text:
Is it necessary to write state symbols in ionic equations and if so, why?
I understand that it is necessary to use state symbols in an equation with compounds shown, such as:
$$\ce{NaCl(aq) +AgNO3 (aq) -> NaNO3 (aq) +AgCl(s)}$$
But is it necessary to use state symbols for a complete ionic equation, such as:
$$\ce{Na+ +Cl- +Ag+ +NO3- -> Na+ +NO3- +AgCl}$$
And if so, why? Can the ions be said to be dissolved in the solvent, or can that only be said for the compound made up of those ions?

Notation is great especially when there is ambiguity. If it's clear that you're doing solution chemistry, I don't see the problem with omitting the state label. Technically, this could be a gas phase reaction, but it's unlikely. And obviously, if you're being graded on writing these, you should do whatever is asked.

Actually, what you have shown is not an ionic equation. By convention (or definition?), an ionic equation does not show the "spectator ions" (i.e. those that do not take part in the reaction). In this case, the ionic equation should not show the sodium and nitrate ions. It should only show the silver (I) and chloride ions.

Hi, Tan Yong Boon. Thanks for the feedback. I intended for the second equation to be a complete ionic equation rather than a net ionic equation, but I agree that it would have been better to use a net ionic equation.

Pinging @TanYongBoon because the OP didn't do it correctly.

It is of extreme importance to state that the dissolution is happening in water, otherwise it could be mistakenly interpreted as a reaction in the gas state (most measurements of dissociation and other energies related to ionic compounds are done in the gas phase, not liquid solutions). If you are writing a sentence and mention that the dissolution is happening in aqueous media, then it's not that important to write the state symbols beside every reagent/product, but if you don't specifically mention it somewhere else then you should write all the details (remember science do not tolerate ambiguity, except for quantum physics haha).

Well if there are only dissolved ions you could (theoretically) leave the state symbols away if it is clear that you're working with solutions.
But it is just a matter of form and definitely not bad to have them there for reasons of clarity and comprehensibility.


text:
What is the nature of the Fe–O2 binding in oxymyoglobin and oxyhemoglobin?
Deoxymyoglobin ($\ce{Mb}$) is known to have iron in the +2 oxidation state; I believe this was deduced from its magnetic moment, which corresponds to four unpaired electrons in high-spin $\mathrm{d^6}$ Fe(II).
However, upon binding of $\ce{O2}$ (which is itself paramagnetic) to Mb, the resultant complex oxymyoglobin ($\ce{MbO2}$) is found to be diamagnetic.
This observation has been rationalised in several ways over the years. As far as I know, the two main camps are:

The oxygen ligand binds to low-spin Fe(II) in the form of singlet oxygen, via $\ce{O2}\rightarrow\ce{Fe}$ σ donation and $\ce{O2}\leftarrow\ce{Fe}$ π backdonation, which mirrors the binding mode of the isoelectronic $\ce{NO-}$. Neither metal nor ligand possesses unpaired electrons;
Fe(II) is oxidised to Fe(III), with reduction of $\ce{O2}$ to $\ce{O2-}$; thus both the metal and the ligand possess one unpaired electron. These two electrons interact via antiferromagnetic coupling to produce a singlet state.

The former viewpoint was championed by Linus Pauling, and the latter by Joseph Weiss, leading to a rather heated debate in Nature.1–3
These descriptions of myoglobin of course also apply to hemoglobin, where each monomer is structurally similar to myoglobin.
What experimental evidence supports either side, and is there any general consensus as to which is correct?

References
1. Weiss, J. J. Nature 1964, 202 (4927), 83–84. DOI: 10.1038/202083b0.
2. Pauling, L. Nature 1964, 203 (4941), 182–183. DOI: 10.1038/203182b0.
3. Weiss, J. J. Nature 1964, 203 (4941), 183. DOI: 10.1038/203183a0.

Would this be any help?

TL;DR: It is not really "one or the other" - it is more of "somewhere in between", like a resonance hybrid. If I had to choose, I'd personally lean towards Weiss's $\ce{Fe(III)-O2-}$ model. However, there will always be people who disagree, and there is still no general consensus amongst the scientific community.
There is an excellent - and recent - perspective article by Bren et al.,1 describing the research carried out on the structure of hemoglobin ever since Pauling and Coryell's initial report2 on the diamagnetism of oxyhemoglobin.

Model systems
A common technique in bioinorganic chemistry is to synthesise "inorganic versions" of enzyme active sites; for example, much work has been done on dinitrogen complexes in the hope of understanding the enzyme nitrogenase. Myoglobin and hemoglobin are not enzymes in the strict sense of the word,3 but the same technique applies: if stable $\ce{Fe(II)-O2}$ complexes could be synthesised, they might prove to be more amenable to experimental investigation.
The main problem was the fact that dioxygen readily oxidised simple Fe(II) complexes to Fe(III). Initially, Co(II) complexes (which only have one unpaired electron) were used: EPR studies showed that the unpaired electron was localised on oxygen,4,5 and the length of the O–O bond resembled that of superoxide:6
$$\begin{array}{ccccc}
\text{Species} & \ce{O2^2-} & \ce{O2^-} & \ce{O2} & \ce{Co(II)-O2}\text{ complex} \\ \hline
\text{Bond order} & 1 & 1.5 & 2 & ? \\
\text{Bond length / Å} & 1.49 & 1.28 & 1.21 & 1.26
\end{array}$$
Of course, Co(II) complexes do not necessarily have the same electronic structure as their Fe(II) counterparts, so such data can only be of limited use. The key to overcoming the early difficulties (of Fe(II) oxidation) was the fact that such oxidations tend to proceed via dimerisation; therefore, if a sterically hindered Fe(II) complex could be made, the oxidation could be prevented. Based on this, Collman and coworkers synthesised so-called "picket fence" complexes,7 which reversibly bound dioxygen, the concept of which is shown below:

Access of other iron centres, as well as the imidazole ligand, to the top face of the metal ion was blocked by the bulky substituents on the porphyrin ring (in one example, $\ce{-C6H4NHC(O)^tBu}$ was chosen). The reported data from different "picket fences" strongly favoured the iron(III)–superoxide model: in particular, the O–O stretching frequencies ranged from $1163\text{–}\pu{1150 cm−1}$ (cf. $1200\text{–}\pu{1050 cm−1}$ in superoxide complexes, $\pu{1556 cm-1}$ in $\ce{O2}(^3\Sigma_\mathrm{g}^-)$, and $\pu{1484 cm-1}$ in $\ce{O2}(^1\Delta_\mathrm{g})$).8

A controversy over magnetic data
It was realised that a key difference between the two schemes was in their predicted magnetic susceptibilities. For the $\ce{Fe(II)-O2}$ binding scheme, one would expect the compound to be diamagnetic at all accessible temperatures (to obtain a magnetic state would require electronic promotion). On the other hand, the $\ce{Fe(III)-O2-}$ binding scheme would be expected to have a temperature-dependent magnetic susceptibility, as antiferromagnetic coupling could be overcome with higher temperatures. In other words, there is a thermally accessible triplet state.
In 1977, Cerdonio et al. published a paper claiming to have observed a temperature-dependent magnetic susceptibility for $\ce{HbO2}$.9 However, their findings were refuted in a later 1984 paper by Savicki et al., which found that $\ce{HbO2}$ was in fact diamagnetic at all temperatures.10 The incorrect magnetic data was attributed to residual deoxyhemoglobin, which is paramagnetic, and in a private communication with Savicki, Cerdonio agreed that his earlier findings were in error.

Spectroscopic data on the proteins
Using infrared spectroscopy, the O–O stretching frequencies in both oxymyoglobin11 and oxyhemoglobin12 were identified as $\pu{1103 cm−1}$ and $\pu{1107 cm-1}$ respectively, again consistent with superoxide.
Furthermore, $\ce{^57Fe}$ Mössbauer spectra of $\ce{HbO2}$ showed large quadrupole splittings, which is consistent with iron being in the +3 oxidation state.13

Computational studies
Early quantum mechanical calculations by Karplus14 showed that the properties of $\ce{HbO2}$ could be explained by a mixture of two $\ce{Fe(II)-O2}$ resonance forms: one with both bonding partners in the singlet state, and one with both in a triplet state. The latter was actually put forth as a separate - third - model, most notably by Goddard in 1975.15
Of course, these are fairly primitive by today's standards. In 2008, Shaik et al. revisited the topic,16 and provided an overview of the numerous computational studies performed up until then, which had failed to reach a conclusion. Instead of trying to discern the appropriate bonding model from indirect parameters, such as the net charge on oxygen or the form of the occupied MOs, the authors opted to transform a CASSCF wave function into a generalised valence bond wave function. They concluded that the Weiss $\ce{Fe(III)-O2-}$ model was dominant for a gas-phase oxygen–heme complex, and that the interaction with the protein further reinforces the $\ce{Fe(III)-O2-}$ character of the wave function.

More recent experimental work
In an entirely separate endeavour, Gray and coworkers found that polyhalogenated iron porphyrins, which possessed unusually high Fe(III)/Fe(II) reduction potentials, did not bind to oxygen.17 This has been taken as evidence for the necessity of electron transfer from Fe(II) to dioxygen in $\ce{Hb-O2}$ binding, and hence the identification of the bonding as being $\ce{Fe(III)-O2-}$ charge-transfer in nature.
X-ray absorption spectra by Wilson et al. further complicate the matter, though. Firstly, their investigation of picket fence porphyrins led to the conclusion that these generally showed characteristics of both models, but were more in line with an Fe(II) description. The effective nuclear charge on iron was found to be closer to that of Fe(II) than to that of Fe(III), and the spectra lacked a low-energy transition characteristic of Fe(III) complexes (arising from the hole in the $\mathrm{t_{2g}}$ orbitals on iron).18
A further study on the protein itself revealed that crystalline $\ce{HbO2}$ mainly has $\ce{Fe(II)-O2}$ character, whereas solution $\ce{HbO2}$ has $\ce{Fe(III)-O2-}$ character.19 They therefore concluded that the bonding was multiconfigurational in nature, and that "secondary changes in the protein environment, crystal packing, and so forth, can tip the electronic structure in either direction".

Notes and references
1. Bren, K. L.; Eisenberg, R.; Gray, H. B. Discovery of the magnetic behavior of hemoglobin: A beginning of bioinorganic chemistry. Proc. Natl. Acad. Sci. 2015, 112 (43), 13123–13127. DOI: 10.1073/pnas.1515704112.
2. Pauling, L.; Coryell, C. D. The Magnetic Properties and Structure of Hemoglobin, Oxyhemoglobin and Carbonmonoxyhemoglobin. Proc. Natl. Acad. Sci. 1936, 22 (4), 210–216. DOI: 10.1073/pnas.22.4.210.
3. Hemoglobin is famously known as an "honorary enzyme"; for an overview of its history, see e.g. Brunori, M. Hemoglobin is an honorary enzyme. Trends Biochem. Sci. 1999, 24 (4), 158–161. DOI: 10.1016/S0968-0004(99)01380-8.
4. Hoffman, B. M.; Diemente, D. L.; Basolo, F. Electron paramagnetic resonance studies of some cobalt(II) Schiff base compounds and their monomeric oxygen adducts. J. Am. Chem. Soc. 1970, 92 (1), 61–65. DOI: 10.1021/ja00704a010.
5. Getz, D.; Melamud, E.; Silver, B. L.; Dori, Z. Electronic structure of dioxygen in cobalt(II) oxygen carriers, singlet oxygen of dioxygen(1-). J. Am. Chem. Soc. 1975, 97 (13), 3846–3847. DOI: 10.1021/ja00846a064.
6. Gall, R. S.; Rogers, J. F.; Schaefer, W. P.; Christoph, G. G. The structure of a monomeric oxygen carrying cobalt complex: dioxygen-N,N'-(1,1,2,2-tetramethyl)ethylenebis(3-tert-butylsalicylideniminato)(1-benzylimidazole)cobalt(II). J. Am. Chem. Soc. 1976, 98 (17), 5135–5144. DOI: 10.1021/ja00433a015.
7. Collman, J. P.; Gagne, R. R.; Reed, C. A.; Halbert, T. R.; Lang, G.; Robinson, W. T. Picket fence porphyrins. Synthetic models for oxygen binding hemoproteins. J. Am. Chem. Soc. 1975, 97 (6), 1427–1439. DOI: 10.1021/ja00839a026.
8. Collman, J. P.; Brauman, J. I.; Halbert, T. R.; Suslick, K. S. Nature of O2 and CO binding to metalloporphyrins and heme proteins. Proc. Natl. Acad. Sci. 1976, 73 (10), 3333–3337. DOI: 10.1073/pnas.73.10.3333.
9. Cerdonio, M.; Congiu-Castellano, A.; Mogno, F.; Pispisa, B.; Romani, G. L.; Vitale, S. Magnetic properties of oxyhemoglobin. Proc. Natl. Acad. Sci. 1977, 74 (2), 398–400. DOI: 10.1073/pnas.74.2.398.
10. Savicki, J. P.; Lang, G.; Ikeda-Saito, M. Magnetic susceptibility of oxy- and carbonmonoxyhemoglobins. Proc. Natl. Acad. Sci. 1984, 81 (17), 5417–5419. DOI: 10.1073/pnas.81.17.5417.
11. Maxwell, J. C.; Volpe, J. A.; Barlow, C. H.; Caughey, W. S. Infrared evidence for the mode of binding of oxygen to iron of myoglobin from heart muscle. Biochem. Biophys. Res. Commun. 1974, 58 (1), 166–171. DOI: 10.1016/0006-291X(74)90906-1.
12. Barlow, C. H.; Maxwell, J. C.; Wallace, W. J.; Caughey, W. S. Elucidation of the mode of binding of oxygen to iron in oxyhemoglobin by infrared spectroscopy. Biochem. Biophys. Res. Commun. 1973, 55 (1), 91–95. DOI: 10.1016/S0006-291X(73)80063-4.
13. Lang, G.; Marshall, W. Mössbauer effect in some haemoglobin compounds. Proc. Phys. Soc. 1966, 87 (1), 3–34. DOI: 10.1088/0370-1328/87/1/302.
14. Case, D. A.; Huynh, B. H.; Karplus, M. Binding of oxygen and carbon monoxide to hemoglobin. An analysis of the ground and excited states. J. Am. Chem. Soc. 1979, 101 (16), 4433–4453. DOI: 10.1021/ja00510a001.
15. Goddard, W. A., III; Olafson, B. D. Ozone Model for Bonding of an O2 to Heme in Oxyhemoglobin. Proc. Natl. Acad. Sci. 1975, 72 (6), 2335–2339. DOI: http://10.1073/pnas.72.6.2335.
16. Chen, H.; Ikeda-Saito, M.; Shaik, S. Nature of the Fe−O2 Bonding in Oxy-Myoglobin: Effect of the Protein. J. Am. Chem. Soc. 2008, 130 (44), 14778–14790. DOI: 10.1021/ja805434m.
17. Grinstaff, M. W.; Hill, M. G.; Labinger, J. A.; Gray, H. B. Mechanism of catalytic oxygenation of alkanes by halogenated iron porphyrins. Science 1994, 264 (5163), 1311–1313. DOI: 10.1126/science.8191283.
18. Wilson, S. A.; Kroll, T.; Decreau, R. A.; Hocking, R. K.; Lundberg, M.; Hedman, B.; Hodgson, K. O.; Solomon, E. I. Iron L-Edge X-ray Absorption Spectroscopy of Oxy-Picket Fence Porphyrin: Experimental Insight into Fe–O2 Bonding. J. Am. Chem. Soc. 2013, 135 (3), 1124–1136. DOI: 10.1021/ja3103583
19. Wilson, S. A.; Green, E.; Mathews, I. I.; Benfatto, M.; Hodgson, K. O.; Hedman, B.; Sarangi, R. X-ray absorption spectroscopic investigation of the electronic structure differences in solution and crystalline oxyhemoglobin. Proc. Natl. Acad. Sci. 2013, 110 (41), 16333–16338. DOI: 10.1073/pnas.1315734110.

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text:
What is the definition of porous materials?
Is there a consensus on scientific definition of porous materials? There are many definitions out there which do not seem accurate enough:
from wikipedia (accessed July 2017):
A porous medium or a porous material is a material containing pores (voids).
-problem : Then almost all materials are porous, since there is some sort of void in everything.
from Merriam Webster (website accessed July 2017):
Containing pores, permeable to fluids, capable of being penetrated.
-problem : A piece of tubing would be porous since fluid passes through it.
At what scale do we consider the pores to qualify a material as porous? How much does the permeability matter in a formal definition? Is there a convention on defining pores and porous materials that is agreed upon by scientific organizations like IUPAC or ASTM etc?

It all depends on your scale. A cellophane membrane is impermeable to starch but porous to water. Gold appears to be non-porous, but mercury poured on it soaks in, leaving a silvery stain until it disperses throughout the gold.

Mercury is dissolving gold. Permeable means can go through generally most of the liquid.

"some sort of void" in everything? Not in most substances unless you call the space between electrons and protons a void. Even then this is practically irrelevant as the space isn't accessible in any meaningful way as interactions between atoms are controlled by the electrons. Most solids are not porous in practice. And tubing isn't a material, it is an object and it would be pretty poor tubing if it were porous to the flowing substance across the walls of the tube.

@matt_black a lower bound for pore size / void size should be defined as well a definition of material vs object. Many synthesized and modified porous materials are made up of non-porous wall and could be perceived as object.

I have used the following definition in my presentations:
"Porosity is where a material has accessible voids which are permeable to liquids or gases".
Another definition:
"a  solid with pores, i.e. cavities, channels or interstices, which are deeper than they are wide."
IUPAC also defines different types of porosity based on the diameters of the pores:

Micropores: d < 2 nm
Mesopores: 2 < d < 50 nm
Macropores: d > 50 nm

M. Thommes, K. Kaneko, A. V. Neimark, J. P. Olivier, F. Rodriguez-Reinoso, J. Rouquerol, K. S. W. Sing, Physisorption of gases, with special reference to the evaluation of surface area and pore size distribution (IUPAC Technical Report), Pure Appl. Chem. 2015, 87, 1051.

Although this answer is helpful it is directed towards defining porosity not porous materials. The question is rather to distinguish between porous and nonporous material. What level of porosity is agreed upon to qualify a material as porous? 1%, 30%, 80% ? Is there a consensus at all? Is there any informal definition anywhere?

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text:
Principle of detailed balance
$$\ce{A -> B -> C -> A}$$
In Alberty's Physical Chemistry (7th ed.), the author says that this reaction mechanism is not possible. The reason given is:

Although this mechanism at first sight appears reasonable, no actual process follows this mechanism because it violates the principle of detailed balance. According to this principle, at equilibrium the forward rate of each step is equal to the reverse rate of that step. Thus equilibrium cannot be maintained by this mechanism.

I understand the statement of the principle ("at equilibrium the forward rate of each step is equal to the reverse rate of that step"), but I don't get how it implies that equilibrium cannot be maintained, or that this reaction is not possible.

The whole thing looks like this https://en.wikipedia.org/wiki/Detailed_balance#Detailed_balance_for_systems_with_irreversible_reactions and I am not sure what point they are trying to make.

So, technically speaking, you could imagine $\ce{IBrClC-CH2Cl}$. There are three staggered conformations that could interconvert in exactly the reaction scheme provided. They are all in equilibrium. This essentially refutes the statement from the book.

@Zhe according to the Wikipedia page linked by Karl, Rudolf Wegscheider proved such a reaction scheme wasn't possible. I doubt the statement is wrong, so my guess is the confusion arises due to the scheme described by Wegscheider not matching what you provided.

Whoa, whoa. The steps are supposed to be irreversible? My example does not at all conform to that. @Tyberius I'll think about the reaction again in this context.

Yes, I think the problem is irreversibility here.

Note that the proof is that irreversible cycle $\ce{A -> B -> C -> A}$ is not possible. Zhe's comment describes a reversible process.

What I am surprised of, is that I never encountered the terminology before. Still we said that such a cycle would violate the second law. Is it no so?

Interesting question. It doesn't make sense to talk about a fully irreversible reaction (which has no reverse rate constants), when also asserting that the forward and reverse rates of each step must be the same. The matter at hand seems to be more subtle than that. Quoting from the Wikipedia page that Karl linked: "... one represents irreversible reactions as limits of reversible steps [...] not all reaction mechanisms with irreversible reactions can be obtained as limits of systems or reversible reactions with detailed balance".

In this triangular scheme, taking it literally, it is clear that all the population will end up in species C. If $A \rightarrow B$ is mathematically irreversible (rate constant back is zero)  it implies that B is at an energy infinitely below that of A, and the energy of C infinitely below that of B, so clearly C cannot revert to A without the input of an infinite amount of energy. Such an argument hardly makes sense in chemistry, however.
If we now assume that the reaction is reversible but with a very small back rate constant a similar conclusion is obtained, i.e. that the overwhelming (but not total) population ends up in C.
Suppose, without loss of generality and for simplicity, that the activation energy A/B and B/C are the same at $E_A$ and that B is at energy E below A, and C at E below B. Now let the forward rate constant A to B be $k_f=k_0\exp(-E_A/RT) $ and the back rate constant is $k_{BA}=k_0\exp(-E_A/RT)\exp(-E/RT)$ and which is going to be smaller, say it is $10^{-3}$ smaller. The rate constant from C to A is therefore $k_{CA}=k_0\exp(-E_A/RT)\exp(-2E/RT)$ which is now $10^{-6}$ times smaller that the rate constant A to B.

I think your anwer is reasonable, I will accept it after waiting for sometime. Thank you.


text:
What is HZSM-5?
What is HZSM-5? I have seen it used as a catalyst support in literature. It seems to be related to the ZSM-5 zeolite, but I am not sure how.

see http://www.chemicalforums.com/index.php?topic=34583.0 $\ce{H^+}$ instead of $\ce{Na^+}$ at ion exchange site.

It can also be used as an acid catalyst in its own right

According to this article(1), the difference between the zeolites HZSM-5 and ZSM-5 is that the first has a monoclinic and the second has an orthorhombic framework.
(1) H. van Koningsveld, J.C. Jansen, H. van Bekkum, The monoclinic framework structure of zeolite H-ZSM-5. Comparison with the orthorhombic framework of as-synthesized ZSM-5, Zeolites, Volume 10, Issue 4, 1990, Pages 235-242


text:
PBE vs. PBEPBE functional
I've found good explanation what the PBE functional is. However, sometimes I see PBEPBE and I cannot find any good information about what this means and how it's different from PBE.
The Gaussian manual explains PBE and also provides the reference but at other points they talk about PBEPBE without any reference.
Can someone explain the difference? Does the second PBE just describe some kind of modification?

Is it PBEPBE or PBE1PBE? The PBE1PBE functional, aka PBE0, would be a hybrid functional based on the PBE GGA functional.

@Philipp PBEPBE. But Feodoran already  cleared up the confusion.

The designation PBEPBE is an actual terrible artefact from researchers using Gaussian. The actual publication[1, 2] only refers to it as PBE, and most other program packages (I know) implement it as such. Often they make the correlation and exchange parts separately available via PBEC and PBEX, or similar. Unfortunately this designation also made it into the literature.
The confusion further continues since Gaussian uses the PBE1PBE designation for the (standalone) hybrid functional, which is in most other packages known as PBE0.
But it doesn't stop there, for TPSS you may find similar naming/ reference schemes. The BP86 functional keyword requests the VWN(III) version, while many other programs use VWN(V) for this. The latter is available via BVP86, but misses any implementation of dispersion. We could go on with this...
In the end what is important is the correct referencing of the methodology so that the results are reproducible, i.e. look at the literature cited. Gaussian actually does a good job referencing those sources. And when you publish, you'd do us all a favour and not use the keyword designations of Gaussian.
[1] John P. Perdew, Kieron Burke, and Matthias Ernzerhof, Phys. Rev. Lett. 1996, 77, 3865. DOI: 10.1103/PhysRevLett.77.3865. Mirrored at Burke's page: dft.uci.edu/publications.php
[2] (Erratum) John P. Perdew, Kieron Burke, Matthias Ernzerhof, Phys. Rev. Lett. 1997, 78, 1396. DOI: 10.1103/PhysRevLett.78.1396

My old group has combined the Becke 88 exchange functional with PBE correlation before and designated this B-PBE, IIRC, for experiments on new GGA functionals. I thus believe that there is some merit to the Gaussian notation, although many of their choices are not good. The point about correct referencing cannot be stressed enough.

@TAR86 Yes, true, there should always be a possibility to arrange functionals differently, and a keyword simply is not the name of the method; unfortunately that does not mean it's not used as such. (I still think they could have made it clearer which one you actually are requesting.)

If you want to use a LDA or GGA functional in Gaussian you always need specify the desired Exchange and Correlation functional. In case of PBE you need to specify it twice, only using PBE will result in an error.
This is also explained in the online manual: http://gaussian.com/dft/ (Tab "Keyword: Pure Functionals")

Oh I seemed to have missed that sentence. So if people speak about PBE they always mean Exchange and Correlation functional being PBE?

I am not sure how PBE is defined, but I think it includes both, exchange and correlation functional. Therefore the term PBE refers to both of them as a pair. The doubling of the name is just a quirk of Gaussians input notation.

+1. Have you considered committing to Materials Modeling Stack Exchange? https://area51.stackexchange.com/proposals/122958/materials-modeling?referrer=MDk5MWVlYmU0NzI0YmM0OTFlODFjNGJhMWM0MGZmMWRlMTJlOTA5YjZmMjYxMzEwNjdhNDFjMDgyMzAwZjdkNQculOIiVn9BSLKjsBjz8Hk5MURzOmnxHOsZp0GKFt6k0

I came across this question by chance, and even if you already solved the problem, I wanted to add my contribution because of the many reads it keeps receiving.
Actually, that notation (which is common mostly in Gaussian) implies that you are specifying both the exchange and the correlation part of the functional. It assumes that you write the functional as exchangecorrelation altogether, i.e. PBEPBE uses PBE exchange and PBE correlation.
Following the same schemes, PBE1PBE (popular because of Gaussian, but it actually makes sense too) stands for "1 parameter hybrid" using PBE exchange and PBE correlation (it is the same as PBE0, as originally defined by Adamo and Barone). B3PW91, the first 3-parameter hybrid proposed by Becke stands for "3-parameter hybrid" using B88 exchange and PW91 correlation. Many other functionals are defined using this scheme. I hope this helps following readers!

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text:
Can't we reduce climate change by converting CO2 & CH4?
Straight off I want to say, I never took chemistry classes, so my understanding is very limited. My question is considering the equations below, why is it so hard to reduce greenhouse gases? Is it simply a matter of conversion requiring too much energy?
Can't we remove carbon dioxide & methane from the atmosphere by converting them into water and carbon?
$$\ce{CO2 + CH4 -> 2H2O + 2C}$$
Or by converting them into water and propane?
$$\ce{CO2 + 5CH4 -> 2H2O + 2C3H8}$$

One problem is that there's a couple hundred times as much CO2 as methane in the atmosphere. Also, there is the energy problem you brought up. Pretty much any reaction to convert atmospheric CO2 or methane to something else will be energetically uphill. Tough problem.

What about capturing it at the source of emission?

But then what do you do with it? There have been lots of ideas, like storing it at the bottom of the ocean, but anything like that will be costly. I think the best solution is to reduce production through conservation and alternative fuels, but we currently burn so much fossil fuels that even that transition is a long-term endeavor.

Well, for example one, it would be solid carbon, right? So it could be used to make graphene and other carbon nanostructures. So, for example, coal plants could make money from their waste. In example two, you could sell the propane. So, for example, industrial farms could make money from their waste.

Well your understanding is quite in track. Forget the equations you wrote but in principle yes it is possible to reduce CO2, obtaining new fuel or useful chemicals while reducing (or not increasing) the carbon content of the atmosphere. And again yes you are right, this is not really viable as it is an energy consuming process with limited efficiency. As in the case of water splitting to produce H2 as fuel, processes like these have cheap/ green energy production as prerequisite.

I see. It's a bit of a catch 22, then. Someone feel free to write up an answer so I can select it.

There are many such schemes as you suggest, most have one drawback or another as pointed out in the comments.  If it could be made to work properly 'carbon capture and storage' (ccs)  methods could be a good way of reducing atmospheric carbon dioxide.

The problem isn't the chemistry, it is the economics. If we knew a good way (other than growing plants) to sequester carbon from the atmosphere we would be very happy even if we didn't convert ti to fuel (|there are good ways to store CO2). But they all cost too much right now to be remotely practical. We need more and cheaper carbon-neutral energy plus better ways to capture the CO2.

There are a few problems with what you're proposing:

The reaction requires energy.
Where do get the methane from?
What will you do with the carbon you're generating?

The energy problem can be solved by using surplus energy from renewable source like solar and wind, but, as airhuff also mentiond in a comment, there is much more CO2 in the atmosphere than methane. Also capturing CO2 from the air isn't simple,  and finally why would you use a valuable fuel like methane to create carbon or propane?
In any case I think a much more useful reaction is
$$\ce{CO2 + 2H2O -> CH4 + 2O2}$$
Water is split into oxygen and hydrogen using electrolysis. The hydrogen reacts with carbon-dioxide to form methane.
There are already small plants that do this, but AFAIK the idea hasn't really caught on yet. This may have something to do with the cost and/or the availability of carbon dioxide or surplus energy.
More recently scientists did something even cooler; they captured CO2 directly from the atmosphere and turned it into methanol (CH3OH) using Ruthenium as a catalyst. A drawback is that the reaction works at high temperatures (about 150 degrees C).

Industrial farms. 3. If pure carbon, sell for use in graphene or bucky balls, etc??? If propane, sell as propane fuel?  "Why use methane to create...?" Because livestock manure and farts contribute to more than 1/3 of current methane emissions in addition to CO2. Also, it's my understanding that when methane hits ozone, even more CO2 (& H2O) is produced. So, if we capture these on-site, industrial farms could immediately & dramatically slow down climate change while also making a buck. "CO2+2H2O⟶CH4+2O2" But, global clean water supplies are dwindling as well. :/

IIRC the price of propane is lower than that of methane so if you can capture and isolate methane it's more economical to use that as a fuel. Perhaps carbon is an option but I think it depends on how high quality you can achieve.

I've been hearing about companies able to extract and concentrate carbon dioxide from ambient air, and was thinking about how it might be sequestered on sufficient scale to remove all excess carbon dioxide from the atmosphere. Pumping the carbon dioxide underground or at the bottom of the ocean would probably work but raises concerns about stability and leakage. It could be reacted with lime or other minerals underground to form stable minerals but the completeness of the reaction would be difficult to monitor. Converting it into methane makes the problem bigger, since then the methane has to be sequestered and it is a more potent greenhouse gas than carbon dioxide.
The carbon dioxide could be converted into carbon, such as by turning organic matter into biochar, and then it would be stable. But why reduce carbon dioxide all the way to carbon ($\ce{CO2 + 2 H2 -> C + 2 H2O}$) when it could be left at oxalic acid ($\ce{2CO2 + H2 -> C2O4H2}$), another stable solid? This could be accomplished electrochemically.
If we were to return the carbon dioxide in our atmosphere to pre-industrial levels (i.e., $\pu{280 ppm}$), it would require the removal of
$$(\pu{410 ppm} - \pu{280 ppm}) \cdot \frac{\pu{2.13 Gt C}}{\pu{1 ppm CO_{2}}} \cdot \frac{\pu{3.664 Gt CO_{2}}}{\pu{1 Gt C}} = \pu{1.01 Tt}$$
of carbon dioxide. This carbon dioxide could be converted into $\pu{1.04 Tt}$ of oxalic acid, with a volume of
$$\pu{1037797146168 t}\cdot\pu{907185 g/t}\cdot\frac{\pu{1 cm3}}{\pu{1.9 g}}\cdot\frac{\pu{1 m3}}{\pu{1000000 cm3}}\cdot\frac{\pu{1 km3}}{\pu{1000000000 m3}} = \pu{496 km3}$$
of clean, beautiful former coal. If we assume that the shape of this mountain approximates that of a pile of salt (where $\pu{1000 t}$ of salt forms a conical pile $67’1”$ in diameter and $40’$ along its slope having a volume of $\pu{25000 ft3}$), then we can calculate the height of that mountain using the fact that the ratio of the radius of a cone of a given shape to its height ($h^2 = \text{slope}^2 – r^2$) is constant, which is
$$\frac{r}{h} = \frac{33.54’}{21.80’} = 1.54.$$
The equation for a cone is
$$V = \frac{πr^2h}{3},$$
or
$$V = \frac{π(1.54h)^2h}{3} = 2.48h^3.$$
Solving for $h$ where $V = \pu{496 km3}$ gives $h = \pu{5.85 km}$, with $r = \pu{9.00 km}$. For comparison, Mt. Fuji is $\pu{3.78 km}$ high and a radius of about $\pu{22 km}$ at its base. Once paved to prevent it from dissolving in the rain, it could provide a convenient skiing location.
Of course, this still leaves the problems of building the factory to do this and supplying renewable energy to run the factory. This article proposes electrochemically reducing carbon dioxide into stable, storable forms to be sequestered, with a potential to reduce $\pu{967 g}$ of carbon dioxide to oxalic acid per kilowatt-hour of electricity. That comes out to at least:
$$\pu{1037797146168 t oxalic acid} \cdot \frac{\pu{1000000 g}}{\pu{1 t}} \cdot \frac{\pu{1 g CO_{2}}}{\pu{1.023 g oxalic acid}} \cdot \frac{\pu{1 kWh}}{\pu{967 g CO_{2}}} = \pu{1.05 * 10^15 kWh} = \pu{1.05 EWh}$$
of electricity needed to sequester the above excess carbon dioxide from the air (not counting the oceans) as oxalic acid.

If your calculations are right that is between 5% and 10% of all the world's electricity consumption (or, possibly, 2-3 times that if conversion efficiency is taken into account). We'd need to build a lot of nuclear plants to cover that and we'd need to spend a huge amount of capital for the conversion plants.

If the scale of the problem wasn't already large enough, it's actually about twice as large as you suggest; a roughly equal amount of anthropogenic $\ce{CO2}$ has been absorbed by the oceans, and must also be removed. Also, I would be wary of making such a massive pile of a highly water-soluble, relatively strong acid, as it would eventually make its way into the ocean. Perhaps it would be best stored as a metal oxalate, e.g. magnesium or calcium oxalate, though of course this significantly increases costs. Very interesting article, though.

@NicolauSakerNeto While checking my reference for the ppm/Gt CO2 figure I discovered that I had accidentally used the Gt C figure instead. After reworking my calculations above they are about 3.7 times worse (the ratio of the molecular weights of CO2 to C). I also shouldn't have worked out the energy required in my head, so I showed my work to get the new insanely large figure. It should be large, since it is only a few fold less than the total energy ever derived from fossil fuels. I think oxalic acid solubility would be the least of our problems since it could be generated in a desert, etc.

Shoot, I briefly thought that $\ce{CO2}$ sequestration as oxalic acid looked feasible with the prior value (relative to a back of the envelope calculation I did a while ago), but $\mathrm{1{\text -}2\ EWh}$ once again squarely puts it in the absolutely bonkers-level of difficulty to implement; that's 6-12 years of all primary energy (electricity + motion + heating) consumed by mankind in 2015. The scale of the problem just escapes comprehension...

This is a very monolithic suggestion. Perhaps it could be one of several sequestration techniques since the end product could be sold to producers of cleaning chemicals. But, a literal mountain of any one substance can't be healthy.

Yeah, if we put it all in one huge mountain, some crazy guy would surely come along and set fire to the thing!


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Chemical water treatment: Acid Base reaction
I was thinking of a hypothetical waste system that uses nanotechnology to its advantage.
At the individual level, waste just passes through into pipes when flushed like it normally does.
But once it reaches the water treatment plant there is an initial filter to catch solid waste(in other words poop) and divert it to a different part of the system where it gets dried and eventually ground into a biosolid that can be used as fertilizer.
Meanwhile all the urine, vomitus, blood, and any diarrhea that didn't get caught by the initial filter is passed through a series of filters to catch smaller and smaller waste products from cells all the way to molecules like urea being blocked with a nanofilter. Only a few compounds besides water are left. Yes there are still small ions like potassium and this might actually pose a problem.
But the real threat is that $\ce{HCl}$ is still in the water. Pepsin and other enzymes have been blocked by the nanofilters but $\ce{HCl}$ is still small enough to pass through all of the filters. A nanofilter that can block $\ce{HCl}$ is so impractical that it would most likely block the water itself until either the water treatment system or the microfilters and nanofilters burst from pressure and you end up with a critical failure either way.
So there has to be a chemical reaction that either deactivates the $\ce{HCl}$ and thus renders it harmless or a reaction that leaves no trace of $\ce{HCl}$.
I was thinking that to render the water safe, $\ce{NaOH}$ should be added to increase the amount of saltwater and totally get rid of the $\ce{HCl}$. But then I realized that with potassium and other ions besides sodium and chloride still in the water this could make the water toxic due to toxic salts forming.
Potassium chloride is the least harmful of all the salts that could form besides sodium chloride. Other than the bitter taste, there is basically nothing wrong with using potassium chloride. Similar for calcium chloride. Magnesium chloride though could cause diarrhea due to the magnesium(I know at least part of that diarrhea is from magnesium because the magnesium supplement I take helps to prevent constipation). I am not as worried about hydroxides because those would react with hydrogen ions to produce water.
But those salts are not the only problem. The other problem is how much $\ce{NaOH}$ to add.
I mean to get $\ce{HCl}$ down to 0 every time, there would have to be sensors to not only know the volume of water but also the concentration of $\ce{HCl}$ and a relatively complicated math problem like this:
$$[\ce{HCl}] * x = a mol \ce{HCl} = a mol \ce{NaOH} = [\ce{NaOH}] * y$$
What is complicated about it? Well for one how would you sense the exact concentration of a strong acid or base without damaging the sensory equipment? And unless you regularly go to the water treatment plant with this nanotechnology, you won't know what the concentration of $\ce{NaOH}$ is. And the concentration of $\ce{HCl}$ will most likely vary day to day depending on factors such as these:

How often any given person vomits
Hydration level before vomiting
Amount of bile in the vomit
Dilution of stomach acid
Amount of blood in the vomit if any
Prevalence of vomiting from any cause
Total Volume of vomit

So basically my question is how can I have the part of the system after the filters be constantly sensing the exact concentration of $\ce{HCl}$, doing the math, and adding the amount of $\ce{NaOH}$ that will get the concentration of $\ce{HCl}$ down to exactly 0?

The question is long and detailed, and deserves a long answer, but I can only hit on the highlights, and urge others with some expertise in this area (which I lack) to weigh in.
First, the science of water treatment is mature and has addressed many of the issues raised here, primarily through biological and chemical processes which are very good at breaking down and dissolving most of the different sized particles you refer to.
As far as the composition of sewage is concerned it contains a lot more water than human waste, and a lot more normal waste (urine and fecal matter) than vomit, which, since most people are sick only a tiny fraction of their lives, and nauseous an even smaller fraction, likely is a vanishingly small contributor to the content of sewage. The composition of sewage at the treatment plant intake varies much less, and more slowly, than you might think, since it is averaging the inputs from people all over a city or region. Still, it may vary seasonally due to changes in temperature or water usage, so the treatment must vary accordingly, as you have surmised.
Finally, you concern about neutralizing every last iota of HCl is misplaced. Adjustment of pH is commonly used in sewage treatment and is done using automated equipment and pH sensors that can withstand extended exposure to sewage and to pH fluctuations. The glass membrane electrode is a workhorse that is stable to extremes of pH well beyond what would occur in sewage.
But I conclude my answer by saying that some of your ideas are very interesting, and there may be many applications of nanotechnology in water treatment along the lines you mentioned, that could have practical benefits for peoples' lives. I urge you to continue your studies of wastewater chemistry with your full vigor and an open mind.

You see, the reason I was thinking so hard about a precisely controlled acid base reaction is so that not only is the water as pure as it can be but so that no toxic hydroxide salts end up in the water and there is no acid or strong base that could cause ulcers at the least and autodigestion(literally a living organism digesting itself to death) at the very worst.

Pure water still contains 0.0000001M hydroxide ion - plus remember that stomach acid contains a lot of HCl, enough to neutralize a low concentration of base in water as would result from a water treatment protocol. Not to worry. Hydroxide ion is toxic only when concentrated enough to dissolve and react with tissue (if you ate Drano for example).

You have a lot of misconceptions in your question. First, the grit screens at the beginning of wastewater (not water) treatment are finely spaced, but they only capture large items that have been flushed down the drain (or captured in stormwater for combined systems). This is mostly just toilet paper. Second, wastewater contains many other compounds - the main ones we are concerned with here are phosphate, sulfate, and carbonate. These are all buffers and will neutralize any HCl that would be present. Third, the HCl concentration from the sources you are referring to (i.e., vomit) will be at extremely low concentrations due to dilution. Wastewater volume is mostly from showering and washing clothes/dishes, and in the case of combined sewers, stormwater. This will dilute everything from toilets. Also, only digested sludge from activated sludge treatment and of a certain grade will be turned into biosolids for land application. And there is already a very established separation technology that is used in (waste)water treatment that is not impractical - reverse osmosis.
If you did assume buffers were not in your system, say for an ultrapure water, then neutralizing a strong acid with a strong base is nearly impossible. Instead, you would add a buffer that has a pKa at your desired pH, e.g., bicarbonate.


text:
Polarisation of a cation by an anion
Shriver and Atkins' Inorganic Chemistry (5th edition) explains amphotericity of the oxides of the heavier elements in Groups III, IV and V by high covalent character of the bonds made by the elements.
It states: "The onset of amphoterism correlates with a significant degree of covalent character in the bonds formed by the elements, either because the metal ion is strongly polarising (as for Be) or because the metal ion is polarised by the O atom attached to it (as for Sb)."
I have heard of many explanations using the polarising power of cations but never have I heard the "reverse", which is the polarising power of anions. Polarisation of an anion by a highly-polarising cation means that the cation distorts the electron cloud of the anion strongly. How would that work for the polarisation of a cation by an anion?

"A useful rule of thumb is that small cations, which are not easily polarized, are
hard and form complexes with small anions. Large cations are more polarizable and are soft." Later the book said similar things about hard/soft acids. I have the same question as you.


text:
How does acid damage skin?
As I understand it, acids are substances which have a high concentration of H+ ion which makes acid an acid. When interacting with our skin, acid can damage it. How does this concentration of protons cause damage to skin?

Those protons don't simply sit around doing nothing. They tend to bind to/attack  the polymers (keratin and such) that make up your skin and form newer, smaller molecules; i.e- it breaks down the polymers that constitute your skin. The stronger the acid is, the higher the concentration of protons in it, and hence, greater the tendency/chances of them binding to your skin.

Also there is a relay proton distribution mechanism which accelerates the impact pointed out by @paracetamol.

Not only high pH but also concentration of anions is dangerous.

@Mithoron High pH is indeed dangerous (dissolves the skin tissue), but acids have low pH. And skin is fairly resistant even to strong acids. The problem are indeed the anions (e.g. the notorious fluoride) and undissociated acids that diffuse through the skin.

In addition, the corrosive (to be taken in a broad sense, here) property of many acid does not result from - or not only from - their ability to donate protons but from their chemistry as a whole . They can dehydrate and oxidize almost everything in the tissues, (eg H2SO4), undergo specific reaction (eg HNO3 reacts with proteins to give yellow xanthoproteins), etc.

Also I would like to note that, as being the question somehow related to safety, one can finally speak of acid as proton donors without starting unnecessary wrong cascade of comments like "it is wrong" or "you refer to centuries year old theory now dismissed". Acid did are doing and will burn the skin. As they were are and always will be donating protons. Of course if they have at least one :)


text:
How does an oscillating reaction work?
I watched a video showing an orange solution that goes to clear and then back to orange (and so forth.)
The reaction goes through a number of cycles before it will no longer oscillate. This tells me that the overall energy in the system dissipates over time, but how does such a reaction work?
What is happening that causes this oscillation in concentration?

If you are concerned in conservation of energy in BZ-reactions, it's all fine: you can imagine the reaction as a physical pendulum whose oscillations are damping over time. More or less complete mechanism includes over 80 steps (L. Gyorgyi, T. Turanyi, R.J. Field. Mechanistic Details of the Oscillatory Belousov-Zhabotinskii Reaction. J. Phys. Chem. 1990. 94 (18) 7162-7170 DOI: 10.1021/j100381a039). If you don't have access to the paper, I can try to summarize the core principles behind in an answer.

Have a look at the Oxford Chemistry Primer by Scott  ' Oscillations, waves and Chaos in Chemical Kinetics'. This is a good starting point to understand these types of reactions.

related https://chemistry.stackexchange.com/questions/15511/can-a-multi-species-system-oscillate-around-equilibrium https://chemistry.stackexchange.com/questions/31383/periodically-oscillating-chemical-reactions?rq=1

https://chemistry.stackexchange.com/questions/267/whats-a-minimal-yet-chemically-meaningful-kinetic-system-for-an-oscillating-rea

I worked on a project using this reaction fairly recently. There are a significant number of intermediate species involved in the reaction with a significant number of autocatalytic steps.
In order to obey the rules of free energy, the reaction may not oscillate about its equilibrium as a pendulum does- there is always a monotonic decrease in reactant concentration and an increase in product concentration, but the multitude of intermediates oscillate in concentration as the reaction switches its reliance on certain sections of the mechanism (dependent upon the instantaneous concentration of stuff in the mixture). The indicator used dictates the colour changes- I used ferroin, and so when the concentration of Ce(4+) (the catalyst used) is high the mixture is red, and when the concentration of bromate is high the mixture is blue.
It should be noted that the reaction will always come to a stop unless you use a continuously stirred flow reactor in which products are removed and reactants added as the reaction proceeds.
There are several mechanisms such as the FKN, MBM, GTF and Oregonator. The Oregonator is by far the most simple but lacks chemical accuracy, the former 3 display real chemical conversions yet still fail to perfectly model the reaction. The mechanisms can be modelled using coupled differential kinetic equations, which I did during my project in Mathematica.
The simplest general reaction scheme for a chemical oscillator is given by the Brusselator:

A → X
2X + Y → 3X
B + X → Y + D
X → E

In this scheme, A represents the reactions and E the products. X is autocatalytic (it catalyses its own production).
Another interesting example comes into play in population dynamics, the Lotka-Volterra equations (also known as predator-prey equations). They can be used to quantify the changes in populations in a predator-prey system such as foxes and rabbits. The reaction itself has also been suggested as a very primitive form of chemical order- interesting stuff.
Disclaimer: Sorry if this seems a little off-topic; the details of the specific BZ mechanisms are far less interesting than the concept of the oscillators themselves. If you want to look into the actual mechanisms though, start with the FKN model, it's fairly easy to digest and even model.

Perhaps the simplest oscillating ''Gedankenexperiment'':
1:  A -> B
2:  B -> C
3:  C -> A

Now we say that A inhibits reaction 2, B inhibits reaction 3, and C inhibits reaction 1. If you start with any pure substance A,B or C, the next step never starts before the previous is fully completed.
Of course this needs an energy source, otherwise the last step could never run:
1:  A     -> B
2:  B     -> C
3:  C + O -> A + OO

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


text:
Peroxide without hydrogen
How come we always see hydrogen peroxide and never peroxide by itself. Is there such a thing as peroxide ? Does this exist in nature? Why is hydrogen always associated with it? Please note: First semester chem student so new to all this. Thanks!

Are you interested in how abundant free $\ce{O2^{2-}}$ in nature, or is there any hydrogen-free peroxides at all?

I'm voting to close this question as off-topic because this can be answered with simple Google search.

Well the peroxide can exist in the nature but it wouldn't be very stable.
In fact ,You could look up the 2015 Nobel Prize owner of medicine.
She actually discover a substance called Artemisinin.
https://en.m.wikipedia.org/wiki/Artemisinin
As the structure of this substance shows that it presents an peroxide bridge bond , which is normally unstable in the nature. But in this case, she also discovered that when this substance heats up, this substance will be stable instead of breaking up. There are also some of the substances that contains peroxide bridge bond. Additionally, the peroxide bridge is also believed to be one of the drug's mechanism.
Hope this helps!


text:
What substance would crawl out of a vessel?
I remember in my first chemistry lessons at high school my teacher told us about atomic properties of materials elastics and stiffness and what ever else. At one point he came up with an example of a (theoretical?) liquid that would even crawl out of its vessel to overcome differences in gravity, desiring to get to as close to the gravity well as possible and even overcoming obstacles by trying to achieve this. Back then the idea quite fascinated me, enough to think about it again every few years.
But today, myself being a hobby astro physician and having at least a layman understanding of how gravity works, I start questioning his statement. I can't really understand how a substance could gain that "information" to when it can get closer to the source of gravity by a ratio between energy required to overcome the obstacle to gain in range reduction to the gravity source.
So my question is, what was the substance he was refering to?
Does such a substance exist? And if so, how does it work?

https://en.wikipedia.org/wiki/Superfluid_helium-4 (don't know any more, so can't give you anything more than the link)

@orthocresol: Quite different in the reasons why it behaves like that from what my teacher back then explained, but in it self sounds like it could have been what he was referring to. Sad that you have not more specific knowledge about it.

I think @orthocresol pretty much answered your main question. Regarding the second part on how this happens beyond the wikipedia article, I'm afraid you need to dive deep into macroscopic quantum mechanics effects, and it's going to be a long reading, there are book chapters if not the entire books devoted to superfluids.

@andselisk: yeah definetly it answered my questions. But sadly I can't accept a comment as answer. Also as he mentioned that he can just give me the link and a link only answer would not be fine. Thats why I said that its sad.

Most liquids will move to a lower potential energy environment using the common device of the syphon.

@matt_black That means what?

You mean POLYOX? https://nnf.mit.edu/home/billboard/topic-4

@paracetamol: Interesting aswell :) But, no actually I'm quite sure it was helium-4, my teacher was referring to.

Liquids flow up a wall as long as the gain in interfacial energy (to the wall) can make up for the additional surface energy and gain of potential energy. If the substance is over the brink at the equillibrium height, it  leaks out. I fail to see what suprafluidity has to do with that, but perhaps someone else can put some light on it.

@Karl: Are you just nit picking on the fact that I didn't specify in the title that the vessel hast to be straightened up? Or is it, that some of my clarifications are ambiguous? Well my chemistry knowledge is very limited and I just tried to describe what my teacher years ago described, so sorry if I made any technical mistakes in my description. And otherwise, well it never occurred to me, that my soda crawled out of the drinking glass I poured it into. And if you try to tell me any liquid can mimic the properties of helium-4 tell me plz how to, I would love to experiment with that at home.

@Karl: Well by "crawling out" I didn't (and my teacher didn't said that back then either) meant that the fluid in question will just decimate a bit out of a beaker. I meant "crawling out" as in having an almost empty beaker after some time. The linked article reads like this is unique to that fluid. But if not so, I'm looking forward for such an answer. But anyways, how is that interfering with OP?

@Karl: Ah, haven't noticed that anyone referred to supra fluids in general. but except that, you are right... I'm not getting your point. But I hope possible answerers will. :D


text:
Single electron reduction of ketone by Na or Zn
Whenever we add Na or Zn metal to a ketone, why does the electron prefer to attack the carbonyl bond and form a radical, instead of removing the acidic hydrogen and forming an enolate and $\ce{H2}$ gas?
I was thinking that usually when we add Na and there is a sufficiently acidic Hydrogen present, it reacts and releases $\ce{H2}$. I just wanted to know if there is an advantage in attacking the carbonyl bond instead of an acid-base reaction. Also, is this dependent on kinetic or thermodynamic control.

What are your thoughts? How do you approach this problem?

Think about the stability of the radical(s) and other species that would form.

@EashaanGodbole But aren't acid-base reactions quite fast, also K(eq) is more than 10^5

@Ayushmaan I won't compare radical reactions with acid-base reactions.

@EashaanGodbole So is there a way to deduce where acid-base or radicle would be preferrable in case of Na?

Why do you think sodium participates in acid/base chemistry? When it produces hydrogen, that's via single electron transfer. It just happens to be favorable to produce hydrogen radicals.

@Zhe           Yes, but why. Creating a radicle would break the carbonyl bond permanently while generating a carbanion does not decrease the stability (atleast not permanently)

I don't think you've considered the mechanism enough. With the carbonyl, you create a radical anion. What does the process for hydrogen abstraction look like? Do you donate an electron to the $\sigma*$ orbital first? What does that species look like? And if it's an $S_{\mathrm{N}}2$ type abstraction as in the answer below, consider how much more unlikely that is compared to the process for just donating an electron to a carbonyl.

@Zhe           Could you frame it as an answer with the mechanism. I've tried and its not becoming clear to me.

I don't know what the exact mechanism for the hydrogen atom abstraction would be. Mostly because it is disfavored over what appears to be an easy reduction of the carbonyl group (see the answer below). The accepted mechanism, if studied, is probably available in the literature.

Let the carbonyl compound under consideration be acetone.
Case I: Hydrogen Abstraction

The species formed are NaH and an allyl-type radical. The resonating system includes an electronegative oxygen atom, which also has an incomplete octet in one of the canonical forms.
In essence, products are not really stable.
Case II: Attack on Carbonyl

The species formed is a radical anion, which are relatively stable as the filled orbital of the oxygen relieves some electron deficiency of the radical. This effect is stronger than the one offered the pi-bond in Case I.

I would suspect that this is kinetically controlled. So I'm not entirely convinced by an argument based on relative product stability. If I had to take a guess I'd say that it is simply because the electron adds into the LUMO of the carbonyl compound, which is the C=O π* (and not the C–H σ*). But I'm not confident enough to post it as an answer.


text:
Etymology of "click chemistry"
According to Wikipedia, the term click chemistry was coined by K. Barry Sharpless in 1998.
What does the word 'click' mean here? I guess it means "join" here but I'm not sure.

"Click" is the sound a closing lock makes. Something that just falls into place, easily, no possible errors, "clicks". The last piece in a puzzle, sth. like that.

It reminds me of click flooring, both in naming and when reading the answers below.

Yes, it is detailed here and in numerous other places. It refers to a class of reactions, and does not mean "join."
From the above-cited page on named reactions:

"Click Chemistry" is a term that was introduced by K. B. Sharpless in 2001 to describe reactions that are high yielding, wide in scope, create only byproducts that can be removed without chromatography, are stereospecific, simple to perform, and can be conducted in easily removable or benign solvents.

Sigma-Aldrich has a primer where they state:

The traditional process of drug discovery based on natural secondary metabolites has often been slow, costly, and labor-intensive. Even with the advent of combinatorial chemistry and high-throughput screening in the past two decades, the generation of leads is dependent on the reliability of the individual reactions to construct the new molecular framework.
  Click chemistry is a newer approach to the synthesis of drug-like molecules that can accelerate the drug discovery process by utilizing a few practical and reliable reactions. Sharpless and coworkers defined what makes a click reaction as one that is wide in scope and easy to perform, uses only readily available reagents, and is insensitive to oxygen and water. In fact, in several instances water is the ideal reaction solvent, providing the best yields and highest rates. Reaction work-up and purification uses benign solvents and avoids chromatography.

A pretty comprehensive overview is given here, in a manuscript entitled Click Chemistry, a Powerful Tool for Pharmaceutical Sciences. Hein, Liu, and Wang. Pharm Res. 2008 Oct; 25(10): 2216–2230.

Click chemistry is a term coined by K.B. Sharpless in 2001. The original paper "Click Chemistry: Diverse Chemical Function from a Few Good Reactions."[1] describes a set of very well working reactions with certain characteristics that, in general, can be used to join molecules together. Such characteristics are for example:

wide in scope
high rates and yields
very selective
no/ inoffensive byproducts
ideally work in water

This was the original definition, however, if people talk about click chemistry nowadays what they often refer to is the copper catalyzed Alkyne Azide Cycloaddition[2] or similar reactions like the Strain-Promoted Alkyne Azide Cycloaddition (copper-free click chemistry)[3] or the Tetrazine Ligations.[4]
References

Hartmuth C. Kolb, M. G. Finn, K. Barry Sharpless, Angew. Chem. Int. Ed. 2001, 40 (11), 2004-2021. DOI: 10.1002/1521-3773(20010601)40:11<2004::AID-ANIE2004>3.0.CO;2-5
Christian Spiteri, John E. Moses, Angew. Chem. Int. Ed. 2009, 49 (1), 31-33. DOI: 10.1002/anie.200905322
Jan Dommerholt, Floris P. J. T. Rutjes, Floris L. van Delft, Topics in Current Chemistry, 2016, 374, 16. DOI: 10.1007/s41061-016-0016-4
Jolita Šečkutė, Neal K Devaraj, Curr. Opin. Chem. Biol., 2013, 17, 761 - 767. DOI: 10.1016/j.cbpa.2013.08.004

Human readable citations are cool!


text:
State symbol for electron
Is it correct to write a state symbol of "g" or "l" for an electron? In the textbook I am currently reading, the state symbol "g" was used for the electron when it described the electron gain by a proton in the gas phase. However, I recall that my chemistry teacher mentioned that electrons should not be given any state symbols, which I agree with. Just like how we do not assign a a physical state to an atom. E.g. We do not say an atom of gold is in the liquid state. I would like to know what is the purpose of assigning state symbols to electrons, if there is one? And would that be chemically accurate?

Maybe related: https://chemistry.stackexchange.com/q/297/40029

I guess a state symbol is only necessary if the electron is in a special state such as solvated when $e^-{solv}, ; e^-{aq}$ or something similar would be used.  With atoms no state symbol is expected if in their normal state  but if gold were in its liquid or vapour state then $\ce{Au_{(l)} ,  Au_{(g)}}$  respectively would be advisable. (btw. electrons are just as much 'physical matter' as protons or atoms are.)

@porphyrin All right. I will edit my post.

no need your question is ok :)


text:
Ring opening of aziridinylmethyl and oxiranylmethyl radicals
When a radical is alpha to a three-membered ring, it is common for the ring to open via β-scission (to relieve ring strain):

When the ring contains a heteroatom there are a couple of different possibilities:

Ab initio studies of these reactions1 showed that for both X = O and X = NH, the C–C cleavage was thermodynamically favoured (presumably due to stabilisation of the subsequent radical by the adjacent lone pair). For X = O, the C–C cleavage was also found to be kinetically favoured, but for X = NH, the C–N cleavage is kinetically favoured!
This regioselectivity is also backed up by experiment2 and also has potential for use in synthesis.3

Is there an explanation for why the kinetically favoured products are different for X = O and NH?

References

Pasto, D. J. Ab Initio Theoretical Studies on the Ring-Opening Modes of the Oxiranyl-, Aziridinyl-, Oxaziridinyl-, and Thiaranylmethyl Radical Systems. J. Org. Chem. 1996, 61 (1), 252–256. DOI: 10.1021/jo9505942.
Marples, B. A.; Toon, R. C. An investigation into the β-cleavage of aziridinylcarbinyl radicals. Tetrahedron Lett. 1999, 40 (26), 4873–4876. DOI: 10.1016/S0040-4039(99)00900-4.
Prévost, N.; Shipman, M. Intramolecular Radical Rearrangement Reactions of 2-Methyleneaziridines: Application to the Synthesis of Substituted Piperidines, Decahydroquinolines, and Octahydroindolizines. Org. Lett. 2001, 3 (15), 2383–2385. DOI: 10.1021/ol016194k.

The 2-methyl-3-phenyloxiranylcarbinyl radical has been shown EXPERIMENTALLY to cleave the C-O bond kinetically while the C-C bond is cleaved thermodynamically. This means that, in this example, The oxygen-centered radical forms faster than the highly stable benzyl radical. The formation of the oxygen radical is necessarily reversible. See ref. 11 in your ref. 2 (Marples paper)
Ziegler, F. E.; Petersen, A. K. Allyloxy Radicals are Formed Reversibly from Oxiranylcarbinyl Radicals: A Kinetic Study, J. Org. Chem. , 1995, 60, 2666.

Fair enough, but there's the followup question: why is C–X cleaved kinetically despite forming a less stable radical? Thanks for pointing this out, nonetheless. I'll edit the question when I get a chance to.


text:
Increasing partition coefficient in an extraction
My friend had this homework question about supposing you had a slightly polar organic compound in an ether/water extraction with a partition coefficient in favor of ether. The question was:

What simple method can be used to increase the partition coefficient?

My thought was to add salt to the extraction mixture. I was thinking that if you saturate the water with salt, there essentially isn't any room for the polar organic compound to stay in the water so it gets extracted into the organic layer. However, I'm wondering if there's a better explanation for why adding salt would increase the partition coefficient. Thank you for the help!

Generally, extraction of substances with organic solvents is influenced by various factors, among which there are the following:

nature of the extracted substance and the extractant (not a variable in your example);
temperature;
presence of electrolytes in aqueous solutions;
$\mathrm{pH}$ of the medium;
rate of agitation etc.

In your particular case probably only temperature and electrolytic presence are relevant.
Change in temperature often affects the distribution constant rather seriously, as not only the solubility of the extracted substances in each phase changes (unequally), but also the mutual solubility of the organic and aqueous phases changes too. When the temperature changes, the dissociation/association of the substance in the corresponding phase can change, influencing hydration (solvation) and therefore extractability. Ideally you might want to check solubility-temperature plots for your system, taking into account that this data often cannot be obtained by extrapolation.
Addition of highly soluble salts (electrolytes) to an aqueous solution of another substance can lower (salting-out effect) or increase (salting-in effect) its solubility in water. Increased high ionic strength also lowers activity of water in terms of depressing its competitive effects (first of all, solvation).
The salting-out effect of electrolytes depends on the nature and properties of the extracting substance and the concentration, charge and ionic radii of the salting-out ions. Smaller ions with larger charge have higher charge density than ions with a larger radius, therefore they are hydrated better.  $\ce{NaCl}$ and $\ce{Na2SO4}$ are commonly used for salting-out organic substances. However, this rule has a number of exceptions. Some non-electrolytes that are well soluble in water also have salting out-effect. For example, ethyl alcohol salts-out acetic acid from its aqueous solutions upon extraction with ethyl acetate.
The salting-in/out phenomenon is often explained based on the electrostatic model proposed by Debye and McAulay, reviewed in [1], and can be approximately described via equation:
$$c/c^\circ = 1 - K_D \cdot c_\mathrm{s} + A \cdot c_\mathrm{s}^{0.75},$$
where $c^\circ$ and $c$ are solubilities [$\pu{mol L-1}$] of non-electrolyte in pure solvent and solvent with salt, respectively; $K_D$ and $A$ - empirical coefficients; $c_\mathrm{s}$ - salt concentration.
Pretty much your explanation is on the same page with the original Debye theory:

This theory pictures the "salting-out" effect as a consequence of the aggregation of the water molecules of greater polarity around the ions owing to the field of the latter. The less polar non-electrolyte molecules tend to congregate in the portions of the solution most remote from the field of the ions, with the net result that an enhancement of the water molecules around the ions and of the non-electrolyte in the solution regions away from the ions occurs. A reduction of the solubility of the non-electrolyte, referred to the total water present, thus results, due to the increase of non-electrolyte-water ratio in those regions of the solution containing the non-electrolyte.
The criterion of polarity which Debye employs is the dielectric constant of the saturated aqueous solution of the non-electrolyte relative to water at the same temperature. On this basis if the saturated solution has a dielectric constant less than water, "salting out" occurs in the presence of the added salt. If the dielectric constant of the saturated non-electrolyte solution is above that of water, the non-electrolyte becomes more soluble in the salt solution or is "salted in". This means that the non-electrolyte tends to aggregate around the ions at the expense of the water, and so the nonelectrolyte-water ratio in regions removed from the ions is lowered and the total water present can hold more non-electrolyte in solution.

Also, in biochemistry so-called Hofmeister series are used to favor protein extraction by salting-out for given conditions.
References

Gross, P. M. The “Salting out” of Non-Electrolytes from Aqueous Solutions. Chemical Reviews 1933, 13 (1), 91–101. https://doi.org/10.1021/cr60044a007.

I am so glad someone mentioned temperature.  This is sometimes used in Industry due to temperature control of the jacket, but I've never seen an academic paper mention it for extraction


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Why does enantiopure sec-butyl alcohol retain its optical activity over aqueous base but forms a racemic mixture over dilute sulphuric acid?
Why does enantiopure sec-butyl alcohol retain its optical activity over aqueous base but forms a racemic mixture over dilute sulphuric acid ?
My reasoning is that, sec-butyl alcohol get dehydrated into a alkene because of sulphuric acid and then get hydrolysed to form alcohol again. Thus a equilibrium is formed between alkene and alcohol and between $R-$ and $S-$ sec butyl alcohol.
Dehydration cannot occur with a base, so the alcohol remains optically active.
I feel that conversion of alcohol to alkene and then back to alcohol seems ridiculous and impossible. What do you think, is this reasoning correct or just plain non-sense ?
To be specific, I have some doubt whether alkene will convert back to alcohol or not in dil sulphuric acidic ?

Why is your speculated mechanism ridiculous? You have proposed a reasonable mechanism. The rate of the racemization isn't given. Even if you think the process will be slow, it explains the observation.

I don't think you need to go all the way to the alkene. The protonated $OH_2^+$ is a good leaving group and makes an $S_N1$ reaction with more water. I'm not sure trans-2,3-butene would hydrolyse in dilute acidic solution?

@jerepierre I have doubts on whether alkene will convert to alcohol or not just as Karl asked.

@Karl In $\ce{S_N1}$ 3-butanesulfonic acid will  form. Won't it react further to produce trans-2-butene?

@Mockingbird Sulfate is a lousy nucleophile, if I remember correctly.

So, what else other than that? Back to alcohol again?

Back to the alcohol by water addition (the medium is aq sulfuric acid)

Although sulphuric acid is a notable dehydrating agent, it is concentrated rather than dilute sulphuric acid that would be typically used for such a purpose.
Here, it is due to the improvement of $\ce{H2O}$ as a leaving group compared to $\ce{OH-}$, due to the lack of any charge as a leaving group.
Under acidic conditions, the sec-butyl alcohol will be protonated in a small amount creating a much better leaving group.  The protonation also makes the alcoholic carbon centre more electrophilic and vulnerable to $S_N2$ attack by other water molecules in solution, leading to inversion of the chiral centre.
This in not possible under neutral conditions as the unprotonated alcohol would have $\ce{OH-}$ as a much poorer leaving group, preventing elimination or substitution reactions.
Under acidic conditions, with neutral water as a nucleophile $S_N2$ substition will be the preferred path.

A secondary alcohol on a small, un-branched carbon chain represents a relatively accessible spot for nucleophilic attack.
$E_1$ eliminiation or $S_N1$ substituion would require the formation of a secondary carbocation with relatively poor stabilisation compared to a tertiary carbocation.
$E_2$ elimination would require the removal of a hydrogen of low acidity from the carbon chain by a very weak base, water.

This allows a equilibrium converting molecules back and forth between the $R$ and $S$ forms of the alcohol to be set up and leads to racemisation in solution.

While there is no clear cut line between the SN1 and SN2, I'd argue that the SN2 is much more pronounced. I doubt that there is the formation of an actual carbocation, and that one or two water molecules be loosely coordinated to the (alcoholic) carbon centre at all times. (Maybe you have switched the two, your explanation otherwise is very sound.)

Dilute sulfuric acid is not dehydrating at all. And $S_N1$ does not lead to inversion, but is not stereospecific at all. $S_N2$ does that. Not that it would matter here.

Thanks for pointing that out, I got $S_N1$ and $S_N2$ labels mixed up. Edited.


text:
Effective nuclear charge on an inner electron
Is the shielding effect in a multi-electronic species caused due to mutual repulsion of electrons?
If it were so, while calculation the $Z_\text{eff}$ on an electron in say the $\mathrm{2p}$ orbital of a $\ce{Na}$ $\mathrm{(1s^2,2s^2,2p^6,3s^1)}$ atom, why don't we also consider the repulsive force of outer electrons in $\mathrm{3s}$ and add it to $Z_\text{eff}$ instead of $Z_\text{eff} = Z - \text{repulsion due to inner electrons}$?
Why doesn't the equation read
$$Z_\text{eff} = Z - \text{repulsion due to inner electrons} + \text{attraction due to outer electrons}?$$

10th grade physics: The inside of a charged sphere is free of field lines. Same as with gravity: If you dig 1km deep, your weight gets lower as if the earth's diameter had shrunk by two kilometers.

Firstly, effective nuclear charge is just a model for predicting trends in atomic properties. The actual solution of the quantum mechanical equations does use the full nuclear charge and explicit calculation of the all electron-electron repulsions (and electron-nuclear attraction).
The point of $Z_\text{eff}$ is to approximate the value of the nuclear charge felt by electrons at a given distance. The answer to your question then is Gauss's Law,  which states that, to determine the field at a given point, you consider all and only the charge inside a certain surface (on which your point sits). Moreover, it states that the field there is equivalent to if all of the charge inside that surface was a point charge at the center.
So if we apply Gauss's Law to our atom, we add up all the charge inside a sphere centered on the nucleus ($Z-\text{effective number of core electrons}$), and regard the system as an effective nucleus with that charge, no core electrons and the electron of interest being the "first" electron and so we ignore the outer electrons.
Here are some physics discussions for why, intuitively, Gauss's Law allows you to ignore outside electrons from the physics stackexchange.


text:
How do you track Iodine on a black surface?
While spraying with starch solution seems to be standard procedure, blue-black colouring seems not to stand out from a black (charcoal) surface.

I would spray some lead nitrate solution to the surface if I didn't care about it at all. It would form nice yellow crystals of lead iodide that could be seen on a black surface. Never tried it though.

Perhaps you have access to test stripes of paper, which are impregnated with starch and potassium iodide.  In presence of molecular iodide, the water wet paper turns blue, due to the formation of a starch-iodine complex (similar to the reaction in solution, shown here.
However, it is not specific reaction as chlorine, bromine and other oxidizers may equally trigger the reaction of the potassium iodide in the paper to form the complex yielding iodine, too.


text:
positive charge on oxygen of carbonyl group in acetic acid
I refer to a previous post by Ron on hyper conjugation in acetic acid(Link:https://chemistry stack exchange.com/.../hyper conjugation in-in-acetic-acid)wherein it is stated that "In acetic acid there is a partial positive charge on carbonyl oxygen". This is confusing me .How can oxygen carry a partial positive charge oxygen being highly electronegative?

In what post? Link? And what's your question really? Edit it!

Partial positive charge of oxygen of carbonyl group in acetic acid .

In a previous post by Mr. Ron "hyper conjugation of acetic acid ?" (Link- https://chemistry stack exchange.com/.../hyper conjugation-in-acetic acid")it s stated that "there is a partial positive charge on carbonyl oxygen ".How can oxygen hold a positive charge being electronegative?

The carbon atom does not have a full positive charge like a carbocation. What happens when a carbon atom is bound to a more electronegative element such as oxygen, is that the electron density from the bond is higher towards oxygen then carbon, therefore leaving the carbon atom with a partial positive charge. When drawing the chemical structure of a carbonyl compound, you can indicate that the carbon atom has a partial positive charge and the oxygen has partial negative charge by using the greek letter sigma as in the picture:

You can also see this through resonance structures for a carbonyl compound

The real molecule (the hybrid) is something between those two first structures in the left (they are called resonance structures and differ only by the electronic configuration around the atoms).


text:
Work done by irreversible expansion of gas against piston of fixed pressure
this has been puzzling me for a while.  An ideal gas expands against a piston with mass M and area A, so that pressure external Pex= Mg/A.  The initial internal pressure of the gas is Pino > Pex.  Because the gas is expanding irreversibly, Pin > Pex, until equilibrium is reached, where Pinf  = Pex.
The physical chemistry texts I've read, including Atkins, seem to characterize the work done by the expanding gas as Pex * change in volume.  I recognize this as the equation to calculate work for lifting an object at constant velocity over a given distance.
However, since the initial internal pressure of the gas is greater than the external pressure, there is an imbalance in forces, and the mass will accelerate upwards, causing it to acquire kinetic energy that was derived from the original energy of the gas.  A rocket is an example of gas causing a mass to accelerate upwards.
My question is why the standard formula of work done by an irreversibly expanding gas is Pex * change in volume, and doesn't include a term for the kinetic energy from acceleration.

In an irreversible expansion like this, the aveage pressure of the gas within the cylinder is greater than the pressure acting at the internal piston face $P_{ext} $ (where the work is being performed).  Of course, at the internal piston face, by Newton's 3rd law, the pressure exerted by the gas on the piston face is equal to the pressure exerted by the piston face on the gas.
The reason that, in an irreversible expansion, the average pressure of the gas (averaged over the volume) is greater than the value at the piston faces is that the gas pressure is non-uniform spatially within the cylinder.  This is the result both of mass times acceleration effects within the gas itself (yes, the gas has mass) as well as viscous stresses present within the gas that are proportional, not to the gas volume, but to the rate at which the gas is deforming locally within the cylinder.  So the mechanical behavior of a gas experiencing an irreversible expansion is very different from that of a gas experiencing a reversible (quasi-static) expansion.
Now let's reconsider the force balance on the piston.  If $P_{gas}(t)$ represents the instantaneous pressure exerted by the gas on the piston at time t, then the force balance on the piston becomes:
$$M\frac{dv}{dt}=P_{gas}(t)A-Mg$$If we multiply both sides of this equation by v=dx/dt and integrate with respect to t (from time = 0 when the piston is released), we obtain:  $$\int_0^{x(t)}{P_{gas}Adx}=W(t)=\frac{1}{2}Mv^2-\frac{Mg}{A}[V(t)-V(0)]$$where W(t) is the work done by the gas on the piston up to time t, v is the velocity of the piston at time t, and V(t) is the volume of the gas at time t.
Basically what will happen here at short times is that the piston will rise and gain velocity, but it will overshoot its equilibrium position (like a mass on a spring experiencing simple harmonic motion).  It will then slow down, until it begins moving downward.  But it will again overshoot the equilibrium position.
If the piston were frictionless and the gas were inviscid, this oscillation would continue forever.  However, even if the piston were frictionless, the gas is not inviscid.  So the viscosity of the gas will act as a damping factor, and the piston, rather than oscillating forever, will experience a damped oscillation until if finally comes to a stop at the equilibrium position (i.e., when v = 0).  So the equation for the work will become:  $$W(\infty)=\frac{Mg}{A}(V_{\infty}-V(0))$$
So, even for a piston with mass, the kinetic energy effect will die out and the work will be the same as just the change in potential energy of the piston.

Thank you for the explanation - I had an intuition that there might be an oscillation.  Can I ask a followup?

Is the energy of the oscillation lost as heat due to dampening?  Is this heat loss the difference in work output between an irreversible and reversible expansion?

Since the max work is obtained when the gas is allowed to expand infinitely slowly by infinitesimally small decreases in Pex.  Does the reversible expansion prevent any overshoot-oscillation?

As a reply to your first question, I suggest reading the following analysis I did to get an understanding of reversible vs irreversible work using a spring-damper analogy:  https://www.physicsforums.com/insights/reversible-vs-irreversible-gas-compressionexpansion-work/

In the reversible expansion, of course, there is no overshoot.

Thanks for the reference, can I ask about why in the compressed spring with dampener, the analysis assumes that the forces acting on both sides of the piston are balanced (F ext = F spring + F viscosity)?  I see that F viscosity would increase until reaching a terminal velocity, but until terminal velocity is reached, I'd think that the forces are unbalanced.

I meant to mention in the article that the "piston" is supposed to be massless.  Also, in this system, there is no terminal velocity because, as time progresses, the spring is carrying more of the load and the damper is carrying less.

my comment after thinking and reading physicsforum: irreversible expansion experience a heat gain from loss of kinetic energy due to oscillation, not heat loss

(I'm solving this assuming the container and piston to be adiabatic).
Now,  Force (on piston)= (Pint-Pext)A - Mg = M(accl.) and as no net energy loss, we can say that,
Work Done (by gas)= (Pint)A(dx)= [(Pext)A(dx) + Mg(dx) + M(accl.)(dx)]. This is the actual equation of the work done by the gas. Now, as there is no theoretical way of deducing the accelaration of the piston without involving more than one variable in the integral(thus making the mathematics lengthy), we have to assume that the piston is either massless, or its accelaration negligible(which it practically is) to ignore M(accl.)(dx) term.
Otherwise, theoretically, you are correct in saying that the change in Kinetic Energy of piston should be included in the work equation, we just choose to ignore it for calculation purposes.

The point that is being missed here is that the Pressure to be used is neither Pint nor Pext, but Poperating, which depends on the velocity of the piston.  Gas molecules striking the moving piston gain or lose speed depending on direction, affecting the energy of the gas.  An approximation is
Poperating = Pint(1 +/- u/v)^2  where u is the velocity of the piston and v is the average velocity of the gas molecules in one direction.
"Thermodynamic Calculation of Work for Some Irreversible Processes"
Gary L Bertrand, J of Chemical Education, Vol 82, pp 874-877, June 2005
The lifting of a mass by a gas is usually slow compared to molecular velocities, so Poperating is essentially the sane as Pint.  For a gas expanding into a vacuum, the imaginary piston moves with the average velocity of the molecules so Poperating is zero.  This relationship is expected to fail for compressions approaching the speed of sound.

Without formatting of equations this doesn't look good...


text:
Conjugation between rings of biphenyls
I thought since both phenyl rings are not coplanar, the resonance between them is not possible. But my book says the following:

Resonance effect is partially nullified

Partially nullified means resonance is relatively weak but it's taking place

What book are you referring to, please cite your source.

Its  M. S. Chauhan

Looking at amazon, there are many books by that author- are you looking at a specific one? A title and page ref would be helpful

It's in solution manual of advanced problem in organic chemistry in 10th edition on pg no.264

Rule of thumb: DOI for a paper, ISBN for a book. This makes things easier.

If I weren't a mod I might have vtc'd as unclear, as I have no idea what "partial nullification" of resonance means. Is there any explanation or justification in the book?

I honestly don't understand what "weak resonance" is. To me it is something like a boolean, it is either there or not. It sound like "she is a little bit pregnant":)

But that's what the book says

To get a qualitative idea of the "amount of resonance", it would be interesting to compare the absorption spectrum of polyphenylenes (where all phenyl rings are free to rotate) and polyfluorenes (where phenyl rings are pairwise fused into a coplanar arrangement). I'm fairly sure the latter can absorb higher wavelength photons, suggesting a smaller HOMO-LUMO gap due to increased delocalization of the $\pi$ electrons.

@andselisk that's not the case. If you twist the rings you still get orbital overlap and resonance. The overlap just isn't as good so the effect is weak. Otherwise for practical reasons resonance between aromatic rings wouldn't exist, since most of the time they are not perfectly planar aligned.

@DSVA Sounds like an answer, go ahead, post it.

@DSVA but isn't the coplanarity the topmost condition for resonance

@andselisk I will do little bit later when I got time including an example.

Coplanarity is in no way a condition for resonance. In its widest scope resonance simply means, how delocalised is a certain system. In biphenyl, you still have two highly delocalised aromatic rings. The overlap, and further delocalisation of those two aromatic systems might not be as large as in a planar system, but it is certainly there. || Please [edit] in the complete citation to the quoted statement, so that it can be seen in context. You might want to tag it [tag:erratum], too.

I thought since both phenyl rings are not coplanar, the resonance between them is not possible.

This is not correct. If the rings are coplanar you get the best orbital overlap and the strongest resonance effect, while if you twist it the effect will be smaller but still present until you are at an dihedral angle of 90°, where no overlap can take place.
Let us look at phenyl-tetrazine. The phenyl substituent loweres the LUMO of the tetrazine through conjugation and raises the HOMO. The most favored confomer is the planar one, so the ideal system to study this. If it's correct that resonance only takes place at a planar conformation we should see a sudden jump in LUMO energy between planar conformation and any other and for all angles not equal to 0° the LUMO level should be the same.

In addition resonance is stabilizing, so the energy should drop rapidly between non-planar and planar.
Calculated energies (M06-2X/6-311+(d,p)) while twisting the bond looks like this:

So the energy goes up continuously if we twist the phenyl ring, there's no jump in energy. Since there's basically no steric effect, unlike in biphenyl, the energy is most likely only influenced by resonance.
Let us look at the HOMO level. I just picked some angles:

As expected the HOMO is raised in case of planar conformation in contrast to 90°, where we expect no overlap but we can clearly see that there's an influence on the HOMO at nearly every angle getting much stronger if we get near planarity.
Since the HOMO is completely localized at the tetrazine even in the planar form let's look at the HOMO-3 as an example. This orbital is part of the conjugated aromatic system and looks like this if the angle is 0°. Of course orbital energies will get shifted if we twist the rings and finding "the same" orbital is hard, but I'll show the orbital with the same symmetry at the tetrazine.
Here's the picture for 0°, a nice conjugated system:

Here's the picture for 90°, there's no conjugation with the pi-system, little bit with some, I assume, sigma* orbitals.

Now here for 15,30 and 60°:

We can see quite nicely that the orbital in case of 15 and 30° still looks quite similar to the one at 0°, while the one at 60° already looks quite like the one at 90°, with a little bit of orbital in para position at the phenyl ring. Showing that there's a gradual loss of conjugation.
In addition, if the conjugation would be possible only at exact 0° dihedral angle then two things could happen: Either we won't see the effect of conjugation ever, since the molecules move all the time and if rotation around that bond is possible then the chance that the molecule is at exact 0° is basically zero. But we know that conjugation exists. Or the planar conformation would be much more stable due to the conjugation and it would be exact 0° all the time, but from experiments we actually know that those bonds rotate quite well.

coplanarity the topmost condition for resonance –

The most important condition is an overlap between the orbitals, this usually works best if planar, but it most certainly doesn't have to be planar.


text:
How fast does atmospheric carbon dioxide dissolve into strongly basic solution?
I'm conducting some pH measurements with solutions containing NaOH and I'm a bit concerned that carbon dioxide will dissolve and affect my measurements by lowering the pH according to the reaction:
$$\ce{2 OH- + H2CO3 -> 2 H2O + CO3^2-}$$
This would consume my $\ce{OH-}$ ions; I obviously don't want that kind of interference.
Are the kinetics such that I should cover my setup, or can I ignore it's effect on a, say ~1 h timescale? Or ~24 h?
Some additional information, after request:
I don't have many cations that would form insoluble compounds with carbonate
I work at room temperature
The setup is a beaker (diameter 10cm-ish) with approximately 200ml volume
The reaction is supposed to be between sand and NaOH (tiny particles are not inert)

Could you include a bit more details, like the volumes you're working with, how you measure pH, what you are actually doing during the measurements, anything that could somehow influence the reaction... For what it's worth, I don't think the effect is very large in this time frame, especially when you have a small surface exposed.

I guess this paper can help you !

Since even modern air is ~400 ppm (0.004 %), then consider how much is in the air-space in the beaker. If it's enough to affect your experiment, then cover the beaker or put a non-reactive oil layer on the solution.


text:
Blue shift in UV-Vis of ZnO?
The characteristic wavelength of ZnO is supposed to be ~380 nm. However, in this article1, the peak has been blue-shifted to 214 nm. This is quite similar to my sample where the peak is at 200 nm.
In the article it is said that:

the blue shift may be due to the transition of electrons from the inner shell of copper to the outermost shell as time passes. It is possible that, due to aggregation and agglomeration, particle size increases and material settled down on the bottom of the container causing decrease in absorbance.

Could someone explain what this means?
Also, I did a UV-dr on the sample and it gives me a peak at 380 nm.

1: Structural and Optical Characterization of ZnO Nanoparticles Synthesized by Microemulsion Route. International Letters of Chemistry, Physics and Astronomy 2013, 14, 26-36.

Where possible, include human readable citations rather than links to reprints. Doing this ensures that if the website changes/removes the PDF file that the original article can still be found by future  users of chem.SE.

I think the term "hypsochromic shift" is more applicable here.

1} Are you taking into account that the peak at 214 nm is possibly explained by the presence of Cupper?  Is it Cu present in your sample? 2} I should see the spectra in their whole. A peak is a feature, not a spot where there is a (rel) maximum. For instance, these measurements should be have done in water. Water cut off is about 200 nm!

3} depending on the size of the particles there can be a baseline shift due to scattering. This goes as inverse lambda^4 so get to max at the blu side of the window( 200 nm in your case, but it not a peak, see comment 1}


text:
Relative Humidity, vapor pressure, partial pressure
The partial pressure of water in the mixture is the equilibrium vapour pressure of water at the temperature specified.
Relative humidity (RH) is the ratio of the partial pressure of water vapor to the equilibrium vapor pressure of water at a given temperature.
So at all temperatures Relative Humidity is 1 .
But this isn't so.
Where am I wrong?

Start with re-examining your definition of partial pressure. When talking about RH, the partial pressure we use in the calculation is the pressure of water vapor in the air-water mixture. It is not the vapor pressure of water at that temperature, where vapor pressure is the amount of gas phase water that is in equilibrium with liquid phase water; I think this is where your mistake is.

Thanks. Does this mean that if we are working in a closed vessel the partial pressure of water is same as its vapour pressure?

@J.Ari And thus partial pressure of water only changes with temperature in a closed vessel?

As long as there is nothing that is affecting the expected vapor pressure from developing (salt effects, water reactive atmosphere), then your statement in the comments is correct for the case of an enclosed vessel.