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Fischer's proof of the structure of glucose
To differentiate between Mannose and Glucose , Fischer developed a series of reactions to make the aldehyde group to alcohol and terminal alcohol to aldehyde. What was this series of reactions ? Even link would be fine because I m not able to find it anywhere!!

Have you seen http://ursula.chem.yale.edu/~chem220/STUDYAIDS/history/Fischer/fischer.html ?

It mentions through a number of chemical transformations he was able to switch the head and tail(C1 andC6) of glucose. I want to know is what r these transformations

One does not have to return to Fischer's papers of 1891. C. S. Hudson (vide infra) provided a semicentennial retrospective of Fischer's work in 1941. That glucaric acid could be produced from a different hexose, gulose, while mannaric acid, owing to symmetry, could only be formed from mannose, established the relative stereochemistry of glucose. The proof requires the formation of lactones and their reduction with sodium amalgam to hemiacetals along with over reduction. It is not necessary that the reactions be efficient, only that they provide some amount of isolable product.
D-glucuronic acid 2 is isolated from urine. It is of the same absolute stereochemistry as D-glucose except that C6 is at the oxidation level of a carboxylic acid. [Note: Throughout, C1 is in red and C6 in blue.]  Thierfelder (1891, loc. cit.) formed D-glucuronic acid lactone 3 from D-glucuronic acid 2. Reduction of 3 converts the aldehydic group to a primary alcohol, L-gulonic acid lactone 4, which in turn undergoes further reduction to the hemiacetal of L-gulose 5. As noted earlier, there certainly may have been overreduction to D-glucitol (L-gulitol). continued

Fischer was able to demonstrate that lactonization of D-glucaric acid 6 provided lactone 9. Whether or not alternative lactone 7 was produced is irrelevant because subsequent operations would only lead to D-glucose, providing no useful information.2 On the other hand, lactone 9 was converted to L-gulose 5 via the lactonization/reduction sequence. Notice that the original C1 red atoms now occupy the C6 position and the original blue C6 atoms are now at C1. Critically, the oxidation product  of L-gulonic acid 10 proved to be identical to D-glucaric acid 6! Thus, the relative stereochemistry of glucose was secured.

Emil Fischer's Discovery of the Configuration of Glucose. A Semicentennial Retrospect, C. S. Hudson, J. Chem. Educ. 1941, 18(8), 353-356; https://doi.org/10.1021/ed018p353
Isolation of the 1,4- and the 6,3-Lactones of D-Glucaric Acid, R. J. Bose, T. L. Hullar, B. A. Lewis and F. Smith, J. Org. Chem. 1961, 26(4), 1300-1301; https://pubs.acs.org/doi/10.1021/jo01063a610


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Iodine formation reaction
$$\ce{IO3-(aq) + 5I-(aq) + 6H+(aq) -> 3I2(aq) + 3H2O(l)}$$
Why does the reaction between iodide and iodate ions have to occur in an acidic medium ($\ce{H+}$) to form the iodine? what do the $\ce{H+}$ ions react with?

Well, you may check for yourself that the reaction contains H+ and is balanced. Consequently, without H+ it won't be balanced. Sounds like enough of a reason to me.

A bit more complex per a source 'Kinetics and mechanism of the iodate-iodide reaction and other related reactions', to quote from an article in the journal Physical Chemistry Chemical Physics (November 1999):

The reduction of iodate by iodide, known as the Dushman reaction, is one of the components of the oscillating Bray-Liebhafsky reaction. The large body of work devoted to the kinetics of the Dushman reaction gives seemingly contradictory results. This work analyses and summarizes them and shows that they are special cases of a complicated kinetics and that they can be explained by a common mechanism. This mechanism can be generalized to all the XO3- + Y- reactions (X, Y = I, Br or Cl). They all involve an asymmetric intermediate YXO2.

See reaction system depicted in Equations (8) to (13). Here is a partial discussion of the system from the available PDF to quote:

The essential hypothesis of this mechanism is the existence of as a definite intermediate species and not as I2O2 an activated complex. Its existence was already proposed in  1930 by Bray [17] in order to explain the classical rate law. We make no distinction between I2O2 and H2I2O3 (I2O2 + H2O) as these two forms are kinetically equivalent. In reaction (12), B~ represents the anion of the buffer....

As to the question on the role of H+, note that the starting Equations (8) and (9) of the system both involve H+, which results in the cited intermediate $\ce{I2O2}$:

$\ce{IO3- + H+ ⇌ IO3H}$  (8)
$\ce{IO3H + I- + H+ ⇌ I2O2 + H2O}$  (9)

Fabian has proposed that the reaction between the ions iodate $\ce{IO_3^-}$ and iodide $\ce{I^-}$ do not react, because the reaction will produce the ion $\ce{O^{2-}}$ which would not exist in water. This is not a good reason, because in water, $\ce{O^{2-}}$ is immediately transformed into $\ce{OH^-}$.  Of course, Fabian recognized this possibility. But he does not explain why $\ce{H^+}$ ions are necessary in this reaction.
The answer is much simpler. The ions iodate $\ce{IO_3^-}$ and iodide $\ce{I^-}$ do not react without $\ce{H^+}$ because they are both negatively charged, and they repel each other in water. In the presence of $\ce{H^+}$, one may admit that the iodate $\ce{IO_3^-}$ and iodide $\ce{I^-}$ produce temporarily $\ce{HIO_3}$ and $\ce{HI}$ which are neutral and do not repel one another.
Another reason is that $\ce{I_2}$ is not stable in basic solution. It reacts with $\ce{OH^-}$ to produce the inverse of the preceding reaction, i.e.:$$\ce{3I_2}  +  \ce{6 OH^-} \rightarrow  \ce{IO_3^-} + \ce{5 I^-} + \ce{3 H_2O}$$

Omitting the hydrogen ions would lead to
$$\ce{IO3-(aq) + 5I-(aq) -> 3I2(aq) + 3O^2-}$$
but $\ce{O^2-}$ would not exist in water. So an alternative could be to write
$$\ce{IO3-(aq) + 5I-(aq) + 3H2O -> 3I2(aq) + 6OH-(aq)}$$
Basically, the hydrogen ions are there to indicate that the reaction takes place in an acidic solution and hint that access hydrogen ions would improve the reaction kinetics.
The version with the hydroxide ions could be used to emphasize that the reaction would cause an increase of the pH value.

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Why does Potassium Sorbate have two CAS numbers? - Should these not be unique?
Potassium Sorbate has two CAS numbers - 24634-61-5; 590-00-1. Should these not be unique?

Related for FeOOH: https://chemistry.stackexchange.com/questions/40572/why-does-feooh-have-two-cas-numbers?r=SearchResults

If the same goes for Potassium Sorbate as for FeOOH - Then can someone enlighten me towards the nature of the two CAS numbers:

Or rather let me rephrase - which is the  the ‘boring’ laboratory version of the Potassium Salt and which is the unambiguous refencing of the preservative used in foodstuffs?

Please [edit] the question, instead of trying to seek clarification in the comments.

all_licenses: Creative Commons - Attribution Share-Alike - https://creativecommons.org/licenses/by-sa/4.0/


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Is sugar in mead different from "regular sugar"?
My understanding of the process of making mead is that you combine honey, yeast and water in an anaerobic environment. The yeast-bacteria ferments the sugar in the honey and produces ethanol (among other things?). If this is true, how come labels for mead still list e.g. 90g of sugars per litre? If I'm consuming mead, am I really consuming 90g of regular sugars as found in fruit, candy etc or is this some variant of sugar that is chemically different (sugar alcohol?) in a significant way such that traditional advise "eat less sugar" do not apply?

Plenty of alcoholic drinks still contain a great deal of sugar (even beer is often as sweet as sugary Coke). Fermentation often doesn't use up all the starting sugar. What is left is still sugar and will affect your sugar levels whether it is fructose, glucose, sucrose or some other specific sugar.

Honey usually contains mainly naturally occuring glucose + fructose, with ratio typically 100:104-170. Sacharose occurs as well, but in minority.
Fermentation consumes just part of sugars, but that is not limited to mead. It applies to beer,wine, and bases for spirits as well.
E.g. typical "future beer" before fermentation has sugar content  $\pu{100-120 g/L}$.

This suggests that mead, despite being very tasty, is not a great choice of brew for someone wanting to reduce their sugar intake.

Well, it is question of amount. One usually does not drink 1 L of mead.

Maybe I should try the experiment, for science, of course! :-)

It is said mead is the good servant to warm you up, but the bad lord, due heavy hangovers.


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Freely available software for generating 3D coordinates of molecules
As part of some research I am doing, I want to do a head-to-head comparison of software for generating 3D atomic coordinates for molecules. Is there a list anywhere of chemical software that does this?
I was able to settle on the following constraints: freely available, or at least free for academic users; can be run on the command line (either Windows or *nix); and, can handle small to medium-sized molecules (I.e. I am not expecting the software to handle oligopeptides or other sizable biomolecules).
The input could be any of 1. a MOL file without 3D information; or 2. line notation like SMILES or InChI. I was envisioning doing tests for at least those formats, unless I am missing anything.
If there is no such list, would you be able to recommend any software for this task?
I am already using OpenBabel and RDKit to generate coordinates, so I got the idea to look for other software to compare with it.
(Survey papers that have previously done comparisons of this sort would also be welcome and appreciated, so that I can see what hasn't already been covered by previous researchers.)

How "good" do the coordinates have to be? Do you want realistic bond lengths and angles only, or a sensible conformation as well?

The "goodness"/"plausibility" of a structure's coordinates (I am still working on making this criterion more concrete and quantitative) would actually be my way of comparing/ranking various generators. (As I mentioned in my question, I want to do a head-to-head.) Certainly, the more "realistic" the generated structures are, the better a certain program is for at least that molecule.

This Wikipedia list should get you started: Cheminformatics toolkits. As far as I can tell, you have at least the dominant ones. For evaluating these structures, I suggest looking at CREST which is a conformer sampler based on the semiempirical GFN-xTB. I'd be very interested in your results.

@Martin-マーチン - CREST is excellent and we use it, but it's much, much slower than these tools on standard organic molecules.

@Geoff I understand completely, and I agree, but I thought it's a good tool to address the "goodness" of a generated structure with some higher level of theory. Obviously, you can go further than that, too.

Summary: RDKit ETKDG is currently the best open source tool
This is an interesting question, since a reviewer just asked us to do such a benchmark.
The trick is that there's a fine distinction between "generating 3D coordinates" (i.e., one conformation) and "generating 3D coordinates and doing some conformer sampling" presumably with the latter helping to find a low-energy conformer, thermally-accessible ensemble, or a pose that might match an experimental structure or drug docking pose.
I'm not sure there are many papers on the first (i.e., generate one 3D structure - how good is it)? For one, it would depend a lot on your definition of 'good.' I personally prefer 'low energy conformer' because it's easy to define. Most people usually mean 'close to the experimental crystal structure' which is not usually the same as 'lowest energy'.
I digress. There are a few benchmark papers - largely grabbing a few conformers, usually including a mix of free or open source tools and commercial tools.

Ebejer, J.-P.; Morris, G. M.; Deane, C. M. "Freely Available Conformer Generation Methods: How Good Are They?" J Chem Inf Model 2012, 52 (5), 1146–1158.
Friedrich, N.-O.; Meyder, A.; de Bruyn Kops, C.; Sommer, K.; Flachsenberg, F.; Rarey, M.; Kirchmair, J. "High-Quality Dataset of Protein-Bound Ligand Conformations and Its Application to Benchmarking Conformer Ensemble Generators." J Chem Inf Model 2017 57 (3), 529-539.
Nils-Ole Friedrich, Christina de Bruyn Kops, Florian Flachsenberg, Kai Sommer, Matthias Rarey, and Johannes Kirchmair. "Benchmarking Commercial Conformer Ensemble Generators." J Chem Inf Model 2017, 57 (11) , 2719-2728.
Naruki Yoshikawa, Geoffrey R. Hutchison. "Fast, efficient fragment-based coordinate generation for Open Babel" J. Cheminf. 2019 11, art. 49.

While the newest method in Open Babel (development for v3) is faster than RDKit, particularly without using force field minimization, RDKit's ETKDG is very, very good - competitive with most commercial packages.

I hope I understand you correctly.
For small size molecules, you can use the Avogadro program. For large systems (I use it with 40K atoms) molecules I would use VMD. If you want to generate better-looking figures I would use Chimera or PyMol which has a free version. Also, there is a very nice trial version of ChemCraft. If I remember correctly all the above-mentioned programs have both a Windows and a Nix version (at least Ubuntu compatible).
If you want to build or edit your current coordinates then ChemCraft is good though it doesn't handle large system so smoothly (although it should be said that I am visualizing on my laptop which does not have a dedicated GPU).
If you are looking for atomic structure 3D analysis like RMSD, bond angles, distances and etc. I myself use cpptraj in the AmberTools suite.
As Karsten already said, it is not very clear what exactly you are looking for in the software you are looking for.

I am not at a computer right now to verify, but if all of your recommendations are usable on the command line, and can operate in batch mode, these would be quite nice.

VMD can be used from the command so is AmberTools cpptraj (trajectory analysis). I am not sure about Chimera, PyMol, ChemCraft or Avogadro. I used cpptraj to analyze large systems, 1us classical MD of 40K atoms size systems.

None of these tools generate 3D coordinates, they display them only, and you can edit them based on fragments and atoms. Avogadro uses Open Babel as an interface for 'creating' structures.

If it's that 3D coordinates then Avogadro works, and if it's just with text I would use SMILES. Avogadro and VMD can be used to build molecules, so is ChemCraft.


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Are all volatile liquids combustible?
I realized that liquids like petrol, kerosene and even perfumes are combustible when they are volatile.
Could that be the reason why water is not combustible is because it is not volatile?
Are volatile liquids all combustible?

No.$\mathstrut$

Do you mean flammable or combustible? https://en.wikipedia.org/wiki/Combustibility_and_flammability

There's lots of selection bias going on here. Water has a higher boiling than most other commonly available liquids that come to mind, and that is exactly how "volatility" is defined. They also happen to be flammable, because they're usually petroleum products. This thought would never occur to someone working  with a broader range of liquids (say, a chemist).

I've tried to rewrite the question so the idea is clear. If I have not captured the original intent, please correct me.

@matt_black after re-reading the original question I still can't say if your edited version is what Michael intended to ask, but somehow I think he didn't manage to capture his intended question in words. Just as well it was entertaining.

Many volatile liquids are not combustible
Dichloromethane (DCM) is a widely used solvent by chemists. It boils at around 40°C (the same as diethyl ether) but is not remotely combustible or flammable. Ether is both very volatile and very flammable, so much so that most labs would prefer not to have it used anywhere where flames or sparks could be present. HFC-134a is a refrigerant gas at room temperature and used to be preferred to alternatives like propane (also a gas) because it didn't risk creating an explosive atmosphere when it leaked.
Combustibility has almost noting to do with volatility (other than in the trivial sense that things that are hard to vaporise are hard to set alight even if they are inherently flammable–like bitumen). Combustibility is determined by the chemical properties of a substance, usually whether the reaction of the substance with oxygen releases energy easily. Ether is both volatile and very combustible as that reaction releases a lot of energy and is easy to start. DCM can be burned but releases far less energy and the reaction is very hard to start or maintain as the chlorine in the molecule inhibits the combustion reactions.
Other compounds, like water, are certainly volatile enough to combust (how would we get rain if water were not volatile?) but there are no possible reactions that release any energy from reacting water with oxygen.
So two factors matter in combustibility: is there an energy releasing reaction from burning the compound?; is there a reaction mechanism that makes it easy to cause that reaction to happen? Neither are true for water; many other compounds either don't release enough energy from reacting with oxygen or have chemical components that inhibit the reaction.
Volatility has little or nothing to do with either.

"Combustibility has almost noting to do with flammability". Following @poutnik logical reasoning, something flammable is combustible (by definition), but not necessarily the other way around. And (if combustible) something more volatile is bound to be more flammable.

@BuckThorn Well spotted. What I meant was "combustibility has nothing to do with volatility". Now corrected.

Volatility ( even if by thermal decomposition ) is the necessary, but not sufficient condition for liquids to be combusted, forming a flame.
Liquid helium is the most volatile liquid ever, but there is no way to burn it ( chemically ).
As other answers mention, there is correlation, as flammable liquids are generally less polar and more volatile than polar and less flamable molecules of similar mass. But there are many exceptions on both sides.
BTW water is volatile as well, more than the diesel fuel.
I am curious, what would you thought there would be the result of water combustion ?

Not always true. Tetrachloroethylene ("perc", as it is sometimes called in the dry cleaning business) is not inflammable, but quite volatile. Carbon tetrachloride, which was also a common solvent some decades ago, is yet another halocarbon solvent that is volatile, but not inflammable (hence its former use in fire extinguishers). In general, volatility and combustibility are not related, but it is true that an inflammable liquid being volatile makes it more hazardous (cf. "flash point").


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Software that determines whether a molecule can exist and draw it from a formula?
I have run calculations that predict atomic configurations.  As a simple example, in a system that contains H and O, I might get a list like:
Configurations for the O atom
O H
0 2
2 6

This would tell me that in my system, there's one O atom bonded to two H atoms and there's also a molecule made up of three O atoms bonded to each other and six H atoms.  My real systems are more complex.
I am not really a chemist and have no idea whether some of the molecules I have calculated actually exist and what they would look like if they did.  Does anyone know if there's software available that might help me with this; i.e., where I can enter a potential formula and the software draws the molecule and tells me whether it exists?
I have so far checked out ChemDraw Professional and Avogadro and it doesn't look like they do what I need.  Thank you for any tips.

Would it be OK if the software does a database search?

Thank you for your reply, Karsten.  Yes, that would be fine--although it would be great to know if there's any software that can maybe make predictions based on more fundamental phenomena.  I know that databases might not contain all possible structures for a particular system, but any guidance would be helpful.  My calculations are predicting polyatomic Na, Cl, H, and O structures and I have no idea whether they can exist.

They can't, unless they are NaCl, or H2O, or a handful of other known compounds. Then again, maybe you are interested in some transient clusters, in which case the databases won't help either.

I know NaCl, HCl, NaOCl, HClOx, NaOH and H2O exist. I am having troubling finding a structure made of Na, Cl, H, and O in any stoichiometry. I did find a paper with hydroxide ion (OH-) impurities in NaCl crystals: https://journals.jps.jp/doi/abs/10.1143/JPSJ.54.175

Thanks Ivan.  These are transient clusters (I'm looking at aqueous fluid).  I am wondering how on Earth to report them or whether I even should.  I have a list that's quite long of entities that may exist.

Thank you very much for that, Karsten.  I have looked at published papers that mention various structures, but so far have not found a resource that lists all possible structures that real chemists have reason to be confident about.

Why list them? I don't think they even deserve to be called structures. True, many of them would pop up for a split microsecond, but that's hardly a fact of any consequence.

I wrote a reply to your comment, Ivan, but deleted it because it was unclear.  You have raised a very interesting point and I'd love to know if anyone out there has any thoughts or knows of conventions related to it: at what point would it be reasonable to say that a structure/compound is stable?  If I run a simulation and predict that the structure is present for >10% of time steps, for example, would it be reasonable to say the structure is stable then?

I believe this website will be of use to you
http://molview.org/
It appears to take names, formulas, smiles etc. If the name/formula/smile ID pops up in the search bar, it will draw it for you. Its database seems quite large, I use it for some pretty big drug molecules.
It draws 2D and 3D images, and it also does single/double/triple bonds.

Thank you very much, Charlie, this does look very useful and easy to use!  I will explore it!

It may not help a ton for your specific problem, but it is quite useful in general

It's definitely more appropriate for my problem than anything else I have come across so far.  I'll have to wait until tomorrow morning to check it out, so don't know yet how many of the structures I'm seeing appear in its database, but it looks like a great start no matter what.  I'd just like to get some idea of whether my predictions are reasonable!  Thank you very much indeed.


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Why is Thorium (At. no. 90) an f-block element at all?
Being an exception of the Aufbau principle, Thorium has an electronic configuration of $\ce{[Rn]}\mathrm{7s^25f^06d^2}$ instead of the expected $\ce{[Rn]}\mathrm{7s^2 5f^2 6d^0}$.
Two other elements, Lanthanum and Actinium, also showed such an anomaly as $\mathrm{6s^2 4f^0 5d^1}$ and $\mathrm{7s^2 5f^0 6d^1}$, respectively. But we placed them both in the d-block of the periodic table.
Since, even in Thorium, the last electrons occupied d-orbitals only (disobeying Aufbau), then why is it placed in the f-block of the periodic table. I mean, it should be placed in the d-block, shouldn't it?
Edit: Note that here, I don't intend to ask or know how or why the 2 electrons disobeyed the Aufbau, and occupied the higher energy 5d instead of lower energy 4f.
Rather, I want to know only that why it is kept in the f-block when the last orbitals which the electrons occupied were of d-subshell.

I don't think it violates the Aufbau principle, but instead it fails the generalised prediction patterns that have been derived from observation, like $n + \ell$ 'rule'. About the placement in d-/f-block, I don't think there is consensus on that either. There recently have been different news about how the elements should be displayed, even turning the PT upside down https://doi.org/10.1038/s41557-019-0253-6

“…even turning the PT upside down doi.org/10.1038/s41557-019-0253-6”: this would be a decent article for a design journal, but how on Earth did this pave its way to Nature (judging from the name of the first author I think I know the answer, so this is more like a rhetorical question)?

Related (or probably duplicates): Anomalous Electronic Configuration of Thorium; Outermost electronic configuration of f block elements.

As one gets more and more electrons, their interactions really start messing with simplistic expectations (e.g. Aufbau) based on hydrogen-like energy levels. But, really, to what purpose does one call something an 'f-block' vs a 'd-block' element - you look at the actual filled levels and nearby levels and try to figure out the chemistry from there. For crystal solids, Thorium is just at the edge of some really weird crystal structures popping up because of all those electrons (like Pu with the first 3 allotropes being specific to it).

@andselisk I edited my question. The first link you related my question to, is demanding the reason why/how it happened, which I'm not. So not a duplicate or related. The second link, which was also my doubt but I later accepted it as one of the abundant errors of chemistry and thus decided not to include in my doubt, is also neither a duplicate of nor related to my question.

The bulk metal actually does involve the $f$ orbitals, distinguishing it from what would be its congeners in Group 4 of the $d$ block.  From Wikipedia:

Despite the anomalous electron configuration for gaseous thorium atoms, metallic thorium shows significant 5f involvement. A hypothetical metallic state of thorium that had the [Rn]6d27s2 configuration with the 5f orbitals above the Fermi level should be hexagonal close packed like the group 4 elements titanium, zirconium, and hafnium, and not face-centred cubic as it actually is. The actual crystal structure can only be explained when the 5f states are invoked, proving that thorium is metallurgically a true actinide.[1]

Cited reference
1.
Johansson, B.; Abuja, R.; Eriksson, O.; et al. (1995). "Anomalous fcc crystal structure of thorium metal". Physical Review Letters 75 (2): 280–283. https://doi.org/10.1103/PhysRevLett.75.280, erratum at https://doi.org/10.1103/PhysRevLett.75.3968


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How to extract force constants for normal modes from ORCA?
I am following the computational method described in Scientific Reports.[1] Where the authors analyze the contribution of each excited state normal-modes to the shift of the transition energy. For this calculation they use the force constants of each normal mode.
I am using ORCA but could not understand how to generate the force constants. I did find that the orca_vib program generates force constants, but I did not find how to use the output to generate a force constant for the specific normal modes.
I also found this question,[2] I am not sure if it solves my problem. I saw the great answer by Jan Jensen who following the equation: $$\tilde{\nu}=\sqrt{k_i^{\prime\prime}}/(2\pi \times 137 \times 5.29\times 10^{-9}).$$
Do I just need to plug in my vibrational frequencies and rearrange the equation to get $k$?
References:

Schweighöfer, F.; Dworak, L.; Braun, M.; Zastrow, M.; Wahl, J.; Burghardt, I.; Rück-Braun, K.; Wachtveitl, J. Vibrational coherence transfer in an electronically decoupled molecular dyad. Sci. Rep. 2015, 5 (1), No. 9368. DOI: 10.1038/srep09368.
How to calculate wavenumbers of normal modes from the eigenvalues of the Cartesian force constant matrix?

This question may be well received at the new Materials Modeling SE: https://materials.stackexchange.com/


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Why has nature evolved to put a porphyrin (i.e. chlorophyll) as the chromophore in a leaf?
I'm stumped by this question:

Why has nature evolved to put a porphyrin (i.e. chlorophyll) as the chromophore in a leaf?

I've thought that it might have something to do with how sun emits light at different wavelengths, in the green wavelength of 565 especially (as the sun emits green light), and therefore, through evolution, plants have evolved to incorporate chlorophyll as the chromophore in the leaf to absorb the wavelength of the sun?

No doubt the chlorophyll's absorption wavelength is tuned to the emission spectrum of the Sun. Why it had to be a porphyrin is another question, though...

Well then, why does it have to be a porphyin? :)

Long story short, we don't know. Sure, it is nice and multidentate and conjugated all through, but that hardly makes it unique.

There are other chromophores, mind you, used by plants. Often a nice early high school lab experiment - separate out the chromophores using filter paper.

Note that the green of plants is precisely because green light is the least useful wavelength for them.

This is an unanswerable question. It's impossible to ascribe why in most contexts but especially in the context of evolution. One can only say how the evolved mechanism increases the fitness of something and therefore how that is useful. But one could imagine a very similar molecule which does about the same thing and it's entirely possible the cell would do just fine with that molecule. That's just not how things played out.

Currently, there are two known photosystems to convert light into energy. One is based on Chlorophyll and the other is based on rhodopsins. Namely, bacteriorhodopsin. Together the two systems span the complete sun's UV/Vis spectrum. But the answer is what @jheindel said, there is no possible way to understand why a molecular mechanism was evolved.

The sun is not green! See https://en.wikipedia.org/wiki/Sunlight for details or briefly and safely squint at the sun!

Chlorophyll (chl) is involved in two ways in photosynthetic organisms firstly as a light gathering pigment and second in electron transfer once the light is captured. It is unique in this role.
In the first case, that of gathering light there are pigment protein complexes containing many chl (100's) and work in such a way that energy absorbed in one molecule is transferred among the others until it reaches the reaction centre where electron transfer starts. The feature that makes chl good for the energy transfer bit is that it has a large overlap in energy (equivalently wavelength) between its fluorescence spectrum and the absorption spectrum. This allows very efficient energy transfer between pigments, each step taking only picoseconds. Chlorophyll is among the best if not the best molecules known to do this.
(In some cases carotenoids may assist this energy capture process and in some antenna called phycobilisomes linear tetrapyrroles augment chl (they extend the wavelength range when the organism normally grows in low light conditions) but in these cases there are also chl pigment-protein complexes.)
The second role is that after energy is absorbed it is funnelled to a Reaction Centre. This is done by the energy transfer steps described above but slight changes in the chl environment change its energy levels slightly so that spatially the energy moves towards the reaction centre where electron transfer begins. The electron produced ultimately reduces carbon dioxide to carbohydrate and is replaced by dragging an electron of a water molecule, this is done in the protein in a sequence of complex steps called the dark reactions.
Returning to the Reaction Centre, this consists of a pair of slightly offset face-to-face chl molecules (the Special Pair)  that act as an energy trap and from here an electron is transferred in a couple of picoseconds to a nearby chl then to a pheophytin (a chl less the Mg atom) then to quinone then to an Fe atom all within a nanosecond. The crystal structures are all known and the photophysics of species involved also measured. The structure of these Reaction Centres can be found on the web.
The important property here is that the special pair of chl molecules has the right redox potential to donate an electron to a nearby chl and this the correct potential to transfer the electron to the pheophytin at the same time preserving as much energy as possible and preventing the electron from returning, i.e. making sure it goes down hill in energy but only slightly and thus preserving as much of the initial photon energy as possible. The special pair does not fluoresce to any appreciable extent and so does not loose energy this way.
Chlorophyll has a unique set of properties, excellent ability to transfer energy among other chl with out being quenched until it reaches the reaction centre where the special pair uses this energy to transfer an electron to nearby molecules and start the chemistry leading to reducing carbon dioxide using water as a fuel. All the variant of photosynthesis, algae, plants, bacteria work in essentially the same way, the bacteria have one photosystem, the plants two (PS1, PS2) that work together.
(You should be able to find lost pictures of xray structures of pigment protein complexes on the web but if not I can post some later)

I voted to close the question but with proper editorial guidance it's probably worth reopening, particularly given the good answer you've provided.

Thank you. Re closing I agree. I think that questions are closed too easily or at least too quickly.


text:
Chemistry Vs. AutoMobile Industry
Well, it may not sound deeply related to chemistry but my question is to some chemistry-experts who knows bit about automobile industry.
I want to ask, if a person is getting graduated by having studied all the chemistry majors and he/she wants to get into any field related to automobile industry or cars to be precise. What would they be?
Which are the jobs one can join that are related to automobiles and at the same time demands a degree related to chemistry rather than mechanical engineering. I just suppose that chemistry is required in making cars efficient through fuel, as fuel science is all-chemistry but I need to know all the possible ways a person can get into automobiles having a chemistry degree. I hope it makes sense :)
Regards

Unfortunately this question is not about chemistry as a subject, so it is off-topic for [Chemistry.se]. I'm not sure if there is a site in the network, where it would be on topic.

@Martin-マーチン But it is a question about the practical applications of chemistry which is surely on topic.

@matt_black Maybe that would be an issue better discussed on meta. If I remember correctly we have relegated questions about careers to academia (when suitable) in the past. If it were on topic, I'd still say it is too broad and a bad fit for our site. But since I'm not making the decisions here, the question is still open, I just noted my concerns.

I want to ask, if a person is getting graduated by having studied all the chemistry majors and he/she wants to get into any field related to automobile industry or cars to be precise. What would they be?

Paints, adhesives, polymers => Polymer Science/ Organic Chemistry. Adhesives is a big industry
Corrosion protection => Electrochemistry
Volatiles in new cars, fuel emissions, regulations => Gas chromatography/ analytical chemistry
Energy, fuel cells => Battery science, electrochemistry
Solar cells => Material science

Of course the first thing to come to my mind is fuel technology. For example st1 makes fuel from waste. I'm pretty sure that tire development also need chemistry in rubber compounds. In addition catalytic converter development needs chemistry because their purpose is to cause reactions.
So as a whole I would say that catalytic converter technology and fuel (maybe bio?) technology are your best bets.

As more cars go electric, battery-related chemistry is a big one as well.

Paint chemistry would be applicable too


text:
How do I calculate the ensemble-average net charge of an amino acid at given pH?
I am given an amino acid with an ionizable side chain at a certain pH. How do I determine the net charge of that amino acid when there are mixed protonation states of one or more of the groups at that pH (pKa of side chain, for example, is really close to the pH)?
Amino acids have terminal carboxyl and amino groups; some amino acids have ionizable side chains. When determining the charge of an amino acid, you have to take into consideration the pH and the pKa's of each of these groups. When the pKa of one group (or more) is close enough to the pH, a fraction of the amino acids will be deprotonated at that group and the other fraction of amino acids will be protonated at that group in solution. Thus, when determining the average net charge across the ensemble (or a time-averaged charge of a single particle), you have to take this into account.
I am asking for the expected value of the net charge (which would not be an integer); this number is relevant, for example, for the migration speed of the amino acid (or a protein) in gel electrophoresis or the strength of interaction with ion exchange chromatography media.
For example, a carboxylic acid/carboxylate group at a pH equal to its pKa would have an average charge of minus one half because half of the functional groups would be protonated (charge of zero) and half would be deprotonated (charge of minus one).

Unclear what you mean by net charge here. Is this different from the charge on the species?

@Zhe I mean the net charge of the amino acid. Not just the charge of each side chain or N/C-terminus-- the sum of all groups. Everywhere else on the internet, I had only been able to find an average/rounded charge. I needed to know, to a decimal's point, what the charge of amino acid is at a certain pH when 1 or more groups has a partial charge.

Why would a group have a partial charge? Charge is quantized...

@Zhe Amino acids have terminal carboxyl and amino groups; some amino acids have ionizable side chains. When determining the charge of an amino acid, you have to take into consideration the pH and the pKa's of each of these groups. When the pKa of one group (or more) is close enough to the pH, a fraction of the amino acids will be deprotonated at that group and the other fraction of amino acids will be protonated at that group in solution. Thus, when determining the average net charge, you have to take this into account.

No, that's not quite correct. What you are asking for is much more complicated than you think. In solution, you have a dynamic mixture of different species with possibly different charges. These species all have integer charges. While you might ask for the expected value of the charge (which would not be an integer), it is not wholly clear how this number is relevant to any useful physical quantity.

The Henderson-Hasselbalch relationship describing each ionizable group is:
$$\mathrm{pH} = \mathrm{p}K_\mathrm{a} + \log \frac{\ce{[A-]}}{\ce{[AH]}}$$
We can solve for the ratio:
$$10^{(\mathrm{pH} - \mathrm{p}K_\mathrm{a})}=  \frac{\ce{[A-]}}{\ce{[AH]}}$$
However, we really want the fraction of protonated among the total (not the ratio of deprotonated to protonated).
$$10^{(\mathrm{pH} - \mathrm{p}K_\mathrm{a})} =  \frac{[\mathrm{total}] - \ce{[AH]}}{\ce{[AH]}} = \frac{[\mathrm{total}]}{\ce{[AH]}} - 1$$
Add one to both sides:
$$10^{(\mathrm{pH} - \mathrm{p}K_\mathrm{a})} + 1 = \frac{[\mathrm{total}]}{\ce{[AH]}}$$
Take the reciprocal:
$$\frac{\ce{[AH]}}{[\mathrm{total}]} = \frac{1}{10^{(\mathrm{pH} - \mathrm{p}K_\mathrm{a})} + 1}\tag{1}$$
This is still general for any acid/base group. For example, we could use it to calculate the charge of ammonia/ammonium ($\ce{NH3(aq) + H+(aq) <=> NH4+(aq)}$). At very basic pH, the charge would be zero, at very acidic pH, +1. To get the average charge at any pH, we take the charge at very basic pH and add the result of equation [1] using the $\mathrm{p}K_\mathrm{a}$ value of ammonium.
For any amino acid (or any other molecule with ionizable groups with $i$ different $\mathrm{p}K_\mathrm{a}$ values), you take the charge of the species at very basic pH (all groups deprotonated), plus the following:
$$\sum_i \frac{1}{10^{(\mathrm{pH} - \mathrm{p}K_\mathrm{a,i})} + 1}\tag{2}$$
This is only an approximation because there might be some cross talk between ionizable groups (i.e. if one group becomes negatively charged, it becomes more "difficult" for the neighboring group to become negatively charged). It also becomes more complicated for polyprotic groups, but all the groups in amino acids are monoprotic with water as a solvent.


text:
DNA pairs (adenine-thymine, guanine-cytosine)
Well I was wondering why adenine pairs with thymine and cytosine pairs with guanine.
From those pictures:

Thymine has the lowest acidity and adenine has the biggest acidity.
So it is logical that the intermolecular bond will be strong.
Adenine and Cytosine have pretty much the same acidity so why is it energetically favorable for guanine to make an intermolecular bond with cytosine?
Is it due to the three combinations this (adenine-thymine, cytosine, guanine) has the lowest energy?

Simplest explanation in that only in G-C there can be 3 hydrogen bonds - 3 beats 2. BTW your reasoning is based on false assumptions as there's no such correlation.

Thymine is the least acidic since it contains 2 O bases.

Adenine doesnt contain any 0 bases so it is the most acidic.

I looked, but I disagree. If you want to have someone look at your comment, use their username prefixed by @, as in @Software_Player.

@Karsten Theis Why do you disagree? O base is less acidic than N base...

That is a new question. Maybe use examples with less functional groups, like acetone vs. 2-amino propane. Acetone has no acid/base chemistry in the pH range of 0-14, and 2-amino propane is a base. Neither is an acid.

@Karsten Theis Amino-propane  is a base indeed.

@KarstenTheis and acetone is a base as well due to the molecule being polar.

@Mithoron there is also repuslion from a partially charged negatively oxygen to a partially charged negatively mitrogen .

In Principles of Nucleic Acid Structure, W. Saenger argues that hydrogen-bonded bases contain at least two hydrogen bonds (forming a "cyclic" pattern). Often, there is a tautomeric form possible that also makes two hydrogen bonds, with two covalent bonds turning into hydrogen bonds, two hydrogen bonds turning into covalent bonds, and double bonds moving around so that each atom still has an octet. In the OPs first example (A:T pair), for example, the ketone would turn into an enol, and the protonation of the amino and imino groups would change.
Saenger goes on to say that 28 pairs are possible.

Many of these are observed (the ones that are labeled are so common that they were given names), in structures of DNA, RNA, and in crystal structures of dinucleotides.

I was wondering why adenine pairs with thymine and cytosine pairs with guanine.

They pair because they make strong hydrogen bonds with a geometry of the base pairs that allows base stacking and is compatible with base pairing of the other nucleotides in a DNA strand. As the discussion above shows, many other base pairs are theoretically possible, and some of them are actually observed in nature.

Thymine has the lowest acidity and adenine has the biggest acidity. So it is logical that the intermolecular bond will be strong.

I'm not sure about the premise, and the conclusion is incorrect, as other base pairs also form. As long as a group has the right protonation state, the pKa does not directly determine hydrogen bond strength.

Hydrogen bond strength  (any intermolecular bond strength)  is determined by the polarity of the molecules.

@SoftwarePlayer OK, but is acidity directly correlated with polarity?

In Hydrogen bonding , Hydrogen is charged partially positive , so this makes the molecule acidic.By definition an acid is a molecule which can donate a proton so yes.


text:
Character table and symmetry operations
It's been a while since I've dealt with these, but do character tables include all possible symmetry operations?
I am looking at the $D_\mathrm{\infty h}$ point group table and it lists $C_\infty$, $\sigma_\mathrm{v}$, $S_\infty$, $i$, and $C_2$. But doesn't it also have a $\sigma_\mathrm{h}$? Why is this not included?
Am I missing something here?

$S_{\infty}$ is equivalent to $\sigma_\mathrm{h}$. $S_{\infty}$ means rotate 0° then reflected by $\sigma_\mathrm{h}$, which is just same as taking $\sigma_\mathrm{h}$ itself.


text:
Electrolytes for Anodization at Home
I'm looking into anodization, and all the people doing it seem to have sulfuric acid as their first choice electrolyte, while others use sodium metabisulfate. Having simple access to exactly neither of these, I was wondering.

Why is sulfuric acid important?
Can I use more accessable (and safer) electrolytes such as vinegar or sodium bicarbonate instead?
How much of a difference would it make?

@EdV, I could possibly obtain sulfuric acid. However, for a simple experiment at home, I'd like to use household chemicals.

@EdV, that's pretty interesting. However I was thinking more on the lines of aluminum. Also, if even diet coke is usable, there are probably other household chemicals that would work as well (maybe vinegar?).

@EdV, that's really my question; why is sulfuric acid necessary? Why not any electrolyte?


text:
The reaction of Group 14 to get its full shell
I was learning about group 14 of the periodic table and in the course, on Alison (link at the bottom), it said a reaction of the elements in group 14, they use group 4, would consist of sharing electrons. They explained it to what I believe is from going to 2,8,4, Silicon, to 2,4,8 in order to get the full shell. I am very confused at how exactly that one works. But everywhere else, it was stated that the elements in Group 14 lost or gained 4 electrons. But the course said it wouldn't gain or lose any electrons. Is the course a bit more advanced than the others or is it just wrong?
Also, is it just called an electron shell or is there some other title for it, because shell doesn't really sound too scientific.
https://alison.com/topic/learn/17074/full-shells-metals-and-non-metals

Thanks for the help!

The content of the link appears to be inaccessible without registration.

Scientifically, it's "shells".  Bohr's model of the atom assumed the electrons are arranged in shells and that nomenclature has carried over even though the model is obsolete.

The course is probably wrong. Chemical elements of Group 4 have 2 lone electrons, but the need 4 bonding pairs with another element to reach noble gas electron configuration.So 1 electron from the other completed subshells moves to the p subshell and now we have 4 lone electrons. Once they all form bonds, the element reaches the noble gas electron configuration.
*The element absorbs energy in order to transfer an electron from a lower-energy to a higher-energy orbital, according to the lowest energy rule.But it is energetically favorable in the end since it reaches electron configuration of noble gas.


text:
Why is Q/nF equivalent to the amount of substance in electrolysis?
I am told that
$$Q = nF$$
where $Q$ is the quantity of current, $n$ is the amount of electrons and $F$ is Faraday's constant. Since Faraday's constant is the charge carried by 1 mol of electrons, multiplying it by the amount of electrons to give the total charge makes perfect sense. But why does dividing $Q$ by $nF$ gives the amount of substance? Won't the answer just be 1 for all possible values?

For a general electrolytic reaction,
$$\ce{M^{n+} + $n$ e^- -> M}$$
where $n$ moles of electrons are consumed in depositing 1 mole of substance ($n$ is also known as $n$-factor). So, for $x$ moles of substance, $nx$ moles of electrons would be consumed. Therefore,
$$Q = nxF,$$
dividing by $nF$ on both sides, we have
$$\frac{Q}{nF} = x,$$
which is the amount of substance.

Ah, that makes perfect sense. Thank you!

@rv7 Please visit this page, this page and this one on how to format your future posts better with MathJax and Markdown.

@andselisk: Thanks for the links. I'll take care of that next time.

Often, $z$ is used for the stoichiometric factor, and $n$ for the amount of substance, so it becomes $n = \frac{Q}{z F}$, see e.g. https://www.bipm.org/utils/en/pdf/SIApp2_mol_en.pdf @rv7


text:
What is the cause of yellow discharge in beaker during the electrolysis of copper electrodes using copper sulfate electrolyte?
I have conducted an electrolysis experiment using a copper anode and cathode, and copper sulfate solution in a beaker connected to a power source using alligator clips. I varied the voltage and measured the current and noticed the theoretical mass values I calculated were consistency lower than the values I obtained.
I suspect the ammeter was not calibrated properly however am not sure what affect the oxidation of sulfate ions has on the current (yellow discharge present during electrolysis) and if that would have affected my results.

"yellow discharge"? You mean an effect with light and noise?

Post a picture. How pure is the copper electrode.


text:
Identifying endothermic and exothermic reaction
How can I know that a given reaction is endothermic or exothermic? I know that all combustion reactions are exothermic. But what about other reactions?
In my school exam I was asked about whether the reaction
$$\ce{N2 + O2 -> 2 NO}$$
is exothermic or endothermic. I didn't know that it is endothermic reaction and left that question. My teacher hence suggested me to learn all exothermic and endothermic reactions! Is it possible to do so? (Obviously not.) Please help me.

Exothermic or Endothermic reactions; Is the reaction exothermic or endothermic?

Well, you may learn just the endothermic reactions. The rest are exothermic.

If the product looks unfamiliar or you have trouble writing a nice all-octet Lewis structure (like you would have for NO), chances are the reaction is endothermic. You could memorize a table of bond dissociation energies for a more quantitative estimate, but maybe there are other things more worthwhile.

Your teacher is being sarcastic. I am sure you have discussed this exact reaction in class, because you have to avoid that it runs in opposite direction during the Ostwald process when producing nitric acid. Because it is endothermic. Classic high school chemistry.

Another hint is, if you need high temperature for the reaction it is probably endothermic.

Standard formation enthalpy of NO is ninety kJ/mol, of NO2 thirtyfour (at RT).


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Organic solvent for cleaning autosampler syringe
I work in a laboratory where gas chromatography is used extensively. We handle phthalates. What are the possible wash solvent for autosampler syringe? I've been using acetone.

You could try use toluene a then ethyl acetate.

Acetone is a remarkable solvent. Now if you use some phthalates which are either particularly polar or particularly non-polar, you may want to change the solvent. For really polar compounds, a mixture of methanol/water/acetonitrile may be great. For non-polar compounds, you may want to use dichloromethane.

I think Waters used to suggest a magic mix of 1:1:1:1 MeOH:IPA:ACN:water with a few drops of ammonia as a good way of clearing pthalates from lines - the same likely applies to autosampler needles

Well, since you have a GC, any volatile solvent for phthalates is good, it may show up as a peak on the chromatography.
If you are not analyzing for the solvent, it is all right.  If one is, switch to another solvent!
Also make sure any cleaning solvent is compatible with the injector diaphragm, syringe, column, or any other parts of the instrument.
It would not hurt to make a few consecutive injections with your sample preparation solution only just to make sure before starting the analytical injection sequence.

Methanol is less expensive. Don’t know how well it would work in your particular situation. We do semi volatiles (EPA 624) .  Methanol works fine for the GC autosampler syringe.


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What is the degree of freedom of the calcium carbonate dissociation reaction?
Question

$\ce{CaCO3}$ dissociated in a closed system according to the reaction:
$$\ce{CaCO3(s) -> CaO(s) + CO2(g)}$$
Assuming the reaction is in thermodynamic equilibrium, what is/are the degree(s) of freedom?

Doubt
I tried applying the condensed phase rule. All that I could arrive at was
$$C - P + 1 = 3 - 2 + 1 = 2.$$
However, the answer is slightly modified in the solution. The solution reads that $$C = N - R$$
where $N = 3$ and $R = 1.$ These are the factors I do not understand. All that I ask myself is where did I go wrong? Where was the exception?Please note here N stands for the number of reactants and R for the number of reactions.

This question might get an answer from someone if it gets some emergency CPR (and N)! How about defining C, P, R, and N?

C are the number of components.P stands for phases .Now C=N-R from the solution.However I am yet to figure out what are they.Secondly,why do I need to use the condensed phase rule and not the simple phase rule?

I have no clue, but maybe someone else will be able to answer.

The degrees of freedom for a closed reacting chemical system are
$$ F = 2 - \text{Num. of phases} + \text{Num. of components} - \text{Num. of chemical reactions} $$
We have:

Three phases: $\ce{CaCO3}$ solid phase, $\ce{CaO}$ solid phase, and a gas phase with $\ce{CO2}$.
Three components.
One chemical reaction.

Thus
$$ F = 2 - 3 + 3 - 1 \rightarrow \boxed{F = 1} $$


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The concept of normal coordinates of a molecule
Sometime ago I had posted the What is the origin of "normal" in normal coordinates and normal modes? in math & sci history problems. Nobody was sure for the reason for using the word normal there - it was an interesting discussion though. The concept of normal coordinates is transiently brought in vibrational spectroscopy in undergraduate textbooks but rarely explained in detail. Certainly, the concept is borrowed from mechanics.
How can we explain the concept of normal coordinates? What is the need of a new set of coordinates if x, y, z can show also the displacements of an atom from its mean position? Let us take the example of a non-linear molecule like water.
Edits
More specifically, how would we mathematically define a normal coordinate for the oxygen(s) and hydrogen during a normal mode vibration of water molecule? Or a "normal coordinate" is a global displacement coordinate for the whole molecule for a given normal mode vibration. Water has 3 IR active modes. Do we have only 3 normal coordinates $q's$ for water? Wikipedia shows a simplistic picture of a normal coordinate $q$ as a measure of displacement but from little bit of reading Herzberg's other specific monographs by Wilson, the concept of normal coordinate does not seem that trivial.

X, Y, and Z can show the same positions all right. But there is no such oscillation that would change, say, just the X coordinate of one of the H atoms and nothing else. Everything is connected with everything, and we didn't like that.

Solving for the normal coordinates in the days of Herzberg wasn't trivial. (It's a 3N x 3N matrix after all) But yes, you have $3N-6$ normal displacements - one for each normal mode.

Since I was reviewing this in some detail recently, I will try to supplement Prof. Hutchison's already good answer with some more detail as to why one would choose to work with normal coordinates, rather than the already quite simple Cartesian coordinates.

The short answer is that, under the assumption of small displacements, normal coordinates decouple the vibrational degrees of freedom from the rotational degrees of freedom and make all vibrations mutually orthogonal, such that the total energy of the nuclear motion of the molecule can be expressed as a sum of translational kinetic energy (3 dimensions), rigid rotation at the fixed equilibrium geometry (3 dimensions), and vibrations about the equilibrium geometry ($3N-6$ dimensions).

Now, it is not so difficult to show that if we allow a molecule to move in all $3N$ degrees of freedom, that the total energy of the system will have a term which couples the rotation of the molecule to the vibrations of the molecule, the so-called Coriolis energy. This is because if we work in strictly Cartesian coordinates, the axes are fixed, which means that as a molecule rotates, a simple displacement of two atoms (imagine a diatomic vibration) will not have the expected periodic behavior in Cartesian coordinates, but will appear to shift amplitude among the Cartesian coordinates.
So, we would like to work with a set of coordinates which circumvents this problem as we can see that it is an artifact of the coordinates we chose from the outset and does not have any useful physical meaning.
As it turns out, it is rather non-trivial to thoroughly show that there is a particular choice of coordinates which transforms the Cartesian coordinates such that the frame of molecular vibrations is fixed and hence eliminates the coupling between vibrational and rotational degrees of freedom. This is where I should mention that, if you like, the Bible of molecular vibrations is the book Molecular Vibrations by Wilson, Decius, and Cross[1]. Chapters 2 and 11 fully motivate and derive the transformation which completes this procedure. The coordinates turn out to be what we now call normal coordinates, and I will only point out that the transformation takes the following form,
$$
q_i=\sqrt{m_i}\Delta \alpha_i
$$
where $i$ is atom index which runs from 1 to $N$ and $\alpha=x,y,z$, so that we rescale the $3N$ Cartesian coordinates into $3N$ mass-weighted coordinates.
It shouldn't be too hard to see that the kinetic energy in these new coordinates takes the simple form,
$$
2T=\sum_{i=1}^{3N}\dot{q}_i^2
$$
Then, using a quadratic approximation to the potential energy, the potential energy takes the form,
$$
2V=\sum_{i,j=1}^{3N}f_{ij}q_iq_j
$$
where $f_{ij}=\left(\frac{\partial^2V}{\partial q_i\partial q_j}\right)$ is the harmonic force constant.
One can show that if you solve Newton's equations of motion using these expressions for the kinetic and potential energy, that one will have to solve an eigenvalue equation where the eigenvalues, $\lambda_k$, correspond to the frequencies of vibration and the eigenvectors correspond to the normal modes, i.e. the actual motion of atoms which vibrate at the the frequency $\lambda_k$.
Now, these $q$'s are not quite normal coordinates, which I will call $Q_i$, but they are very closely related to normal coordinates. Namely, what we call normal coordinates are the ones which have one additional nice property of having a potential energy of the form,
$$
2V=\sum_{k=1}^{3N}\lambda_k'\dot{Q}_i^2
$$
That is, we want the potential energy to not contain any terms involving more than one coordinate. Thus, we have to determine the coefficient $\lambda_k'$ which makes this transformation.
In Ref. [1], sec. 2-4, this derivation is performed and one finds the marvelous result that $\lambda_k'=\lambda_k$. Hence, one can make this representation of the potential energy diagonal by multiplying by the characteristic frequency which we got from each $q_k$.
Lastly, lest you convince yourself that vibration and rotation are not accounted for anywhere in this, when you solve the eigenvalue I mentioned above, you will find six eigenvalues which equal zero. This is only the case because we made this transformation to mass-weighted coordinates, and these six zeros tell us that six of our degrees of freedom appear to be completely stationary. These are translations and rotations.
So, people work with normal coordinates because they have these nice properties of providing a diagonal represent of the kinetic and potential energies when vibrations are harmonic, and giving a mutually orthogonal set of coordinates with which to work. This is nice because even when we wish to include anharmonicities and other corrections, we have a set of coordinates which have desirable properties and which are a usually a good approximation to the true "vibrational motions" of the system.
I put "vibrational motions" in quotes because it isn't clear that talking about the motions of atoms in a vibrational state is all that meaningful in quantum mechanics, and one can easily find a unitary transformation which causes the motion to look different in Cartesian space, but which leads to the same observable properties.

[1]: Wilson, E. B., Decius, J. C., & Cross, P. C. (1980). Molecular vibrations: the theory of infrared and Raman vibrational spectra. Courier Corporation.

Excellent reference, this is the type of reference I was looking for. There is company by the name of BrightSpec named after this great Wilson.

If we consider N atoms in a non-linear molecule, then each atom can move independently on the X, Y, and Z axes. That's $3D \times N = 3N$ degrees of freedom.
But if I move the whole molecule 3 Å along the x-axis, that doesn't constitute a vibration - it's just a translation. So we have to remove 3 degrees of freedom for translations.
Similarly, if I rotate the molecule along the x- or y- or z-axis, that's not a vibration either. You mentioned water, which is non-linear, so I remove another 3 degrees of freedom for rotations.
I'm left with $3N-6$ degrees of freedom - which are the normal modes of vibration. Your question then becomes "what are those normal modes" (e.g., for water).
Okay, for water, we have $9 - 6 = 3$ normal modes. As mentioned above in a comment, it's not like you can just pull an atom along an x-axis.. As it turns out, the normal modes will be dictated by the potential energy surfaces of the molecule.

In general, one normal mode is a "symmetric stretch" - usually expanding and contracting bonds. Other modes will depend on the molecule, but will depend on the geometry/bonding and elements involved: stretching (symmetric and asymmetric), bending (e.g. changing the bond angle in water), out-of-plane bending (e.g. flexing a benzene ring), etc.
Note: The reason I mention normal modes in regards to the question about "normal coordinates" is that the two are directly linked. The "normal coordinates" are the displacements along the normal modes in a molecular vibration:

The normal coordinates, denoted as ''Q'', refer to the positions of atoms away from their equilibrium positions, with respect to a normal mode of vibration.  Each normal mode is assigned a single normal coordinate, and so the normal coordinate refers to the "progress" along that normal mode at any given time.

The reason that we use the term is that the Cartesian x, y, and z axes are meaningless with respect to a molecular geometry, whereas the normal modes and thus the normal coordinates are derived directly from the molecular potential energy surface.

Thank you Geoff, what you have discussed is the concept of normal modes. I am more specifically looking for the mathematical concept of normal coordinates (q) as used in vibrational spectroscopy.

@M.Farooq - but the 'normal coordinates' (q) are simply the displacements along the normal modes, e.g. https://en.wikipedia.org/wiki/Molecular_vibration#Normal_coordinates

@M.Farooq - no worries - I could see that you didn't make the connection, so I clarified. I rarely teach the details of normal coordinate analysis because most people now just leave it to the computer. "Simply" was meant more as a mathematical term than a value judgement. :-)

There are excellent answers already, but I wanted to address the following question

[...] how would we mathematically define a normal coordinate for the oxygen(s) and hydrogen during a normal mode vibration of water molecule?

The first step is to switch from cartesian coordinates to internal coordinates. For water, it would be the two bond lengths $L_1$ and $L_2$ and the bond angle $\alpha$. This separates out translations and rotations (internal coordinates are not affected by those degrees of freedom). The second step is to turn these internal coordinates into normal coordinates so that the conformational energy is minimal when all normal coordinates are zero, and so that each normal coordinate corresponds to a normal mode.
I will call the normal coordinates $q_s$, $q_a$ and $q_b$, for symmetric stretch, asymmetric stretch and bend (symmetric), respectively. Separately, they are scalars. Also, let's call the lowest energy bond angle $\alpha_0$ and the lowest energy bond length $L_0$.
For small amplitudes, the bond lengths don't change for the symmetric bend. We can simply define $q_b$ as:
$$q_b = \alpha - \alpha_0$$
For the symmetric stretch, the sum of the bond lengths changes, so we can define:
$$q_s = L_1 + L_2 - 2 L_0$$
For the asymmetric stretch, the difference of the bond lengths is nonzero, so we can define:
$$q_a = L_1 - L_2$$
This should work for small amplitudes, again. Now, you can express the conformational energy of the water molecule using expressions containing the square of the normal coordinates, separately for each normal mode.
Conversely, we can explore how bond angles and lengths change depending on the values of the normal coordinates:
$$\alpha = q_b + \alpha_0$$
$$ L_1 = \frac{q_s + q_a}{2} + L_0$$
$$ L_2 = \frac{q_s - q_a}{2} + L_0$$
So you can see that as a first approximation, the normal coordinates are linear combinations of the internal coordinates and vice versa. It gets more complicated if there are torsion angles and tetrahedral or octahedral centers.
Water is a good example for figuring out the logic of normal coordinates on paper. It is neither too simple nor too complex.


text:
What are the effects of radio waves on matter?
Different regions of the electromagnetic spectrum interact differently with matter:

Microwave radiation can induce molecular rotation.
Infrared radiation can induce molecular vibration.
Visible and ultraviolet light can induce electron excitation.
X-rays and gamma rays can induce ionization.

Is there any activity specific only to radio waves? I kept on thinking how radio waves are used in NMR but I don't know what to call it.

Radio waves are weak; they can't do anything of the above, which leaves us with your suggestion on NMR.

While NMR is in principle the energy range of radio waves, actual instruments do not use interaction with electromagnetic radiation, but only induce and detect near-field magnetic interactions. There are no actual photons emitted or absorbed by your sample. The advantage is of course that you can create and perfectly detect (phase sensitive!) any kind of waveform.

"actual instruments do not use interaction with electromagnetic radiation, but only induce and detect near-field magnetic interactions." Certainly NMR is not like UV-Vis, but pray what is the job of the radio-frequency transmitter then?

@M.Farooq The "transmitter" powers the pulsed radio frequency $B_1$ field. It never decouples from the probe coil to become electromagnetic radiation, i.e. actual photons. Here https://onlinelibrary.wiley.com/doi/abs/10.1002/%28SICI%291099-0534%281997%299%3A5%3C277%3A%3AAID-CMR1%3E3.0.CO%3B2-W is the classical text on the matter.

@Karl, the article is worthwhile and they correctly suggest that the concept of radio wave absorption and emission is rampant. However, no one can generate an isolated oscillating magnetic field without an accompanying electric field in a RF coil. This pulse is electromagnetic in nature. See RF coils - for non physicists in the same journal https://www.ncbi.nlm.nih.gov/pmc/articles/PMC6175221/

@M.Farooq The oscillating magnetic field is certainly accompanied by a corresponding E field. Im just saying they do not form a classic electromagnetic wave, because you cannot confine an electromagnetic wave into a 1ccm probe chamber.

This is a bit of a stretch, but the Zeeman and Stark effects are linked to radio frequencies, in that line splitting of a visible spectral frequency (~10^15 Hz) can give rise to a beat-frequency in the RF. Your answer of NMR, though, is more applicable. The most general term for precession in a magnetic field is Larmor precession.

Radio waves $10^4$ to $10^{11}$ Hz are not that innocent as is commonly purported. Long time ago there was an demonstration that radio waves of certain frequency can decompose salt water into hydrogen and oxygen (and ignite). There was an article in Popular Mechanics. No other type of radiation can cause this effect. See the video of burning here Burning salt water. John was trying to cure his cancer but died at young age in early 60s.
Radiofrequency is routinely used to generate argon plasma for atomic spectroscopy (which heats it up to the temperature of the Sun). One spectroscopist had jokingly mentioned that a senior advised him not to work with this equipment because it may make you sterile.
For the information of some readers who think microwaves and radiowaves are different, radio waves include microwaves. Microwaves are basically high frequency radio waves. http://wifiinschools.org.uk/15.html
Both microwaves and radiowaves can easily generate plasmas and atomic spectroscopy can be done with both.

This video and the now missing self-published journal report are highly suspect. Nowhere do they mention the intensity of the radiation required (while seeming to imply that they get more energy out than put in). Yes, high intensity RF can generate plasmas and possibly other effects (the 1kW or so of RF power in a microwave can generate plasma easily) but this is hardly more impressive than being burned by the IR from a domestic toaster.

$10^{11}$ is deep in the microwave regime. A hundred Gigahertz. Your kitchen microwave oven runs at 2.45 GHz. And a plasma is electrically conductive, and you need an electrical discharge to start it.

https://en.wikipedia.org/wiki/Rotational_spectroscopy , done in the tens of GHz.

Radio waves do not generate plasma, you can heat and thereby keep alive a plasma with high power radio waves. Or you can generate an electric spark with radio waves, if you have a conducting antenna. Youre leaving out the central pieces of your statements.

No need to split hairs here. It might be better if you write a separate detail reply to the original query. In the ICP torch, there is an initial seeding to create ions in the argon gas, and the RF coil transmits power (inductive coupling) and creates a sustained plasma.

Radio waves have a longer wavelength than infrared radiation and is classified between 3Hz and 300MHz frequencies. Due to its lower energy/longer wavelength, radio waves are able to penetrate deeper than higher energy radiation. For example, the skin depth is a function of frequency:
$$\delta = \sqrt{\frac{2 \rho}{\omega \mu}}$$
where $\rho$ is the conductivity, $\omega$ is the angular frequency, and $\mu$ is the magnetic permeability. As the frequency increases, the skin depth decreases. This is the reason AM and FM radio (in the kHz range) is able to travel very large distances, while your standard 2.4GHz wireless router has poor connectivity through walls.

Radiofrequency energy possesses quite important heating capabilities. What matters is not the energy hf carried by the wave, but rather its intensity and focusing.
Induction heating generators, with power ratings from a few kilowatts to several hundred kilowatts and running in the range from a few kilohertz to several hundred kilohertz are routinely used in the metal industry for heat treatment processes, such as induction hardening, brazing, or forging. The intense heating effect owes its efficacy to the induced parasitic currents flowing within a relatively shallow "skin" region in the heated material.
In addition, a dielectric heating effect may be obtained by using radiofrequency generators in the megahertz range for myriad processes such as adhesive bonding, plastic forming, wood drying, and even radiothermal healing in medicine.

Radiofrequencies can induce changes in proton and other nuclei energy levels in a magnetic field. Guess what? the entire Earth is in a magnetic field. All those protons, phosphorus atoms, C-13 atoms, etc. are dithering when exposed to radiowaves.  Are there natural radiowaves? Yes, in blackbody radiation. Measureable? Who knows but Gravity waves were recently not detectable.
A Story: Years ago when my children were about 7 years old [they are now 50] [and my hearing had a wider high frequency range] We were at our cottage in the Adirondack Mountains of NY. The Adirondacks then and still do have minimal light pollution and the Perseid Meteor shower coincided with a new Moon. We spread blankets in a clearing surrounded by trees and underbrush, lay down and looked up to Blackness and some stars. After several minutes someone said "I saw one!" then "Me too, Me too". Every minute or so a large meteor flashed overhead. As our vision accommodated the sky became full of tiny meteoric flashes with occasional large trails; it was almost magical! Suddenly one of the kids said "I HEARD that one"! We were a little concerned about occasional rustling in the woods thinking animals were approaching to pounce. We said NO they are too high up to hear. SSSSH lets listen. We soon realized that there was sound coinciding with the meteors; We could hear them in real time. The perfect combination of darkness and silence. We still talk about it today.
Some thirty years later, browsing a Nature journal, I encountered an article claiming that meteors emitted radio waves that could be absorbed by dry plant matter and converted into sound enabling meteors to be heard as they are seen. Unfortunately I did not copy the article.

Here is an explanation and more descriptions of the effects: https://earthsky.org/space/whoosh-can-you-hear-meteors-streak-past/


text:
Why there are more examples of carbonylate anions than metal carbonyl cations?
I know that metal carbonyl complexes that do not follow EAN rule or 18 electron rule try to achieve that by gaining electron (forming carbonylate) or loosing electron (forming carbonyl cations). But this question is way too dicey. It came in a national level exam in our country. I am yet to find a solution.

not a duplicate, but addressed here https://chemistry.stackexchange.com/questions/118739/what-is-the-oxidation-state-of-mn-in-hmnco5/118742#118742

Yes there are more carbonylate ions than metal carbonyl cations, but the latter do exist.  A salt $\ce{[Mn(CO)6^+][BF4^-]•SO2}$ has been synthesized in a superacid medium.
Metal carbonyl cations are often disfavored because they have to contend with counterions that are anions, which may compete with the carbon monoxide ligands.  Such a competition is tilted towards the anion winning out if the metal is positively charged.  Solvents with significant Lewis-base character are also apt to displace carbon monoxide from the coordination sphere, for a similar reason.  Carbonylate anions do not face this situation (or at least not as severely) because cations are more likely to bind with the solvent than with an an ionic metal center that is dispersing its charge through pi donation to the carbon monoxide ligands.
Going back to the referenced salt, we can see features that protect $\ce{[Mn(CO)6^+]}$ from such an ignominious fate.  First note the counterion, $\ce{[BF4^-]}$which is a very weak nucleophile and has its negative charge buried inside the relatively bulky fluorine "shield".  Then note the superacid medium; perforce the solvent is not competing as a Lewis base either.


text:
Euclidean distance between atoms using RDKit
I'm trying to find the Euclidean distance between two atoms in the molecule with SMILES representation O=CC1OC12CC1OC12 using the rdkit package. Looking online, I have converged to the following code.
import numpy as np
from rdkit import Chem

mol = Chem.MolFromSmiles('O=CC1OC12CC1OC12')

conf = mol.GetConformer()
at1Coords = np.array(conf.GetAtomPosition(bond_i.GetBeginAtomIdx()))
at2Coords = np.array(conf.GetAtomPosition(bond_i.GetEndAtomIdx()))
print(np.linalg.norm(at2Coords - at1Coords))

But I get the error
conf = mol.GetConformer()
ValueError: Bad Conformer Id

I was wondering how to fix the issue. Thanks!

The issue was that I had to embed the molecule to have a 3D conformation. So I added following line:
AllChem.EmbedMolecule(mol)

Feel free to answer with better suggestions and alternatives.

This is a bit late but there is an easy way.  You have no conformer and to get the Euclidean distance, you need to embed the molecule ( as mentioned ) and optimize it in 3D.  Unless, you load from a mol file with coordinates.
Below is an implementation for a smiles string.
from rdkit import Chem
from rdkit.Chem import AllChem
import numpy as np

def generateMolFromSmiles( smiles ):
    m = Chem.MolFromSmiles( smiles )
    m = Chem.AddHs( m )
    AllChem.EmbedMolecule( m, randomSeed=0xf00d )
    AllChem.MMFFOptimizeMolecule( m )
    return m

def getDistOfMol( smiles ):
    m = generateMolFromSmiles( smiles )
    distMat = Chem.Get3DDistanceMatrix(m)
    return distMat

smiles = "O=CC1OC12CC1OC12"
distMat  = getDistOfMol( smiles )
print( distMat ) # full matrix of numOfAtoms x numOfAtoms
print( distMat[0,2] ) # distance between atom 0 and atom 2

Output:
[[0.         1.22448701 2.34475022 3.53889923 3.25859597 4.5416131
  4.77052328 5.13509918 3.71333938 2.03965411 2.78446249 4.68794261
  5.37807671 5.09749518 3.36268049]
 ............
 [3.36268049 3.19077316 3.11178336 3.25145896 2.22885191 3.06533768
  2.21724756 2.17967672 1.08128432 3.7068481  4.00560363 3.67573384
  3.91252705 2.52605715 0.        ]]

Note the matrix is numOfAtoms x numOfAtoms.  You only need one row to know the distances between all atoms.  The first row is the distance between atom 0 and atoms 0-n.  The second row is the distance between atom 1 and atoms 0-n.  etc...
Note there is no direction here.  I've done an implementation that gets direction but it's a bit more complicated.  I just parsed the molfile but GetAtomPosition() will return the x,y,z coordinates. Then numpy transformations can be done to get any geometric value.  The  rdGeometry module provides many options as well.
The distance between atom 0 and atom 2
2.344750223949128


text:
Doubt in the word infinite dilution
At times I find the concentrations being expressed as weight percentage. However I do not understand why molarity is not chosen.
Secondly, which close reference to the problem that I have been facing this is a follow up question:

The change of standard state from pure liquid to 1 wt % for Si dissolved in liquid Fe at 1873 K is expressed as:
  $\ce{Si(liq)=Si(1 wt\%)}$. Given that the activity coefficient of Si at infinite dilution is $10^{-3}$, what is the standard Gibbs free energy change (in kJ) for this equilibrium.

Doubt What is so special here about the word "infinite dilution?"

If a substance has unknown molecular weight, molarity is not feasible. But if the substance can be weighed, then the weight percent option is viable.

Also w% either referred to solution or solvent is very practical WHEN the solution is very diluted and even more when the solvent is water. This is what is easily forgotten even by experienced scientists leading to almost useless protocols. 90% of the protocols I see in interdisciplinary research can be used only assuming an incorrect compilation of them. This is just a rant because something so easy should be not accepted. For the answer see both mothgod and M. Farooq.

The phrase "infinite dilution" is to introduce the idea that the only intermolecular interactions the solute experiences are from the solvent while dissolved in it.
This is understood to be a solution at "infinite" dilution — or a solution where the interaction between solvent and solute physically and energetically does not change upon further dilution.
So then, the question is essentially asking what the Gibbs' Free Energy change is when dissolving liquid $\ce{Si}$ in liquid $\ce{Fe}$ to make a $1\%$ solution. Since you are working with a solution at infinite dilution, the problem allows you to ignore any additional interactions between dissolved Si particles, and can use the activity given in the problem.
I hope this helps clarify the concept. Here's a nice section from Chemistry LibreTexts that mentions it in the context of solution thermodynamics.

Infinite dilution is a hypothetical construct. Only homeopathy believes in a practical infinite dilution but for the rest of scientific world, infinite dilution means that the concentration has been mathematically extrapolated to zero.


text:
In High Performance Liquid Chromatography, why are ratios of solvents used?
How do they allow for better separation? For example, why isn't 100% hexane used?

You answered your own question: better (or even possible) separations. The chromatographers here, e.g., M. Farooq, will have lots to say, but consider this simple thing: hexane is non-polar. You can only do so much with that. Mixtures of polar and non-polar solvents gives you a 'knob' to adjust when you need to perform a separation. But just wait for the chromatographers to post a real answer!

Not sure if I can fulfill Ed's "real answer". I like the word you used for tuning solvent polarity- a knob. Modern students may understand this better.
There is no theoretical restriction in chromatography to use multiple solvents or a single solvent. For example in gas chromatography, you always use a pure gas. The reason for using a mixture of solvents in liquid chromatography originates from the concept of "general elution problem of chromatography" which basically says that there is no single column or a single mobile phase which can separate everything. Not only separation scientists use a single mixture composition of mobile phase (isocratic), they can also continuously change the mobile phase composition as a function of time. This is called gradient elution.
When you do real separations, you have no idea beforehand about the solubility of analytes injected into the column. If these injected solutes are not soluble in a pure solvent they will permanently absorb on the column. A real sample may contain 30-40 compounds. Say a petroleum sample, literally have thousands and thousands of different molecules. Now think yourself: will they all dissolve in 100% hexane?

Great answer (+1)! Chromatography is ubiquitous in modern chemistry research and an expert chromatographer can separate highly complex mixtures with an ease that us non-chromatographers find almost incomprehensible!

Mixture of solvents is used for 2 main reasons:
Elution time
For given HPLC column and set of analytes, the mobile phase must have the proper degree of general polarity, what is often called "solvent strength".
For polar sorbents like silica or alumina, more polar solvents have generally bigger strength with shorter elution times. Note that the solvent strength is compound specific.
For non polar sorbents with silica substituted by C8 or C18 alkyl chains, common for RP ( reversed phase ) HPLC, the strength order is reversed as well.
The ideal elution time is 2-4 times the column "dead time" of passing the column without any retention.
If compounds leave the column too fast they would not be separated well.
If they leave the column too slowly,  elution would take too long time and chromatographic peaks would be too broad.
In the case of RP HPLC, pure methanol may lead to too short elution times, pure water to too long times.
Selectivity
Various analytes have various interaction with particular solvents, leading to various elution times.
Major contributions to solvent polarity are:

dipole dipole interaction
solvent acidity ( Bronsted, Lewis )
solvent basicity ( Bronsted, Lewis )

That leads to different positions of chromatographic peaks and their mutual separation for various mobile phases.
Each pure solvent has its own combination of the above contributions.
The optimal combination usually happens to be somewhere between properties of pure solvents, therefore mixing is necessery.
For the common reversed phase HPLC with non polar column, the frequent procedure to determine the proper mobile phase is this.

Find the methanol-water solution to get elution time of the main/reference component as 2-4 times the dead time.
If peak separation  is not satisfactory, find the solutions acetonitrile-water and tetrahydrofurane-water with the about same elution time of the main/reference component. The rule of thumb is: 50% methanol, 40% acetonitrile and 30% THF have about the same general "solvent strength".
Try combinations of the above 3 mobile phases to get the optimal separation of peaks.
In case the analytes have significant acido-basic behaviour, there are usually used buffer solutions, instead of pure water, for better and consistent distinguishing of their dissociation.
There is often used gradient HPLC with progressively increasing solvent strength to compress chromatograms. But it is usable for shifting the solvent selectivity as well.

See  Using a Solvent Triangle to Optimize an HPLC Separation
Selectivity in reversed phase LC separations - part 1 - solvent-type selectivity.

It depends on what you want to separate or purify on your column as well as what type of column you have.
Generally, you will run many normal phase columns with varying mixtures of hexane and ethyl acetate and most reverse phase columns with acetonitrile and water or methanol (each lab usually has its two standard solvents for given HPLC systems and rarely deviates). Each solvent has a certain polarity as does the column. Neither of these are variable. But the compound you want to purify can have all sorts of polarities from the polar end of what is separable on said column to the nonpolar end.
For most compounds, there will be a ratio of the two solvents generally used that is ‘best’ for separation, whichever goal is most important (time saving, purity, a certain persistent impurity to be removed or something else). But it does happen now and again that the ideal solvent for a given application is ‘100 % A’ or ‘100 % B’. I have had it happen to me but I can’t recall what the system was.
Outside of the isocratic argument above, many HPLC runs are gradient runs, meaning you start at 100 % A and end at 100 % B (or whichever ratios are best for your application). This allows for a better overall separation, especially when you have both polar and less polar compounds to separate. Of course, running gradients is impossible with only one solvent.


text:
Out of CaCO3 and MgCO3, which has higher electrical conductivity of molten solution?
According to me, Mg will be more hydrated and so should have lesser conductivity. Is that correct?

The 'hydration' makes this question very unclear.

This question needs to be fixed: neither carbonate is soluble in water and neither melts without decomposition to the respective oxide. If the question is about transport coefficients or whatever, it should ask that. Otherwise, the question should be on hold or closed.

"Molten solution" is a contradiction in terms.

@EdV - but they do melt, just not at STP in air. For example https://www.geochemicalperspectivesletters.org/documents/GPL1813_noSI.pdf - Properties of molten CaCO3 at high pressure - important in earth sciences.

@IvanNeretin - would 'liquid solution' be better? Consider a mixture of liquid CaCO3 and MgCO3. I have no idea whether it would phase separate into two incompatible liquids or not.

@JonCuster Quite honestly, do you really think this is what the question is about? The OP should replace this with a well-formed question and title. Otherwise, it is just leading to non-productive mind reading.

@EdV - honestly I think the question is quite unclear, and have voted to close based on that. But, there seem to be a lot of assumptions and statements being made based on those assumptions. Yes, those compounds melt, and I bet the different ions in the melt have different mobilities.

Do you really think molten inorganic salts will have a trace of water? Second question is do these carbonates melt? Don't mix molten state with aqueous state. No correlation.
When these compounds are heated both MgO and CaO are formed releasing carbon dioxide. They don't like to melt at all. Have you heard of limelight? This comes from CaO glowing brightly at high temperatures.

And the connection of this answer to conductivity is what, exactly?

The answer is basically reductio ad absurdum of the original query of molten calcium carbonate and magnesium carbonate. If someone can actually melt them without decomposition, then they should enlighten us. If molten means aqueous state, then it is another story.

You are thinking too narrowly, seemingly limiting your response to STP in air.

Consider papers such as http://www.electrochemsci.org/abstracts/vol13/131009771.pdf titled "Effect of Temperature and Voltage on the Preparation of Solid
Carbon by Electrolysis of a Molten CaCO3-Li2CO3-LiCl
Electrolyte"

Sure, interesting idea but that is a special case when we melt CaCO3 in a certain atmosphere or in the presence of other salts. The OP should clarify the question. It makes no sense as written. "Molten" is not compatible with "hydration."

I fully agree the 'hydration' suggests the question is unclear. But we do plenty of chemistry under non-STP conditions (and I don't want to be anywhere near molten CaCO3 or MgCO3 live and in-person).

"Molten" here probably means "liquid".  While the carbonates gave too little solubility to be considered for electrolyte, we can compare the conductances of $\ce{Ca^{2+}}$ and $\ce{Mg^{2+}}$ in dilute solution.  In this reference from the USGS, conductances from various common ions are given and, indeed, calcium ion has a greater conductance than magnesium ion in solution.  But the difference amounts to only a few percent for the overall conductivity of a chloride salt solution at a given concentration.


text:
IRC analogue of conical intersections and minimum energy crossing points?
In my project, there are some spin forbidden organometallic reactions that involves both the triplet minima and singlet transition state (TS). Using the penalty method in qchem as well the method of Harvey, two candidate structures of the minimum energy crossing point (MECP) were identified. However, these two structures, while similar in energy, do not agree with each other in geometry.
Since these structures are not stationary points, IRC is not applicable to check whether one or both of these structures connect to the aforementioned TS and mins. Are there any known systematic methods in DFT (because CASSCF is impractical for molecules this big) to check connectivity of a MECP to specific TS and mins besides the more brute force method of checking vibrational mode surfaces and look for degeneracy when scanning along them?


text:
In Flame Emission Spectroscopy, what part of the flame is used to measure the concentration of the analyte?
Flame Emission Spectroscopy is an analytical measuring device that relates the intensity of the emitted light relative to to the concentration of the sample.
As I am reading an article about FES, I noticed how the author purposely inserted the different parts of the flame and their activity.

The above image was from an article in Chemistry LibreTexts about FES.
The author said "The Primary Combustion Zone is where the initial decomposition occurs and molecular fragments are observed. The Interzonal Region is the hottest part of the flame and atomic fragment are observed. The Secondary Combustion Zone is cooler overall and a conversion is seen from atoms back to stable molecules and oxides."
I have read the article but it was never mentioned what part of the flame does the transducer or sensor was placed on.

I have read the article but it was never mentioned what part of the flame does the transducer or sensor was placed on.

It was never mentioned because no sensor or transducer is actually placed on or in the flame. What spectroscopist do is that they focus the light (coming from the flame) into a device called the monochromator. The job of the monochromator is to separate the wavelengths of the light from the flame. The desired wavelength is then focussed on the detector. Thus the detector is really far from the actual flame.
Now the key question is which part of the flame is useful. There is no single correct answer. The criterion is we scan the height of the flame and check which part of the flame is showing the maximum intensity of the desired signal. This is done by changing the height of the burner. Most spectrometers do it automatically but old lovely instruments had knobs for manual adjustment.
Normally for most elements one would like to see the hottest part of the flame, where the concentration of the atomic emission is the highest.


text:
Point group of cis- and trans-decalin
What is the point group of of cis- and trans-decalin?

I watched a video saying that it is $C_\mathrm{2h}$ for cis-isomer, but my friend says it is $D_\mathrm{2h}.$ I'm so confused.

D2h should contain quite a few mirror planes. Where are they?

Please edit to add a link to the video (link to your friend is not necessary).

This video gets it right: https://www.youtube.com/watch?v=GERJoub3LVo

cis-Decalin
Here is a view of cis-decalin with the bridging C-C bond in the plane of the paper:

(It was made using the Jmol software, e.g. at https://chemapps.stolaf.edu/jmol/jsmol/simple.htm using the "Load by name" button and entering "cis-decalin".) At https://www.chemtube3d.com/stdecalinflips/, you can see that this can flip into the mirror image (much like a cylcohexane chair flip).

What is the point group of of cis-decalin?

I see a two-fold axis (perpendicular to the paper). I don't see a center of inversion or any mirror planes; the molecule looks chiral (the flip mentioned above changes it to its mirror image). So maybe C2?
trans-Decalin
Here is a view of trans-decalin with 5 carbons closer to us and 5 further away from us:

I see a center of inversion, a mirror plane (left:right swap), and a two-fold horizontally in the plane of view. I guess that's C2h.

Related: Does trans-decalin really have a plane of symmetry? Trigger warning: You might be watching the gif forever...

I have run some conformational checks on the structures. The maximum point group for cis-decalin is as you propose C2. For trans-decalin, we do indeed find C2h as already stated. There are other (higher-energy) conformations with twist-boat rings in their conformations, which (mostly) would be of C1 symmetry.


text:
Defining the position of equilibrium
I've read quite a few other answers on this site such as this one, but can't quite seem to understand fully yet.
Say we have a container with gases reacting such that the number of moles on both sides of the equation are not equal. If we then, for instance, reduce the volume of the container, the total pressure increases and the value of the quotient Q will also change. The net reaction then favours a particular direction so that the mole fractions change sufficiently for Q to return to the value of K, which remains constant.
This is commonly described by saying equilibrium shifts to either the left or the right. Whilst it is true that after the system has again reached equilibrium the mole fractions have changed (so in a sense, the new equilibrium has shifted to one side in terms of number of moles), the value of Q is equal to its initial value so in this sense the position of equilibrium as defined by K has not changed.
The same applies to changing the concentration of a species; the actual concentrations of every species after the system has re-equilibrated will be different, however the value of Q will have returned to its previous value.
The only situation that I can think of where the position of equilibrium actually shifts is when a change in temperature alters the value of K.
My question is, essentially, is the term 'position of equilibrium' more of a qualitative descriptor of the composition of reactants and products? I initially thought it meant the value of Q at equilibrium (or K), but evidently in gaseous reactions the equilibrium yield does change with changes in pressure though K remains constant, so such a definition would not work.
Thank you!

Yes, the 'position of equilibrium' is but a vague descriptor and certainly not the value of Q. Then again, vague as it is, you can tell quite definitely the direction of its change: if you run the forward reaction, it shifts to the right, and vice versa.

The equilibrium constant is just that at a given temperature, constant, but perhaps the position of equilibrium could be understood by calculating the degree of dissociation in a reaction such as $\ce{A2 <=>2A}$

"Shifting" an equilibrium
Unfortunately for learners of chemistry, statements like "the equilibrium shifts to the right" are quite common jargon.
What is meant by this, speaking in more accurate technical terms, is the following: A reaction had reached equilibrium (net reaction is zero), and then some change occurred so that it was no longer in equilibrium. Now, there is a net forward reaction in the direction of the products ("to the right" refers to reactants turning into products).
"Shifting to the left" describes a similar sequence of events, just in the reverse direction.
New equilibrium or reestablish equilibrium?
The OP is correct in saying that unless the temperature changed, the equilibrium constant does not change, and the reaction quotient Q of the first equilibrium state is equal to that of the second. So you could say you are back to the same equilibrium.
Typically, however, the mole fractions, concentrations or partial pressures will be distinct for the first and the second equilibrium. So you could also say the reaction reaches a new equilibrium.
If you say it reaches equilibrium again, you are sufficiently vague to be correct.
Position of equilibrium
The term "position of equilibrium" is ill-defined. To avoid any confusion, it is better to distinguish between reaction quotient (which is equal to the equilibrium constant for both the first and second equilibrium) and the set of concentrations (which is typically different).

For graphs to illustrate, see here