with STO-3G basis, to represent carbon you would need the following basis:
Carbon atom:
$$ \begin{align*}
\Phi_{1s}(r) &= d_{11} g_{11}(r) + d_{12} g_{12}(r) + d_{13} g_{13}(r) \\\\[10pt]
\Phi_{2s}(r) &= d_{21} g_{21}(r) + d_{22} g_{22}(r) + d_{23} g_{23}(r) \\\\[10pt]
\Phi_{2px}(r) &= d_{31} g_{31}(r) + d_{32} g_{32}(r) + d_{33} g_{33}(r) \\\\[10pt]
\Phi_{2py}(r) &= d_{41} g_{41}(r) + d_{42} g_{42}(r) + d_{43} g_{43}(r) \\\\[10pt]
\Phi_{2pz}(r) &= d_{51} g_{51}(r) + d_{52} g_{52}(r) + d_{53} g_{53}(r)
\end{align*} $$
where above, $d_{ij}$ are coefficients and $g_{ij}$ are gaussians.
And, for Carbon, here is the JSON for STO-3G:
[
  {
    "function_type": "gto",
    "region": "",
    "angular_momentum": 0,
    "exponents": ["0.7161683735E+02", "0.1304509632E+02", "0.3530512160E+01"],
    "coefficients": [
      ["0.1543289673E+00", "0.5353281423E+00", "0.4446345422E+00"]
    ]
  },
  {
    "function_type": "gto",
    "region": "",
    "angular_momentum": [0, 1],
    "exponents": ["0.2941249355E+01", "0.6834830964E+00", "0.2222899159E+00"],
    "coefficients": [
      ["-0.9996722919E-01", "0.3995128261E+00", "0.7001154689E+00"],
      ["0.1559162750E+00", "0.6076837186E+00", "0.3919573931E+00"]
    ]
  }
]

To quickly explain this JSON, for Carbon there are two energy levels, 1S and 2S + 2P. Therefore you have two sets of brackets which represents the energy levels. The second set  has one set of exponents and two sets of coefficients. The two coefficient sets are for 2S and 2P orbitals, and because both the 2S and 2P orbitals use the same exponential there is only one set of exponents.
So, looking at this, the basis functions:
$$ \begin{align*}
\Phi_{2pz}(r) &= \Phi_{2py}(r) = \Phi_{2px}(r) \\\\[10pt]
&=0.1559 e^{-0.29 r^2} + 0.608 e^{-0.68 r^2} + 0.392 e^{-0.22 r^2}
\end{align*} $$
So, these are not linearly independent. Then, why do we call them a basis? Is STO-nG just an improper basis set?

Atomic orbitals also contains an angular momentum part, or if you use a cartesian representation, a polynomial part, which makes them linearly independent even if they have the same Gaussian exponents for the radial part. For example, you have to multiply the $p_x$ orbital with x, while $p_y$ gets multiplied with y, etc. What you wrote down are not the complete/proper basis functions.

Oh so the angular term is different for each P orbital? Thanks that does clear it up!

BTW it should be "carbon" not "Carbon".

Its also a good idea to check Matter Modeling Exchange for questions like this. This question/answer discusses how you can transform cartesian basis functions to spherical functions and mentions some useful references.

Do you want to answer or should I delete the question? @HansWurst

@Frank I have no intention to write more on the matter. But I would recommend to leave it open as is. Deleting questions is generally not a good idea. Even in its current form it can be helpful to other people and in the future someone else or even you yourself could write a proper answer.


text:
Why is there internal energy change in a bomb calorimeter?
In a bomb calorimeter, the reaction occurs at a constant volume, hence we say that the heat absorbed by the water in the surroundings is equal to the change in internal energy for the reaction. But,  problems in textbooks involve the reaction inside the calorimeter to be occuring at constant temperature, but for an ideal gas, internal energy depends only on temperature, so if temperature remains constant, what actually causes the internal energy change?

Try to pay more attention to the question formulation. While the topic may be confusing to you, the question itself, including your own prior analysis, should be clear.

The total differential for the inner energy is:
$$ \mathrm{d} U = T \mathrm{d} S - p \mathrm{d} V + \mu \mathrm{d} n$$
In a chemical reaction, the chemical amount $n$ for each species changes (and the chemical potential is not the same for each species). So you expect a change in inner energy (even ignoring the $T \mathrm{d} S$ term, which is discussed further here).
Another way of saying this is that you break bonds and make bonds (and they don't have the same strength, and you might have more or fewer bonds after the reaction), turning one ideal gas into another, and that changes the inner energy.
Take the simplest example:
$$\ce{2H(g) -> H2(g)}$$
The number of particles changes, you have bonds in the product and none in the reactants - surely the inner energy is allowed to change.

If I for example consider the combustion of 1mol liquid oxalic acid to give carbon dioxide gas and liquid water at 27°C in a bomb calorimeter, if I subtract the values of the absolute value of the internal energy of the products from reactants, by using the formula U=f/2nRT for finding absolute value of internal energy, I find that the internal energy change for the reaction is +ve, but it is exothermic reaction so, Q is-ve, how is this consistent with the 1st law of thermodynamics?

That formula just describes the translational energy of the gas. This is correct for mono-atomic ideal gases. Here, all your reactants and products have bonds, and most of them are not even in the gas state, so you are missing a lot of "types of energies" in your formula.

@Kartsen , ok I understood that, can you also tell why when finding the enthalpy change for a reaction occuring in a bomb calorimeter at constant temperature, in the formula delta H=deltaU+deltaPV,  in place of delta PV we use delta n(g)RT, where delta n(g) denotes difference in number of moles of gases after and before the reaction, this formula is only for ideal gases, but as in the reaction of oxalic acid is stated above, some of the products are liquid, but an ideal gas can never liquify, but still how we use the ideal gas formula for enthalpy calculations?

The melting point of anhydrous oxalic acid is about 190 deg C.

@Kartsen , is the formula U=f/2nRT not valid for diatomic or triatomic gases? I thought it was valid for all ideal gases, only the values of f will change accordingly as the gas is diatonic, monoatomic or triatomic

@AdityaMukherjee Please ask a new question about this. It will invite others to reply as well, and will encourage you to do a bit of your own research and to explain the quantities in the formula, and allow you to format it properly.

Ok, I have posted a new question, could you please also reply to the previous question I asked.


text:
Number of particles at a distance of √11 (a/2) from a single particle in a body centered cubic lattice
Take a particle on BCC lattice and from that we have to find number of particles at a distance of $\displaystyle \sqrt{11} \cdot \frac{a}{2}$ (where a is side length of cube). For this, the answer that I saw somewhere gave 24 particles. However, I am not getting as many as that. Could someone please explain how 24 is coming?

$$11 = 3^2 + 1^2 + 1^2$$

(3,1,1), (3,1,-1), (3,-1,1), (3,-1,-1), (-3,1,1), (-3,1,-1), (-3,-1,1), (-3,-1,-1) is 8, and permuting the 3 from the x to the y and z axes is 3, and 8x3 = 24. Not unreasonable.

Is there a practical application?

@Karsten But, wouldn't some of them get repeated?

@Karsten I don't think there is, but it came up in a discussion, so I was curious.

@Karsten However, could you explain what you did there, since the coordinates you mentioned correspond to distance root(11) not root(11)/2, or perhaps I am missing something?

To get to a distance of $\displaystyle \sqrt{11} \cdot \frac{a}{2}$, you have to go half a step in one direction, half a step in another direction, and one and a half steps in a third. In the scheme below, I am using a/2 as the yard stick to have to write less:
(3,1,1), (3,1,-1), (3,-1,1), (3,-1,-1), (-3,1,1), (-3,1,-1), (-3,-1,1), (-3,-1,-1)
(1,3,1), (1,3,-1), (-1,3,1), (-1,3,-1), (1,-3,1), (1,-3,-1), (-1,-3,1), (-1,-3,-1)
(1,1,3), (1,-1,3), (-1,1,3), (-1,-1,3), (1,1,-3), (1,-1,-3), (-1,1,-3), (-1,-1,-3)
You can check that each of these is unique. With a little bit of fiddling, you can also check that you end up on a lattice point (there is a 1/2, 1/2, 1/2 translation, and you can add unit cell translations on top of that).


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Electron energy shells/ levels
Essentially, I am told electron shell closest to the nucleus is the lowest energy level and subsequent shells have higher energy (I.e. those further from the nucleus).
But..... electrons in the furthest shell require the least amount of energy to remove them, so why is this not the lowest energy level?
I think I may be conflating different concepts,  but want to understand the fundamentals so that I can build on that.
Any advice gratefully received.

Think of the energy levels like steps going down into a hole in the ground. If an object is on a step way down in the hole, it takes more energy to lift it out than if the object was on a step much higher up, near the rim of the hole.

As an electron moves from a higher, further from the nucleus, energy level to a level closer to the nucleus it releases energy as a photon. The electron is now of lower energy. The electron is in effect the orbital it occupies so the orbital is of low energy by association. The lowest energy orbital is the 1s orbital [except in the case of K-capture]. Spontaneity involves loss of energy and increase of entropy so the only way to remove an electron is by a surfeit of energy: high temperature [flame], an appropriate photon flux [uv or xray], or high impulse mechanical action [steel on flint, thunderheads, high energy electrons in a scanning electron microscope]. Read about atomic emission and atomic absorption spectrometry to get a better feel for both the absorption and emission of energy.


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Why don't I get a whole number when determining the vibrational energy level of F2?
This is a cross post from physics stackexchange. I hope to get more answers here, because I think chemists have more to do with such things.
So I was playing around with some data and formulas and wanted to calculate the index for the wave number of the vibration of F2 that I got from here, i.e. which allowed energy level n this corresponds to.

Permitted energy levels are given by:
$$\epsilon_n = h\nu\left(n+\frac{1}{2}\right),\quad n = 1,2,3,\ldots \tag{1}$$
The given wave number ($\pu{893.9 cm^-1}$) can be used to calculate $\epsilon$ with $\pu{1.986E-26 kJ cm}$ (however, now that I think about it a second time, I'm not so sure whether I can determine the energy of something like the wavenumber for vibrations of molecules such as electromagnetic waves via $h$ and $c$ so easily, which leads me to the question of how one is supposed to find out at what temperature/energy this wavenumber was determined using the above Web site?):
$$\epsilon_n = \pu{1.775E-20 J}$$
Now I just have to convert (1) to $n$ and insert the values:
$$n = \frac{\pu{1.775E-20 J}} {h \cdot c \cdot \pu{89390 m^-1} } - \frac{1}{2} = 0.499.$$
What am I doing wrong?
Edit: In the end, I can't do much with the value $\pu{893.9 cm-1}$ for F2 without knowing to which energy this frequency belongs. After all, I can generally only calculate an energy for electromagnetic waves via Plank's constant and $c$ with the help of the frequency, but here we are dealing with molecular oscillation; and as long as I don't know at which energy this frequency was measured, this tells me nothing about the nature of F2 (?)
I'm questioning how molecular vibrations can even be expressed in wave numbers $\pu{cm^-1}$, a unit that seems more fitting for spatial measurements. I'm aware that electromagnetic waves have wave numbers tied to spatial propagation due to the relationship $\lambda v = c$. However, I'm struggling to comprehend how a molecule's vibration relates to this. Unlike electromagnetic waves that propagate spatially, how can molecular vibrations be associated with this unit which normally represents energy? Is ν in (1) even the frequency associated with the molecular vibration or the frequency associated with the photon which is measured in IR Spectroscopy?

I think units conversions is hurting this problem really badly. Make sure at each step, dimensional analysis is done correctly.

Why do you have units of kJ.cm?

@AChem didn't done the whole calc (I was in a hurry) but used "1.196266 x 10-2 kJ mol-1 cm" from https://cccbdb.nist.gov/wavenumberx.asp and divided by N_a to get kJ * cm

Recheck unit conversions. This is not right (kJ cm).

But generally my focus shifted even more to the Edit part at the end.

@AChem I don't see a mistake to be honest

Wavenumbers when converted to energy do not have kJ.cm as a unit. Use a paper and pencil and try again. Search how to convert wavenumbers to Joules.

@AChem I know, wavenumbers converted to energy well... have J. It's E = hc(wavenumber). My number was simply h*v. You need to read my question till the end.

@AChem as I stated, with 1.986E-26 kJ * cm I calculated $\epsilon$ with the given wavenumber: 1.986E-26 kJ * cm * 893.9 cm^-1 = 1.775E-20 J.

To answer the first part spectroscopy doesn't measure energy levels, it measures the difference between energy levels, what does this imply? To answer the edit wavenumber isn't an energy, it is a unit that can be related to energy by some fundamental constants, and this scaling  is so common people don't bo5 to mention it, leaving it implied. There's a duplicate to this somewhere here.

Please note that cross-posting is frowned upon in SE.

@Leonard Note chemistry.se allows for the body of questions, answers and comments to use mhchem. Because it is not processed equally well by the web browsers, do not use it in the headers of questions.  Special to your post: Though primarily set up to assist for chemical formulae, commands around \pu{} offer here an easier input of values (note the E vs e for exponential notation) with units which renders them upright and with an non-breakable space to the numeric value.

I’m voting to close this question because it is generating responses on the Physics site as well.

Firstly the link you have provided unfortunately has already rotted. I suspect it was a link to a database query which disappear very rapidly. In future can you please provide a link to the original data, not a database query? This would preferably be as a doi of the original paper - e.g. if I were referencing one of my own efforts I would give https://doi.org/10.1016/j.cpc.2006.05.001 . I suspect what you want here is https://doi.org/10.1063/1.2436891
So I am guessing that the number given refers to the lowest observed energy transition in the vibrational spectrum. Note the word transition - it is the difference between two states, not the energy of any one given state. In the harmonic oscillator model assuming an allowed transition of $\Delta n=\pm1$ this is particularly easy, all transitions have an energy given by $E=h\nu$ where h is Planck's constant, and $\nu$ is the observed frequency - which is trivially derived from your equation (1). Thus from the data presented you can't actually get the number you want - and as an aside I wonder if in fact what you want really makes any sense? It is only Energy differences that mean anything, all energies are quoted relative to some zero. And where have you defined your zero in your question? Only once you have defined that can you talk about the Energy of a given level.
[Will come back later and edit this to link to/talk about wavenumbers and why they are used. But there is a duplicate somewhere ...]
Finally note this is a question about spectroscopy, not thermodynamics. Thermodynamic quantities may be derived from the vibrational frequency combined with other things, but that's the next stage, not this one.

You are using the energy equation for a harmonic oscillator, the  $893.9$ is most probably the $n=1\to n=2$ transition but this is a difference in energy (as already pointed out by by Ian Bush) and is $\epsilon_{n+1}-\epsilon_n= hv$ so $n$ disappears as all transitions are of the same frequency in the HO. So you cannot get at $n$ so you will need another model, say Morse Potential and more transition energies.


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Why does copper(II) sulfate or iron(III) nitrate work as a catalyst for the iodate variant of the Iodine Clock?
In the iodine clock reaction (iodate variation), the reaction of iodate and bisulfite ions apparently is the rate-determining step. I was wondering if $\ce{Cu^2+}$ and $\ce{Fe^3+}$ will act as homogeneous catalysts in the following rate-determining step (or so wikipedia claims): $\ce{IO^-_3  + 3 HSO^-_3 -> I− + 3HSO^-_4}$.
The steps in the iodate variant:
$\ce{IO^-_3 + 3 HSO^-_3 -> I− + 3HSO^-_4}$
$\ce{IO^-_3 + 5 I− + 6 H+ -> 3 I2 + 3 H2O}$
$\ce{I2 + HSO^-_3 + H2O → 2 I− + HSO^-_4 + 2 H+}$
$\ce{iodine + iodide + starch -> blue/black complex}$
In control experiments, in absence of a catalyst added, the reaction took $\pu{20 s}$ to finish.  However, in presence of copper it took $\pu{10 s}$, and if iron was added it took like $\pu{6 s}$. So there must be something happening between the metal catalyst and the rate-determining step, but I just simply cant find out why. This means that the catalysts must be reacting with the reagents in the rate-determining step.
The famous reaction of $\ce{2I− + S2O^2-_8 -> I2 + 2 SO^2-_4}$, where $\ce{Fe^3+}$ and $\ce{Fe^2+}$ can catalyze that reaction. Therefore something similar must be happening in the iodate variant too right?
However, from the countless research I've done, both $\ce{Cu^2+}$ and $\ce{Fe^3+}$ doesn't react with both of the reactants in the rate-determining step. But both $\ce{Cu^2+}$ and $\ce{Fe^3+}$ will react with $\ce{I-}$, which is not in the rate-determining step.
Perhaps I'm not looking hard enough :( , but maybe there are experts in here that may help? help would be significantly appreciated!

For future reference: chemistry.se permits to use mhchem to edit chemical equations in bodies of questions, answers, and comments.  Because it is a specialty not all browsers process equally well, don't use in the headers of questions, though.  Here: especially the rendering of more complex ions as e.g., $\ce{S2O^{2-}_8}$ becomes easier to read.

Generally, oxidation of one anion by another anion may be slow due coulombic repulsion. And it is generally catalyzed by cations of transition metals with more oxidations states, with reduction potential nearby the ones of both major redox systems. The notorious case is oxidation of oxalic acid by permanganate, autocatalyzed by Mn(II) ions.

Thank you you @Poutnik I am aware of this, but HOW does Cu2+ and Fe3+ work in this case?

@Buttonwood Im so sorry but I do not understand you mean here :(

Fe(III)/Cu(II) oxidizes I- and IO3- oxidizes Fe(II)/Cu(I). Also at least Fe(III) would oxidize S(IV), it has higher redox potential than iodine/iodide.

@Metron In the web browser I currently use (Firefox), the rendering of e.g. sulfate, hydrogensulfite/bisulfit, or peroxodisulfate did not process well the charges. Have a look at the revision history for version 2, option «side-by-side» (rendering).  With characters already small (because by their design already prepares them to be a super- or subscript (see option «side-by-side markdown», same page and version, there still were some issues (e.g., negative charge on hydrogensulfite/bisulfite), too.

@Poutnik But the iodide and iodate is in the 2nd step, which is not the rate-determining step according to wikipedia. So are you saying that instead of the catalysts reacting with the rate-determining step(Step 1), it is for some reason reacting with Step 2?

The 1st, rate determining slow step is about I- generation from IO3-.  This is bypassed by metal catalytic system.

@Poutnik but didnt you mention: "Fe(III)/Cu(II) oxidizes I- and IO3- oxidizes Fe(II)/Cu(I)." Only IO3- is in Step 1(rate-determining step). I- is the product of Step 1, and catalysts do not react with products to my knowledge

Catalysts accelerate both forward and backward reactions. If the Haber-Bosch catalyst accelerates 3 H2 + N2 -> 2 NH3, it accelerates  2 NH3 -> 3 H2 + N2 too. Catalyst do not shift the equilibrium, they just accelerate reaching the equilibrium.  // Fe(III) oxidizes hydrogensulphite, Fe(II) reduces iodate.

@Poutnik That is very interesting indeed, does "Catalysts accelerate both forward and backward reactions" this only happen in reversible reactions like the do you mentioned? If so, Is there any souces that elaborate on your point further? I would love to look more into it.
Another question: So what will "Fe(III) oxidizes hydrogensulphite(aka bisulfite)" form? I cant seem to find the half reaction of HSO3- losing electrons in the Standard Cell Potential chart. If I were to guess then it must be HSO4-? but then again how does gaining 1 electron lead to a completely new chemical formula?


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Commutating operators of angular momenta
I've studied the formal procedure to pass from the uncoupled basis set of individual angular momenta to the coupled basis set of total angular momenta for polyelectronic atoms.
I start from an electronic configuration, write down all the possible combinations of quantum numbers, each row is a Slater determinant, and then evaluate the range of total L exploiting the commutation between total Lz and the individual ones. I can apply ladder operators to find the "correct" linear combinations of Slater determinant (rows) which determine eigenfuntions of the CSCO of the coupled set. Pretty clear so far.
Nevertheless i have read that Hamiltonian doesn't commute with the modulus of individual momenta. But this procedure mixes microstates with the same individual quantum numbers l (same configuration). Is this the reason why these wavefunctions are not completely exact? However, can we say they're correct zero-th order wave function and why?
Can I improve them by mixing with combinations constructed in the same way and with the same type of term (same L, same S) but from others configurations?
So, is the Hamiltonian matrix diagonal in this momenta CSCO only limiting to a certain configuration and off-diagonal elements appears when extended to more configurations?


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Why is coal and charcoal a good fuel, but not graphite?
Correct me if I'm wrong, but coal(after coking) and charcoal are essentially hard dry lumps of pure carbon.
But of course so is graphite. I understand of course the structure is different lending them different properties, but I'm not really sure why one burns better than the other. Being purer, wouldn't something like powdered graphite burn better than powdered charcoal?

It would "burn better" if you managed to overcome activation energy, which is higher.

https://chemistry.stackexchange.com/questions/84380/does-graphite-burn

https://chemistry.stackexchange.com/questions/67228/can-diamond-undergo-a-self-sustaining-combustion-reaction-all-the-way-to-carbon https://chemistry.stackexchange.com/questions/44463/what-temperature-is-required-to-burn-pencil-lead-graphite

It is a financial question. Coal costs nearly nothing. Graphite is a relatively rare stuff. So it is more expensive. You would hesitate to burn it.

Diamonds are bad fuel either, :-P

What this "burn better" and "good fuel" are supposed to mean exactly, though? Is this about why is graphite difficult to burn? Because it does have high autoignition temperature.

Dry wood burns even better than coal. Wood is made of hydrocarbons, which is essentially carbon with unnecessary substituents that summarily amount to water and do not contribute much to burning. How so?

@Ivan I'm sure you meant carbohydrates not hydrocarbons, they should have name them more differently :(

Yeah, sure, thanks for the correction.

The key differences are mostly to do with physical form with some contribution from impurities
Coal is largely carbon but, depending on type, contains a range of impurities. Some anthracites are low in impurities, smokeless coals have been treated to drive off many impurities.
Charcoal is usually made from heating wood in an oxygen depleted atmosphere. It is, like smokeless coal, mostly carbon.
Graphite is mostly mined from mineral deposits and is almost pure carbon.
So why do they all burn differently?
The biggest factor is their physical form. But some coals also burn because they have some impurities that burn more easily than pure carbon. Purer coals  are harder to ignite than "raw" coals, partly because of this.
But the major factor is the physical form of the substance. Charcoal is inherently porous partly because of how it is made. That porosity makes it much easier to ignite than many coals which are usually less porous and more dense. Porosity makes it easier for oxygen to penetrate the bulk solid, making it easier for the burning to happen and speeding the rate of combustion once burning has started. Coals are also often somewhat porous, though less so than charcoal. And the impurities in raw coals often lead to higher porosity when burning starts. Coked and smokeless coals tend to be porous as the coking process also enhances porosity by driving out impurities and leaving voids or because coal powder is treated and reconstituted into not-very-dense lumps with voids between the particles.
Graphite is created geologically when coal is subject to heat and much pressure. This, like the treatments that make smokeless coal, drives out impurities and compacts the result leaving dense, pure carbon (or because graphite crystallises out of a liquid rock as fairly pure graphite). This leaves very few voids in the solid so the only way it can burn is at the surface which limits the speed of combustion. It will still burn but can only do so slowly. By the way, the other major allotrope of pure carbon, diamond, will also burn but is also poor fuel for much the same reason.
If you crushed graphite into a powder and blew it into a furnace, it would be  as fine a fuel as coal or charcoal. As would coal or charcoal if powdered.
So the primary differences are the physical form of the material: porous materials make it easier for oxygen to get "inside" the material to propagate the burning reaction.

See also wikipedia - History_of_synthetic_graphite // I assume burning graphite is kind of raw heresy.


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What is the meaning and unit of the integral in the local density approximation (LDA)?
According to Parr and Weitao (1995), the Dirac exchange-energy formula (1930) comes from

[I am looking only at the last line of the equation and the rest for completeness]
It's an energy, so I'd expect the whole expression $K_D$ to be in untis of energy. Evaluating the dimensionality of the integral, I get $(L^{-3})^{4/3} L^3 = L^{-1}$. From this, I expect $C_x$ to be in $L$ (or even $E L$, where $E$ is a composite for energy?), so length units, which doesn't feel true and I think I also read a few times, it's dimensionless. But if it were dimensionless, $K_D$ would be in $L^{-1}$ which is strange (and false?).
Furthermore, I am curious for the interpretation of a density to the power of 4/3. It sounds very strange. But on the other hand, in thermodynamics for instance, we have exponents of 3/2 all the time, which start to make sense after some stat mech, so I'm sure 4/3 can be squared with some intuition.
TL;DR:

What is the unit of the integral $\int \rho^{4/3} d\mathbf{r}$ and of $C_x$?
What is the interpretation of the exponent 4/3?

Please explain what  $k_F$ is, have you included $dr$ in your dimensions ?

The derivation starts in Parr&Weitao p 105 but I only look at the last line. The derivation is imo correct and understandable. For completeness: The Fermi wavevector is $k_F = (3π^2\rho(\mathbf{r}))^{1/3}$ and $t=k_F s$. The integral in the second line evaluates to 1/4. And yes, I have included $d\mathbf{r}$, it's the last factor $L^{3}$ in the dimensionality analysis of the integral.


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Magnetic surface removal
I have a DIY project made from used hard disk. Certain HDD models contain precision glass disks plated with magnetic surface, usually done with magnetron sputtering. I am searching for a substance I can use to etch that magnetic surface to reach glass. Would be nice to have solution for etching with photoresist solution or complete removal. Wikipedia says magnetic surface consists of several layers, mostly metallic and non-magnetic, but I have no clue what metals are used and I guess its patented. Is there any guess of chemical process which I can try?

Modern hard drives use layered materials to take advantage of magnetostrictive effects. If there is an Fe layer, the standard etchant Nital may do the trick, but the layering could cause issues.


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What does the 2 in t2g stand for?
I have read so far that it is about whether the d-Orbital is symmetric to a C2 element perpendicular to its main rotational axis. If all the given orbitals in a group are symmetric to that element, you assign a 1 towards it, otherwise a 2. Anyway, I still don't get a few things:
First: Is it enough for one orbital of a given group to be not symmetric concerning that C2 element, for the whole group being asymmetric towards C2?
Second: I cannot get my head around e1 and e2 in the crystal field splitting of linear complexes. Do I have to keep the C2 axis the same to check whether it is e1 or e2? Because if I change the axis I get e1 twice, if I don't change it, I get e2 twice. My textbook says it is e1 for d(xz)/d(yz) and e2 for d(x2-y2)/d(xy)...

Labels such as $T_{2g}$ means that the irreducible representation, irreps, (the row of characters as in the point group in the answer by Buttonwood) is triply degenerate, hence the $T$. Singly degenerate irreps are labelled $A$ or $B$ and doubly degenerate $E$ (not the be confused with the identity). The subscript $g$ means gerade i.e. of even symmetry wrt to inversion at the centre of symmetry and $u$ (ungerade) means odd symmetry here. Not all point groups have irreps with this $u,g$ label, e.g. $C_{2v}$.
In singly degenerate irreps only the Mulliken label is
(a) $A$ if it is symmetric about rotation about the highest order axis, but if it is antisymmetric then the label is $B$.
(b) A subscript $1$ is given if the irrep is symmetric about a $C_2$ axis perpendicular to the principal axis or if no such axis exists to reflection in a $\sigma_v$ plane. If antisymmetric then the subscript is $2$.
(c) The superscripts are $'$ or $"$ for symmetric and antisymmetric wrt reflection in $\sigma_h$ plane.
However, the subscripts $1$ or $2$ are not straightforward to generate for $E,T$ groups and it is best just to consider them as labels and to work other things out, look at the symmetry operations and the value in the irrep in that particular column; the irreps do contain all the information.

The denomination $t_{2g}$ in the ligand/crystal field theory of transition metals consists of one part which describes the field.  It can be tetrahedral ($t$), or cubic ($c$), octahedral ($o$), square/quadratic ($q$).  Second, the subsequent subscript relates to group theory and character tables. Here, entries may be considered either as gerade (German for even, hence subscript $g$), or ungerade (German for odd, hence subscript $u$).  The integer is both a label of book keeping and to "denote symmetry and antisymmetry".  See, for example, the character table for point group $O_h$ in Wikipedia's compilation:

Thanks! Which symmetry element did you refer to when you said "denote symmetry and antisymmetry"?

To quote the introduction of Wikipedia's List of character tables for chemically important 3D point groups: «...g and u subscripts denote symmetry and antisymmetry, respectively, with respect to a center of inversion. Subscripts "1" and "2" denote symmetry and antisymmetry, respectively, with respect to a nonprincipal rotation axis. Higher numbers denote additional representations with such asymmetry. ...»


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Free alternatives to ChemDraw
My school doesn't offer me a ChemDraw license and I need to be able to draw quite complex chemical structures (e.g. porphyrins). This is why I am interested in some good free alternatives to ChemDraw. So far I have only been able to find programs that are a pain to use and it is very hard for me to draw anything more complex.


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Is the "heat or UV" necessary for PVC10 + Cl => CPVC10 catalytic or endothermic and if endothermic how much energy?
Production of Chlorinated PolyVinyl Chloride (CPVC) from PVC and chlorine requires incorporating about one part chlorine in 10 PCV to achieve around 63% chlorine mass CPVC.  This reaction is "initiated" (according to the Plastic Pipe Institute) with UV and, according to Wikipedia "thermal or UV".  However, I have not located a source that says whether this energy is catalytic or endothermic and if endothermic, how much energy is required.

It is catalytic, as you only need to break the first chlorine-chlorine bond and then, the entire reaction is a chain reaction.


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Group theory and exact Eigenfunctions of Hamiltonian
I think I've understand why the real Eigenfunctions of Hamiltonian belong to a given irreducible representation and I've read that also MOs have to transform as irreducible representation due to the commutation properties of the individual hamiltonian and the point group operators.
My question is how the fact that real solutions have this symmetry is exploited in practice (no need complex discussions, only intuitive ones).
And mainly if and how the fact that we try to construct correct symmetry MOs is exploited in methods like CI.

Related: https://chemistry.stackexchange.com/questions/82656/what-constraints-are-imposed-on-a-wavefunction-by-the-symmetry-of-the-system/82660#82660


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How does MeOH absorb into polypropylene?
Currently working on a project where we want to functionalize PP membranes with various monomers.  Our chemistries are aqueous and have therefore not been compatible with the membranes.  The work-around we've been using is to utilize methanol to "wet-out" the PP.
I'm curious as to why this works. There isn't too much of a difference between water and methanol. Both are low molecular weight, both are polar and protic, both are capable of hydrogen bonding. What explanation is there for methanol readily absorbing into the membranes when water cannot?

MeOH has both hydro- and lipophilic part. Hydroxyls can bind together, leaving Me to interact with polymer.

MeOH also has about 1/3 the surface tension of water: https://en.wikipedia.org/wiki/Surface-tension_values, and about half the viscosity, too.

@DrMoishePippik The values tabulated there are about the compounds' surface against air.  Contrasting to e.g., density of a material, the values of surface tension depend on interaction of two two materials.

@Buttonwood, true for surface tension. One could measure the contact angle of MeOH and H2O drops on pp, to get valid values, but as Mithoron states, the Me part is likely to be much more atracted to PP.


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Using a sulfate test to determine % sulfuric acid
I work as an amino acid lab technician in a production facility, and we've been tasked with figuring out how to determine the amount of sulfuric acid remaining in a solution made in our plant.  Ideally, the amount would be zero, or almost zero.  We already have a sulfate test we use for a fertilizer product we produce, and someone suggested using that test.  It's a Hach spectrophotometer test kit.
My question is, if we use that test kit to determine total sulfates in the sample, is there a conversion factor to determine sulfuric acid, or is it more of a 1:1 result?  I realize total sulfates won't necessarily all be from sulfuric acid.  Without divulging too much info, the solution is a reaction with soybean meal and sulfuric.  Ideally, the sulfuric is completely used up, but production is wanting to have a test available to confirm this.
I hope I've given enough info.  Thanks in advance for any and all help.
Joe

I would either use pH measurement either titration by NaOH.

I suggested titration with Barium hydroxide also.  If we use a known concentration (50%) of NaOH, what would be the calculation to determine sulfuric acid concentration?  Sorry if this is a dumb question.  I'm really good at analyzing pig feed, and I can understand some chemistry, but it's not my background.  I'm still learning.

Just to be clear, your sample is a supernatant solution with residual sulfate/sulfuric acid after the product has been isolated?

You give NO info. If the acid reacts acid-base the amount of sulfate remains constant analysis of SO4= is not useful, a pH should work. A reaction such as H3PO4 from calcium phosphate uses sulfate, a sulfate test will work. Specific info is needed to recommend a test.

The question is, if there is really the need to determine sulfuric acid content, or if there is enough to determine the remaining acidity, expressed in the equivalent amount of sulfuric acid. As if a major part of the acid is already neutralized, sulfate content is irrelevant to the acid content.

In a solution that contains various sources of hydrogen ions, it will be impossible to calculate the amount of free sulfuric acid by any means. You have a natural product broth (perhaps soya sauce?), so that is even more complicated because sulfate can also come naturally from food products. Remember that all classical analytical chemistry (titration or gravimetry) is very accurate and precise but only when the sample consists of one or two components.
The only accurate solution is to determine free sulfate by ion chromatography on an anion exchange column or quite crudely by a spectrophotometry. This will require extensive sample clean up. One can only quote total sulfate but not free sulfuric acid. It will be hard to make a correlation.


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Reduction of direct product representation
When we do the reduction of the reducible representation generated from the total wavefunction expressed as product of MOs of appropriate symmetry, we can find the direct sum of more than one irreducible representation.
How to distinguish them? Can we find the way to espress functions of the basis set which generate irreducible representations from the original product of MOs?

Projection operators can be used to extract irreducible representations.

@HansWurst so if a have, for example, a Slater determinant of spin-MOs have I only to apply the projection operator? But how to apply it to a product of functions?

Operators acting on this product are obtained forming the tensor product of the single particle operators.

@HansWurst and the use of these operators has some practical applications? Maybe to decrease the computational cost of some computation?

@HansWurst last curiosity: with this projection operator can I, for example, combine Salter determinant which describe atomic terms to find correct function for the specific crystal field? And from a correlation diagram between the limits of infinity crystal field and infinity repulsion can I obtain informations on which of these determinants will be combined?


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Does dilution of titrant gives a more accurate result?
When I see demonstrations of titration of acid solutions of unknown concentration with phenolphthalein as the indicator, when the last drop of NaOH went in the analyte solution became permanently pink. This means that more than enough NaOH was used and the recorded endpoint has some error (by 1 drop?). If we use a diluted titrant, the error is still 1 drop but it is diluted so could the margin of error be lower?

The use of a burette in titration, once considered an art, has nearly disappeared from modern educational practice in schools and universities. This decline is due in part to the lack of expertise in classical analytical techniques among current teaching assistants. In precise titration, even an extra drop of titrant can significantly skew results i.e., an extra drop is too much! Experienced chemists could accurately dispense fractional volumes of liquid (e.g., 0.05 mL) with practice and would rinse the burette tip upon observing a slight pink tinge during acid-base titrations.
If you are really keen, then search Vogel's textbook of Quantitative Analysis. It is available on Internet Archive (free for reading). Search the sections on burette usage.

Is not a "standard drop" rather 0.03 mL? Using hydrophobic PE burette tips can lead to even smaller drops.

I have not seen any documentation from standard sources about the volumes of the so-called standard drop because who is going to standardize a drop :-) Even 0.05 mL was a guess. Do you recall a good quality reference for 0.03 mL?

I have used it quoted. I am not sure if it is any standard nor official value, but seeing the value 0.03 mL over the years many many dozen times. Few time also 0.02 mL. All probably from weighting the drops.

@Poutnik Now you have done it: the various standards organizations will form committees to study and propose standards for the standard drop, then the disparate proposals will be studied by harmonization committees. After 20 years or so, we will have a standard drop definition, complete with turgid footnotes and provisos. Of course, no one will follow it. ;-)

@EdV you understand the system too well :-)

Each burette has its own "standard drop".  :-) :-P


text:
Study of superconductivity from organic compounds
What advancements have been made in understanding and applying organic superconductor materials?
Although traditionally superconductivity has been studied in inorganic materials, are there any organic compounds showing superconducting properties?
As far as I know, superconductivity is a state where materials conduct electricity without resistance, observed in inorganic materials at extremely low temperatures.

There's a very nice Wikipedia page you can start from.

There certainly are organic superconductors, but they are not very practical in use. Even things like cuprates, are still pretty early in introduction to practical usage.

As you can find on the Wikipedia, many organic materials were found to show superconducting properties. These organic superconductors are intriguing because they offer the possibility of understanding superconductivity in a different structural and electronic context compared to inorganic superconductors. They might also lead to the discovery of materials that become superconducting at higher, more practical temperatures. Additionally, the flexibility and tunability of organic chemistry mean we can design and modify these compounds more easily, potentially optimizing their superconducting properties.