text:
Why Use Lewis Structures to Determine Radicals
As far as I know, Lewis Structures are convenient for representing molecules, but give no insight on the actual electron orbitals.
For example: The Lewis Structure of $\ce{O_2}$ does not reflect paramagnetism. Therefore, we use MO theory to explain it.
Then, why are Lewis Structures used to show if a molecule is a radical?
For example: hydroxyl is drawn as $\ce{.OH}$ to reflect the unpaired electron. That is a Lewis Structure.
Why do Lewis Structures work in this case?

Look at the history of atomic models.

Lewis structures are excellent for showing radical character for an odd number of electrons.
The reason they fail for molecular oxygen is that they Lewis representation carries no intrinsic information about the molecular spin, and as such it cannot distinguish the unpaired electrons in molecular oxygen's antibonding orbitals as spin matched (triplet) or spin opposed (singlet).
However, when there are an odd number of electrons, it is clear there will be one unpaired spin, and it is not relevant whether what the spin orientation is for these cases.
That being said, and somewhat outside the scope of this question, Lewis structures cannot distinguish between doublet and quartet states.

Once you've counted your electrons and ended up with an odd number, you don't need Lewis structures (or anything else, for that matter) to conclude that you have a radical on your hands.


text:
How to understand Nelson-Obert charts?
The compressibility factor is given by:
$$
z=\frac{P\overline{V}}{RT}
$$
The Nelson-Obert chart is:

This chart brings the following information:

At very low pressure (Pr << 1), gases behave as an ideal gas regardless of temperature.
At high temperatures (Tr > 2), ideal gas behavior can be assumed with good accuracy.
The deviation of a gas from ideal gas behavior is greatest in the area of the critical point.

Where:
$$
T_R=\frac{T}{T_{(At\ critical\ point)}}\\
P_R=\frac{P}{P_{(At\ critical\ point)}}
$$
What I don't understand is:

Does this chart describe the ideal behavior of a supercritical fluid or a superheated gas or plasma?

Having in mind any phase diagram:

In the critical point, Tr=Pr=Vr=1 (under van der waals equation), then Z=3/8=0.375. But the chart shows Z=0.23. The deviation is somehow big, any reason?

It describes the entire region to the right of the vertical dashed line through the critical point.

For the values of Pr that they show on the graph, beyond Pr = 1, it is a supercritical fluid.  But, there is really no distinction between a supercritical fluid and a superheated gas.

Why, it pretty much does. I'd probably add that it does not describe the ideal gas, for there is no such thing as ideal gas. Also, it does not describe the plasma or ionized gas, for the same reason (I mean, they of course do exist in nature, but that's well outside the present chart and the phase diagram).

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text:
Can oxidation of ethanol by copper(II) oxide yield copper(I) oxide as one of the products?
We know that ethanol is oxidised by copper(II) oxide to an aldehyde. Copper is reduced from $\ce{Cu^2+}$ to $\ce{Cu}$. Can this reaction, with some specific condition, yield $\ce{Cu2O}$ instead? That will also be a reduction of copper, only partial.
The question was asked on a Russian chem forum and it made me curious.

If you add an excess of a reducing sugar to the mix, the copper(II) should all get reduced back to copper(I), i.e. Cu2O. I'm pretty sure that's not what you mean though ;)

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text:
How to calculate the amount of substance of nitrogen that dissolves in water?

The Henry's law constant for the solubility of $\ce{N2}$ gas in water at $298~\mathrm{K}$ is $10^5~\mathrm{atm}$. The mole fraction of $\ce{N2}$ in air is $0.8$. The amount of substance of $\ce{N2}$ for air dissolved in 10 moles of water at $298~\mathrm{K}$ and $5~\mathrm{atm}$ pressure is ___.

I think the mole fraction of nitrogen will be calculated using the formula $$x(\ce{N2})=P/K_h.$$ But the answer is wrong.
In the solution for the question, the mole fraction $x(\ce{N2})$ is multiplied further by $0.8$ which seems to the mole fraction of nitrogen in air.

For all such calculations you have to use the partial pressure of the respective chemical species, not the absolute pressure of the gas phase. Hence that factor ~0.8.

Unfortunately, various definitions of Henry’s law and the corresponding proportionality constant $H$ or $K_\mathrm H$ exist. (For several definitions and corresponding parameter values, see Sander, R. Compilation of Henry’s law constants (version 4.0) for water as solvent. Atmos. Chem. Phys. 2015, 15, 4399–4981.) Therefore, it is important to identify the dimensions of the given data. In the question, the proportionality constant is given as Henry volatility $K_\mathrm H$ with
$$K_\mathrm H = 10^5\ \mathrm{atm}$$
Apparently,* since the given Henry volatility $K_\mathrm H$ is expressed in terms of pressure (the unit symbol “atm” stands for “standard atmosphere”, which is an obsolete unit of pressure; the use of this unit is actually deprecated), the used definition is
$$K_\mathrm H=\frac{p_{\ce{N2}}}{x_{\ce{N2}}}$$
where $p_{\ce{N2}}$ is partial pressure of nitrogen and $x_{\ce{N2}}$ is amount-of-substance fraction (the use of the unsystematic name “mole fraction” is deprecated) of nitrogen in the aqueous phase.
The amount-of-substance fraction $x_{\ce{N2}}$ is defined as
$$x_{\ce{N2}}=\frac{n_{\ce{N2}}}{n}$$
where $n_{\ce{N2}}$ is the amount of substance of nitrogen and $n$ is the total amount of substance. For dilute aqueous solutions, the total amount of substance is approximately equal to the amount of water
$$n\approx n_{\ce{H2O}}$$
which is given as $n_{\ce{H2O}}=10\ \mathrm{mol}$.
Thus, the amount of nitrogen $n_{\ce{N2}}$ can be calculated from the partial pressure of nitrogen $p_{\ce{N2}}$ as
$$\begin{aligned}
n_{\ce{N2}}&=n\cdot x_{\ce{N2}}\\
&=n\cdot \frac{p_{\ce{N2}}}{K_\mathrm H}\\
&\approx n_{\ce{H2O}}\cdot \frac{p_{\ce{N2}}}{K_\mathrm H}
\end{aligned}$$
For a mixture of gases, the partial pressure of nitrogen $p_{\ce{N2}}$ is defined as
$$p_{\ce{N2}}=x_{\ce{N2}}\cdot p$$
where $x_{\ce{N2}}$ is the amount-of-substance fraction of nitrogen in the gaseous phase (as apposed to the above-mentioned parameter in Henry’s law) and p is the total pressure.
Since the total pressure is given as $p=5\ \mathrm{atm}$ and the amount-of-substance fraction of nitrogen in air is given as $x_{\ce{N2}}=0.8$, the partial pressure of nitrogen in air is
$$\begin{aligned}
p_{\ce{N2}}&=x_{\ce{N2}}\cdot p\\
&=0.8\times5\ \mathrm{atm}\\
&=4\ \mathrm{atm}
\end{aligned}$$
* This use of the unit is in the question is actually not permissible. The unit symbol should not be used to provide specific information about the quantity and should never be the sole source of information on the quantity.

I hate to say but I need to find the mole fraction of nitrogen in the solution.

@SiddharthPanchal
I am not sure if I understand your problem with finding the amount-of-substance fraction of nitrogen in the solution. According to Henry’s law, $K_\mathrm H=\frac{p_{\ce{N2}}}{x_{\ce{N2}}}$; therefore, the amount-of-substance fraction of nitrogen in the solution is $x_{\ce{N2}}=\frac{p_{\ce{N2}}}{K_\mathrm H}=\frac{4\ \mathrm{atm}}{10^5\ \mathrm{atm}}=4\times10^{-5}$. In the end, however, the question is asking about the amount of substance $n_{\ce{N2}}$ and not about the amount-of-substance fraction $x_{\ce{N2}}$.

atm is a prefectly normal unit for pressure. Just because it's not SI is no reason to tell students to reject it. Also "mole fraction" is totally standard https://en.wikipedia.org/wiki/Mole_fraction , who says that term is deprecated and what's supposed to be misleading about it?


text:
Geometry of tetrabromidomanganate(II)
What is geometry and hybridization of $\ce{[MnBr4]^2-}$ for $\ce{Mn}$ ($Z = 25$)?
I am not sure if it is tetrahedral or square planar.
I assumed $\ce{Br}$ is a weak ligand and got its geometry to be tetrahedral.
Am I right?
I am a 12th grader and I only know the basics of coordination chemistry.

A square planar geometry is somewhat constrained, if you wish. There need to be compelling electronic reasons to move four coordinating anions (especially large ones like bromide) closer together than tetrahedral — which is the case in square planar, cf the smaller bond angles. Usually, this geometry is associated with $\mathrm{d^8}$ ions but it can happen for other compounds, too.
Another thing to consider is the field split. Its size is influenced by the metal’s charge. Higher charge typically means greater field split. Square planar complexes typically require a large field split to stabilise their low-spin state.
Manganese(II) is a $\mathrm{d^5}$ ion. Since it only has a low charge, it is very likely to be in the high-spin state. The high-spin state of a $\mathrm{d^5}$ ion does not stabilise any geometry whatsoever. Thus, no reasons exist to go square planar and the tetrabromidocomplex must be tetrahedral.


text:
Voids vs Interstitial Site?
I am studying solids states.
So we studied different lattices of Ionic solids by introducting smaller Cations into VOIDS.
Next topic is of defects. SO it is written Frankel defect arises when a smaller cation (or anion) shifts from its lattice site to Interstitial site.
Now something is wrong here. I have seen all the threads and topics, didnt find answer to it.
If we have already discussed all kind of Empty spaces as voids (octa, tetra etc), and have already filled them with cations while making ionic crystals, Now where these Interstitial spaces rises from?
Moreover, Cations are already in interstitial site, why they are even shifting to another interstitial site (which technically is already filled with cations, because we made ionic crystals by placing cations into interstitial sites.)

Yes, it can be confusing. But, take something simple like NaCl. In a perfect crystal, yes, each one will sit quite nicely on their own sub-lattice. To a Cl atom, it is symmetric with respect to the Na atoms, and vice versa. (Note that I don't put the cations on an 'interstitial' site - they have their own sublattice). But, for the combination of Na and Cl, there are now a new set of you 'empty' spaces defined by the spaces between all the Na and Cl atoms - those are the interstitial sites in a NaCl crystal.

So Is there any difference between VOIDS and Interstitial Site

@aman           Would be much clear if use the words with respect to

Technically, I would consider a 'void' to be an empty volume much larger than one lattice site. But, in any crystal structure there will be interstitial sites, often several different sites with different symmetries. Furthermore, the exact configuration of an 'interstitial' is often not as well defined as you might like. For example, in GaAs, the As 'interstitial' is often configured as two As atoms sharing one As site, the so-called split-interstitial.


text:
Zigzag line in the structural formula of budesonide
Excuse me if this question is already answered, but while reading about budesonide, if came across a strange notation I have never seen. I am talking about zigzag line on the right sine. Can somebody, please, tell me what it is? Thank you very much.

http://i.stack.imgur.com/yQWfl.png

I understand, thank you very much for your help.

more information in http://chemistry.stackexchange.com/questions/28503/what-are-the-meanings-of-dotted-lines-and-waves-in-structural-formulas


text:
How much "cleaner" does summer fuel burn?
Well, it's that time of year again: the switchover to "summer" fuel and resulting price increases. This EPA regulation system requires gasoline producers to blend additives into the gasoline that reputedly make it burn cleaner.
What exactly does it mean "burn cleaner" and how much "cleaner" is summer fuel than regular gasoline?

Gasoline, diesel fuel, and ethanol-gasoline blends are adjusted seasonally and geographically to ensure proper starting and performance. Winter blends contain higher levels of high vapor pressure compounds like butane to ensure the fuel is sufficiently volatile to ignite in cold temperatures. This in turn makes the gasoline cheaper to produce as it does not have to be as pure as the summer blend$^{[1]}$.
Conversely, summer blends contain lower levels of high vapor pressure liquids to ensure that the fuel doesn't evaporate away in the heat and pollute the atmosphere. This is why summer blends are marginally cleaner than winter blends. A study on winter versus summer emissions near tunnels form the University of Wisconsin collected the following data on non-methane hydrocarbon emissions$^{[2]}$:

As for fuel efficiency, winter-grade gasoline yields $1.7$% less energy on average than the summer. This may seem like a considerable amount, but energy content can vary widely from station to station in either season from $3.4$-$4.8$%$^{[3]}$.

$^{[1]}$ The Oil Drum
$^{[2]}$Univeristy of Wisconsin, Summer and winter nonmethane hydrocarbon emissions from on-road motor vehicles in the Midwestern United States
$^{[3]}$ EPA, Fuel Economy Impact Analysis of RFG

Those are pretty huge margins of errory.

It's the only data I could find. I'll keep looking though.

@ShakaBoom Wow, the top two, especially. "X ± X, give or take."


text:
How is volatility useful in the production of acids?

Sulfuric acid because of its low volatility can be used to manufacture more volatile acids from their corresponding salts.

How does volatility affect the production of acids? Isn't it that sulfuric acid being stronger than the salt of weak acid replaces the anion part of salt so the weak acid is produced or does just the low volatility of sulfuric acid matter? Will it be feasible to produce a highly volatile acid even stronger than $\ce{H2SO4}$ by exploiting the low volatile nature of $\ce{H2SO4}$?  What is the real process involved?

Can you please tell where did you quote that statement from?

@Kartik From NCERT chemistry class 12 p block pg.no:190 under uses of sulfuric acid.

@Kartik No, I can't find it on page number 190

Can anyone please give a list of many important inorganic acids arranged in the order of volatility ? I can't find it on internet

Yes, this is indeed the case. The reasoning behind it is using chemical equilibria to their fullest.
If you have a Brønsted acid and a Brønsted base in the same vessel, you will always have an equilibrium of the following kind:
$$\ce{HA + B- <=> A- + HB}$$
It depends on the nature of the acid and the base — i.e. their $\mathrm{p}K_\mathrm{a}/\mathrm{p}K_\mathrm{b}$ values — which side of the equation is favoured in a closed system (i.e. solution). For example, dissolving $\ce{NaHSO4}$ and $\ce{NaSH}$ in the same sample of water will result in the following set of equations:
$$\ce{H2SO4 + Na2S <=>> NaHSO4 + NaSH <=>> Na2SO4 + H2S}$$
Because the $\mathrm{p}K_\mathrm{a}$ values of both compare as follows:
$$\begin{array}{ccc}\hline
\text{acid} & \mathrm{p}K_\mathrm{a1} & \mathrm{p}K_\mathrm{a2}\\
\hline
\ce{H2SO4} & \approx -3 & 1.9\\
\ce{H2S} & 7.0 & 12.9\\
\hline\end{array}$$
We already have a way of producing $\ce{H2S}$ by means of protonating sulfide ions in solution here. However, $\mathrm{p}K_\mathrm{a1}\left (\ce{HCl}\right ) \approx -6$, which is more acidic than sulphuric acid, so adding $\ce{NaCl}$ to $\ce{H2SO4}$ should result in a net reaction of nearly nothing.
This is where vapour pressure comes in as a second factor. $\ce{HCl}$ is a gas under standard temperature and pressure while $\ce{H2SO4}$ is a liquid. ($\ce{H2S}$ is also a gas. If we added liquid sulphuric acid to sodium sulfide, $\ce{H2S}$ gas would evolve, but that’s what the $\mathrm{p}K_\mathrm{a}$ value predicts anyway.) If we have an open vessel — i.e. gases can diffuse away — then any $\ce{HCl}$ produced in equilibrium will dissociate away in the long run. This is due to a second equilibrium that we could write as follows:
$$\ce{HCl (g) <=> HCl (aq)}$$
The ‘equilibrium constant’ of this physical process is more or less what we call vapour pressure, and for hydrogen chloride both sides are significantly more balanced than for sulphuric acid. Therefore, we should describe the entire system in the following way:
$$\ce{NaCl + H2SO4 <=> NaHSO4 + HCl (diss) <=>> NaHSO4 + HCl (g) ^}$$
Where $\ce{(diss)}$ is a shorthand for dissolved in sulphuric acid, our reaction medium.
Drawing away the hydrogen chloride gas in the rightmost equation, for example by reducing pressure or inducing an air flow, will shift all equilibria to the right since that product is constantly being removed. And thus we can liberate $\ce{HCl}$ gas with sulphuric acid, even though the $\mathrm{p}K_\mathrm{a}$ of hydrogen chloride is lower than that of sulphuric acid.

An example of this would be the reaction between sulfuric acid and potassium nitrate, the salt of nitric acid. When this salt is mixed with sulfuric acid, nitric acid and potassium acid sulfate are the result, although the reaction is incomplete. If the resulting mixture is then heated the nitric acid evolves as a vapor because it is much more volatile than sulfuric acid. This vapor can then be condensed separately. In this way relatively pure nitric acid can be produced.

Great, that's exactly what I needed in solving a textbook problem right now. +1


text:
Is HF the only method for trying to solve the many-electron Schrödinger equation?
The Schrödinger equation can only be solved analytically for the smallest of "molecular" systems. The Hartree-Fock method is a method of obtaining approximate solutions to the many-electron Schrödinger equation, and a bunch of methods try to reduce the error associate with the HF method.
However, all ab initio electron correlated methods I know of and have read about are based on HF; that is, they all use the HF solution and adds to it. So basically there is only one way in use today of attempting to solve the many-electron Schrödinger equation?
Then of course there is density functional theory, but here you strictly don't try to solve the Schrödinger equation, you just try to obtain the solution, right?
So is this a correct assessment? Do we truly only use one method of trying to solve the many-electron Schrödinger equation? Is there any research being done on alternative methods (other than DFT)?

Ab-initio valence-bond method, maybe?

I'm not sure I'd characterize Hartree-Fock as 'solving' it either, although it is perhaps semantics to distinguish 'solving' from finding a 'solution'. If you have a solution, doesn't that solve the equation?

There are Quantum Monte Carlo methods.

Also, DFT does actually solve the Schroedinger equation (at least in the same sense as HF does). Especially when you look at Levi's constrained search formalism and Kohn-Sham Theory you see that you start out from the many-body Schroedinger equation and through a series of constrained minimization steps arrive at the Kohn-Sham equations.

There are something called reduced density matrix metods (RDM). Also if you are interested in alternative methods i can recommend a book from  Paul Popelier called Solving The Schrödinger Equation: Has Everything Been Tried?

MCSCF is not based on HF

So is this a correct assessment? Do we truly only use one method of trying to solve the many-electron Schrödinger equation? Is there any research being done on alternative methods (other than DFT)?

No, it is not correct. Saying that Hartree-Fock(HF) theory is the only method is falling short. Hartree-Fock is only one of many existing methods. While it is true that some single reference methods have a dependence on the HF solution (because they build upon it) when they include a reduced number of determinants, it is not the case for other. Particular mention deserves Coupled Cluster since it is insensible to the reference determinant found by HF. The proof is given by Thouless theorem (see Joshua Goings' post, or via The Internet Archive).
Thus, to give you an overview of the grand landscape of possible approaches I tried to compile the families of methods better established nowadays. I did not intend to specify individual methods because there are so many ... and people continue to investigate new ones. These are:
Deterministic

Semi-empirical (non ab initio): Hückel1/Tight binding2, Hubbard, ...
Wavefunction methods [Trygve Helgaker, Poul Jørgensen, Jeppe Olsen:
Molecular Electronic‐Structure Theory. John Wiley and Sons, Ltd: 2000. DOI: 10.1002/9781119019572]

Hartree method. Caution: mathematicians use this name for a related method.
Hartree-Fock (HF): can be Restricted (RHF), Restricted Open (ROHF), Unrestricted (UHF) or Generalized (GHF).
Configuration Interaction (CI), up to order $N$, which is equivalent to Full-CI1/exact diagonalization2/direct variational approach3.
Multi-Configuration Self Consistent Field (MCSCF). [Chem. Rev. 2012, 112 (1), 108–181.]

Complete Active Space (CASSCF).
Two Configurations.
Manual selection of configurations or other.

Multi-Reference Configuration Interaction (MRCI)
CASPT2, NEVPT2, partially (PC) and strongly contracted (SC)
variants of the N-electron valence state second-order
perturbation theory
Multi-Reference Coupled Cluster methods (MRCC)
Many Body Perturbation Theory methods (MBPT) [Isaiah Shavitt, Rodney J. Bartlett: Many-Body Methods in Chemistry and Physics, MBPT and Coupled-Cluster Theory. Cambridge University Press: Cambridge, 2009. DOI: 10.1017/CBO9780511596834]

Coupled Cluster methods and its simplifications
Möller-Plesset perturbation theory of order $n$ (MPn)
Random Phase Approximation (RPA)
GW-Approximation

Explicit correlated methods R12/F12 [Chem. Rev. 2012, 112 (1), 75–107.]
Valence Bond Theory [Sason Shaik, Philippe C. Hiberty: A Chemist's Guide to Valence Bond Theory. John Wiley & Sons, Inc.: 2008. DOI: 10.1002/9780470192597]

Density Functional Theory (DFT). [Robert G. Parr, Yang Weitao: Density-Functional Theory of Atoms and Molecules. Oxford University Press: USA, 1994. ISBN: 9780195092769]

Thomas-Fermi theory. Orbital-free methods.
Kohn-Sham. Many density functional approximations developed, families are:

LSDA
GGA, hybrid GGA
MGGA, hybrid MGGA
OEP

Pair density functional theory [Comput. Theor. Chem. 2013, 1003, 91–96.]
Natural Orbital Functional Theory (NOFT) [S. Goedecker, C. J. Umrigar: Natural Orbital Functional Theory. In: J. Cioslowski (eds) Many-Electron Densities and Reduced Density Matrices. Mathematical and Computational Chemistry. Springer: 2000, Boston, MA. DOI: 10.1007/978-1-4615-4211-7_8]
Geminal Functional Theory [J. Chem. Phys. 2000, 112 (23), 10125–10130.]
k-particle density cummulants methods [Int. J. Quantum Chem. 2003, 95 (4-5), 404–423.]
Density Matrices methods

Density Matrix Renormalization Group (DMRG) [Annu. Rev. Phys. Chem. 2011, 62 (1), 465–481.]
Density Matrix Embedding Theory. Can be combined with several methods. [J. Chem. Theory Comput. 2016, 12 (6), 2706–2719.]
One-body Reduced Density Matrix Functional Theory (1-RDMFT) [J. Chem. Phys. 1985, 82 (12), 5604–5607.]
Variational 2-RDM Theory [Phys. Rev. Lett. 2012, 108 (26).]

Dynamical Mean Field Theory (DMFT). [J. Chem. Phys. 2011, 134 (9), 094115., arXiv:1012.3609 [cond-mat.str-el]] Starts with a Hubbard model of a lattice problem, then connects it to an impurity problem that can be solved with other methods.

Non-deterministic (stochastic)

Quantum Monte Carlo [Chem. Rev. 2012, 112 (1), 263–288.]

Variational Monte Carlo (VMC)
Fixed-Node Diffusion Monte Carlo (FNDMC).
LR-DMC, lattice-regularized diffusion Monte Carlo
Self-Healing Diffusion Monte Carlo
Green Function Monte Carlo (GFMC). GF2, self-consistent second-order Green’s function
Auxiliary Field Quantum Monte Carlo (AFQMC)
Reptation Quantum Monte Carlo
Full CI Quantum Monte Carlo (FCIQMC) [J. Chem. Phys. 2009, 131 (5), 054106.]
BDMC, bold diagrammatic Monte Carlo
Time-Dependent Quantum Monte Carlo

There are also mixtures of various methods.
The methods above have been tested with molecules by the quantum chemistry community but there are others that have been proven only for one dimension
or toy models. Operator methods are one example.
Many of them try to approximate the Full CI tensor that is described in a basis of determinant functions. It is impossible to treat such tensor for medium to large systems so the point is to take the minimum number of determinants that contribute significantly. The difference lies in how they choose those determinants. There are also other important distinctions among them, like if they are variational, perturbative or none, size-extensive, size-consistent, ...
In summary, each has its advantages and disadvantages. I recommend anyone interested to read
SOLVING THE SCHRÖDINGER EQUATION. Has Everything Been Tried? 2011, Imperial College Press. Ed.: Paul Popelier.
Furthermore, the analytic properties (read regularity) of the wavefunction can be exploited to devise new methods. As Harry Yseretant puts it in his book:

Approximating the solutions is thus inordinately challenging, and it is conventionally believed that a reduction to simplified models, such as those of the Hartree-Fock method or density functional theory, is the only tenable approach. This book tries to convince the reader that this conventional wisdom need not be ironclad: the regularity of the
  solutions, which increases with the number of electrons, the decay behavior of their mixed derivatives, and the antisymmetry enforced by the Pauli principle contribute properties that allow these functions to be approximated with an order of complexity which comes arbitrarily close to that for a system of one or two electrons.

Also, I would like to note that there is a collaborative project under the hood of the Simons Foundation whose purpose is precisely finding better methods to solve the electronic structure problem. And, of course, there are many more people working on the same task.
Footnotes

Naming adopted by the chemistry   community
Naming adopted by the physics     community
Naming adopted by the mathematics community

References

Mario Motta, David M. Ceperley, Garnet Kin-Lic Chan, John A. Gomez, Emanuel Gull, Sheng Guo, Carlos A. Jiménez-Hoyos, Tran Nguyen Lan, Jia Li et al. Towards the Solution of the Many-Electron Problem in Real Materials: Equation
of State of the Hydrogen Chain with State-of-the-Art Many-Body Methods. Phys. Rev. X 2017, 7, 031059. DOI: 10.1103/PhysRevX.7.031059

Just transforming all the citation made me realise how much work this was in the first place. Thanks for the effort. I have put up a bounty, which I will reward to your answer after the weekend.

@Martin-マーチン Thanks to you for taking the initiative of doing the boring and hard job of making the references consistent with the style accepted in the site.

You are welcome! And for future reference, I can recommend the user script which is presented in the following answer: Are there any tools to help me format citations appropriately?  It makes the job much easier.

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text:
Bonding in alkali metal complexes
How exactly is the bonding described in complexes involving alkali metals? In particular, how much of a covalent component is there?
Take three examples:
$\ce{[Na(H2O)6]+}$: This previous answer by @tschoppi suggests that the bonding in this complex is purely electrostatic in nature due to the lack of available d-orbitals for covalent bonding. This seems like it might be true because it would explain why the water complexes are not strongly bound.
$\ce{Na2(edta)}$: This previous question suggests that the sodium here is not complexed with the EDTA but rather that it again forms an essentially ionic (i.e electrostatic) bond with little covalent character.
$\mathrm{[Na(\text{15-crown-5})]^+}$: This is very stable, suggesting a strong bond of some sort, probably with some covalent character. However, it doesn't seem to be radically different from the previous ligands, particularly EDTA, which has similar oxygens available for bonding.

Well d-orbitals are there, they’re just not accessable. I would assume that this is a similar case to $\ce{Zn^2+}$, where complexes do exist but are often kinetically very labile. There is simply no compelling reason for sodium to stay in a certain complex environment.

QTAIM analysis of $[\ce{Li}(\text{12-crown-4})]^+$ indicates pretty strongly that the interaction between the $\ce{Li+}$ and the crown oxygens is almost purely ionic in nature (very low $\rho$, with $\nabla^2\rho > 0$. I would assume $[\ce{Na}(\text{15-crown-5})]^+$ is similar. One key difference b/w carboxylic and etheric oxygens is charge: the excess electron at the carboxyl probably results in an appreciably more diffuse electron cloud, making it less favorable for tight ionic binding.

Binding doesn't have to be covalent in nature for it to be strong - it is just because of the chelate effect (for both edta and crown ethers) and macrocyclic effect (for crown ethers).

The bonding of alkali cations to water, to EDTA, and to crown ethers is strictly electrostatic in all three cases, at least based upon QTAIM analysis$^{[1]}$ of representative systems.

For this analysis, I ran gas-phase quantum chemical optimizations on $[\ce{Li}(\text{12-crown-4})]^+$, $[\ce{Na}(\text{EDTA})]^{3-}$, and $[\ce{Na}(\ce{H2O})_6]^+$ using ORCA v3.0.3. (I can post the computation inputs/outputs if anyone is interested.) I also optimized $\ce{NaCl}$ as an additional system with uncontroversial ionic bonding. While the gas-phase results will poorly represent a variety of aspects of the dissolved species, I think they should capture well enough the characteristics of the wavefunction necessary to study the types of bonding involved. Other gas-phase calculations I've run on, e.g., $[\ce{Cu}(\ce{H2O})_6]^{2+}$ have optimized smoothly to the expected octahedral ligand arrangement, lending credence to this assumption.
Some notes on the optimizations:

Geometry optimization of $[\ce{Li}(\text{12-crown-4})]^+$ converged readily.
For $[\ce{Na}(\text{EDTA})]^{3-}$, despite starting in a prototypical octahedral chelation geometry, the EDTA molecule immediately began to 'loosen its grip' on the $\ce{Na+}$, clearly heading toward a less compact configuration. In fact, one of the oxygen atoms actually discarded its bonding interaction with the $\ce{Na+}$ in favor of an intramolecular hydrogen bond.  I performed the QTAIM analysis on the last geometry obtained before ORCA reached its iteration limit in the geometry optimzation procedure.
Similarly, for $[\ce{Na}(\ce{H2O})_6]^+$, despite starting the optimization in a prototypical octahedral coordination geometry, the water ligands 'wandered' throughout the optimization process, in a fashion loosely reminiscent of a molecular dynamics run. As with the EDTA complex, I just chose the final geometry after the optimizer halted as the one on which I ran the QTAIM analysis.

For illustration, I generated GIF animations of the $[\ce{Na}(\text{EDTA})]^{3-}$ and $[\ce{Na}(\ce{H2O})_6]^+$ optimizations. The individual frames were produced with the 'Movie Maker' module of VMD 1.9.1 and the final GIFs were generated using EZgif.com.

Several metrics generated by QTAIM analysis argue for strictly ionic bonding of the alkali metal atoms in these systems:

Low electron density $(\rho \substack{<\\\sim}0.1)$ and positive density Laplacian $(\nabla^2\rho>0)$ at the relevant line critical points between the alkali cation and the coordinating oxygen (or nitrogen) atoms
High localization index $(\mathrm{LI}\substack{>\\\sim}0.9)$ in the alkali atom basin
Low delocalization index $(\mathrm{DI}\substack{<\\\sim}0.75)$ between the alkali atom basin and those of the coordinating atoms

Strictly speaking, in addition to $\#1$ above, the terms of the Laplacian perpendicular to the bond path must also be small in magnitude in order to diagnose ionic bond character$^{[2]}$, but I have omitted those values here.
The table below presents these metrics for the above representative chemical systems, as well as some reference molecules possessing uncontroversial bonding types.  Due to the fairly regular geometry of $[\ce{Li}(\text{12-crown-4})]^+$, the metrics didn't vary much throughout the system and I averaged them for each bond and atom type.  Despite the lack of a deep energy well, the metrics were also similar for the six oxygens in $[\ce{Na}(\ce{H2O})_6]^+$, so I averaged the values here as well.  For the irregular geometry of $[\ce{Na}(\text{EDTA})]^{3-}$, the values differed enough that I chose to report them indivdually; the numbering of the coordinating atoms is arbitrary.  All non-literature data were generated by MultiWFN v3.3.7 on Windows 7 using the default settings and the "Medium" grid for generation of the atomic basins for the $\mathrm{DI}$ and $\mathrm{LI}$ calculations. All values are in atomic units: $\rho\equiv{e^-\over\mathrm{Bohr}^3}$ and $\nabla^2\rho\equiv{e^-\over\mathrm{Bohr}^5}$ ($\mathrm{DI}$ and $\mathrm{LI}$ are dimensionless).
$$
~ \\
\textbf{QTAIM Results} \\
\begin{array}{ccccccccc}
\hline
\mathbf{Species} & ~ & \mathbf{Bond} & \rho_\mathbf{LCP} &
    \mathbf{\left(\nabla^2\rho\right)_\mathbf{LCP}} & \mathbf{DI} & ~ &
    \mathbf{Atom} & \mathbf{LI} \\
\hline
 & &  \ce{Li-O} & 0.036 & +0.26 & 0.077 & & \mathrm{Li} & 0.922 \\
[\ce{Li}(\text{12-crown-4})]^+ & & \ce{O-C} & 0.25 & -0.50 & 0.856 & &
     \ce O & 0.870 \\
 & & \ce{C-C} & 0.26 & -0.70 & 0.949 & & \ce C & 0.656 \\
 & & \ce{C-H} & 0.28 & -1.01 & 0.901 & & \ce H & 0.420\\
\hline
& & \ce{Na-O}1 & 0.015 & +0.086 & 0.064 & & \ce{Na} & 0.974 \\
& & \ce{Na-O}2 & 0.021 & +0.131 & 0.096 & & \ce{O}1 & 0.899 \\
[\ce{Na}(\text{EDTA})]^{3-} & & \ce{Na-O}3 & 0.020 & +0.121 & 0.089 & &
     \ce{O}2 & 0.900 \\
& & \ce{Na-N}1 & 0.014 & +0.074 & 0.056 & & \ce{O}3 & 0.900 \\
& & \ce{Na-N}2 & 0.018 & +0.094 & 0.065 & & \ce{N}1 & 0.766 \\
& &  & & & & & \ce{N}2 & 0.769 \\
\hline
[\ce{Na}(\ce{H2O})_6]^+ & & \ce{Na-O} & 0.014 & +0.086 & 0.057 & & \ce{Na} & 0.975 \\
& & & & & & & \ce{O} & 0.916 \\
\hline
[\ce{NaCl}]^0 & & \ce{Na-Cl} & 0.035 & +0.197 & 0.321 & & \ce{Na} & 0.978 \\
& & & & & & & \ce{Cl} & 0.975 \\
\hline
[\ce{LiF}]^{0\,\ddagger} & & \ce{Li-F} & 0.079 & +0.749 & 0.179 & & \ce{Li} & 0.957 \\
& & & & & & & \ce{F} & 0.991 \\
\hline
[\ce{CH4}]^{0\,\ddagger} & & \ce{C-H} & 0.291 & -1.168 & 0.980 & & \ce{C} & 0.661 \\
& & & & & & & \ce{H} & 0.469 \\
\hline
^\ddagger~_{\text{Values from Ref. [2]}}
\end{array}
$$
As can clearly be seen, the interactions between the alkali metals and the ligating atoms are uniformly of ionic character: low electron density and positive Laplacian at the LCP; low $\mathrm{DI}$ between the paired basins, and quite high $\mathrm{LI}$ for the alkali metal basins. This is consistent with the ionic species $\ce{LiF}$ and $\ce{NaCl}$ in the table, and is in marked contrast to the covalent systems included.

$^{[1]}$ More information can be found on Wikipedia and at RFW Bader's page at McMaster University.  A more readable (but unfortunately paywalled) description is provided in Ref. [2].
$^{[2]}$Bader & Matta, Found Chem 15: 253 (2013). doi:10.1007/s10698-012-9153-1.

Very nice analysis! Is there a plus sign missing in the $\nabla^2\rho$ column of sodium chloride? All other values are signed. And also: Do you know how zinc-edta and zinc hydrates compare, or should I ask that in a separate question? ;)

@Jan Yup. Fixed - thanks!  I don't know specifically how $\ce{Zn}$ complexes compare, but what QTAIM analysis I've done on aquo-$\ce{Cu}$ complexes indicates strictly ionic character. I would assume $\ce{Zn}$ complexes would be even more ionic. As I noted, the aquo-$\ce{Cu}$ complexes optimize to a stable configurational minimum - I don't know if the $\ce{Zn}$ complexes might "wander" more like the sodium.  I'd think $\ce{Zn}$ would compare better to, say, $\ce{Ca}$, though, what with them both being divalent.

NaEDTA complex is very poorly chosen since, your know, it has rather high charge that will undoubtedly force chelation rings to open (i'm surprised it didn't dissociate) . Calling LiF in gas phase ionic is an interesting and novel idea.

@permeaka Would you prefer "non-covalent" for $\ce{LiF}$, then? I did think about optimizing, e.g., $[\ce{Na2H2EDTA}]^0$ instead.  But, e.g., $[\ce{CuEDTA}]^{2-}$ presumably stays chelated... is there something more problematic about the triply negative charge?

@permeakra That being said, I'm not particularly interested in the stability or macroscopic physical "existenceness" of these systems, just the properties of the electron density between the alkali atoms and the ligating oxygens/nitrogens. I presume you don't have the same complaint about the aquo complex...given how similar the various metrics are between the aquo and EDTA complexes, I would argue that, indeed, the high negative charge matters little for the present purpose.

It is puzzling that your analysis reveals that the hexaaquacopper (II) complex has strictly ionic character in terms of bonding. The origin of the Jahn-teller effect assumes that d orbital splitting has taken place via ligand-metal covalent interactions. Without covalent interactions, we would not be able to explain splitting and hence, there would be no JT effect, from the point of view of ligand field theory. Unless, the JT effect occurs from the splitting provided from the electrostatic crystal field theory model? Did you also try to compare your findings with similar computational studies?

@TanYongBoon Looking back on that comment you're referring to, I'm no longer strongly confident that the water-Cu(II) bonding is strictly ionic.  In exploration I've done since the above discussion, I have some tentative theories about a more robust bond-characterization approach that would distinguish ionic from coordinate bonds.  If I recall correctly (been awhile since I've looked at it), coordinate bonds have small or positive $(\nabla^2\rho)_{LCP}$, similar to ionic bonds, but the properties of the ELF field are appreciably different.


text:
Formal charge and net charge
What is the basic difference between formal charge and net charge . Does formal charge take part in resonance .
I searched it on wikipedia , but it is mostly discussing how to find formal charge.
https://en.m.wikipedia.org/wiki/Formal_charge

http://chemistry.stackexchange.com/questions/48189/difference-between-oxidation-and-formal-charge?s=4|2.7337 http://chemistry.stackexchange.com/questions/14478/the-definition-of-formal-charge?s=2|2.7995

Net charge is the sum of all formal charges of the atoms in a molecule. Net charge is the charge of the molecule.
Formal charge is the charge of an atom in a molecule. Formal charge varies when you look at resonance structure. See this post of the nitrate resonance structures. It can be obtained through:
\begin{equation}
Formal\ charge\ =\ Valence\ electrons\ -\ no\ bonding\ electrons\ -\ \frac{bonding\ electrons}{2}\quad\quad\quad\quad\quad\text{(Eq. 1)}
\end{equation}
Example: I take the example given previously with $\ce{NO3^{-}}$, in order to give a complete answer to the present post.
So, Having in mind the rules to draw the Lewis Structure:

Operations

Sum the valence electrons of all atoms. When the system is an anion, an electron is added. When the system is a cation, an electron is subtracted.
Sum the 'octet-electron duet' of all atoms.
Subtract step 2 of 1. Results corresponds to shared or bonding electrons.
Subtract step 3 of 1. Result corresponds to the nonbonding electrons.

Indications

Assigns two electrons to each bond.
If electrons remain from step 3. Add them in pairs creating double or triple bonds. Having in mind the duplet/octet rule.
The obtained electrons from step 4. Add them in pairs to the more electronegative atoms.
Calculate the formal charge of each atom.

Then:

Operations

$$valence\ electrons\ \cdot\ number\ atoms\ of\ \ce{N}\ +\ valence\ electrons\ \cdot\ number\ of\ \ce{O}\ +\ anion\ condition $$ Then $$5\cdot 1+6\cdot 3+1=24$$
$$octet\ of\ \ce{N}\ \cdot\ number\ atoms\ of\ \ce{N}\ +\ octet\ of\ \ce{O}\ \ \cdot\ number\ of\ \ce{O} $$ Then $$8\cdot 1+8\cdot 3=32$$
$$32-24=8$$
$$24-8=16$$

Indications

After doing the first three steps, you will get:
 (Source: Stackexchange)
Now, taken equation 1 to nitrogen:
$$Formal\ charge\ of\ \ce{N} =\ 5\ -\ 0\ -\ \frac{8}{2}\ =\ +1$$
Now, taken equation 1 to oxygen bonded to nitrogen through single bond:
$$Formal\ charge\ of\ \ce{O} =\ 6\ -\ 6\ -\ \frac{2}{2}\ =\ -1$$
Now, taken equation 1 to oxygen bonded to nitrogen through double bond:
$$Formal\ charge\ of\ \ce{O} =\ 6\ -\ 4\ -\ \frac{4}{2}\ =\ 0$$
Therefore
Net charge of $\ce{NO3^-}$ is the sum of all formal charge of the atoms in the molecule equals to -1


text:
Resonance condition for absorption of energy
In NMR, for example, why it is not possible to excite nuclei from one spin state to another using energy of arbitrary frequency?

This is indeed the basis of modern Fourier transform NMR (the technique that all modern spectrometers use).
The molecule is irradiated with a range of frequencies and the response detected. Application of some clever maths (the Fourier transform) then allows the individual signals to be observed.
You can think of this a bit like bashing every key on a piano and recording the noise. Application of Fourier transform would then allow you to get back the sound for the individual keys.


text:
Is there any way to refine Feldspar?
Feldspars are mostly composed of three compounds:

KAlSi$_3$O$_8$
NaAlSi$_3$O$_8$
CaAl$_2$Si$_2$O$_8$

I notice they each have Aluminum. Feldspar is far more common than Bauxite (the only Aluminum ore commercially mined). As it stands now, Feldspar is used in glass-making, but I'm wondering if there's some chemical refining process that can extract the Aluminum somehow?---especially that third one, since it has two Al's.
Note: I'm not looking for an economical method. That's proly asking too much. I'm not worried about aluminum reserves, because bauxite is still very plentiful. I'm simply interested in a chemical method to extract Aluminum, or at least Alumina (Al$_2$O$_3$), from Feldspar, purely for reasons of chemical curiosity.
The only thing I've researched is the Bayer Process, but I have no idea if it can be applied or modified for Feldspar.

here is a link to a patent for such a process. http://www.google.com/patents/US1036897

Aluminium oxide can be isolated from feldspar by first acid digestion with a mixture of hydrofluoric acid and sulfuric acid (get rid of silicon by formation of silicon tetrafluoride), then digesting the residue with sodium-potassium carbonate, dissolving the obtained mass in dilute hydrochloric acid and then precipitating $\ce{Al(OH)3}$ by adding ammonia. The $\ce{Al(OH)3}$ can be calcined to aluminium oxide by heating to over 1100°C.
Note that the described procedure requires a suitably equipped laboratory .

Thank you. To be honest it doesn't sound very expensive compared to the Bayer Process for refining Bauxite. It does, however, seem a bit more complicated since it involves more chemicals. I don't think those acids or ammonia will make it much more expensive.

The price of hydrofluoric acid alone is probably at least ten times higher than the price of sodium hydroxide. Additionally, the handling of hydrofluoric acid is quite difficult since it is volatile, corrosive and highly toxic.

I see. I imagine it's expensive largely because of safety precautions slowing down the workforce. I suppose a large fully automated plant could be set up to make it, but such a plant would be very expensive in its own right. One more thing, though: does your process work on all three species of feldspar that I listed?

I think the procedure would work with all three species of feldspar you have listed.


text:
Rhodizonic Acid and Silver Citrate?
I have used some of those lead check swabs from 3M. I used them on some ceramic tile and received strange results. I called the tile manufacturer who was insistent that lead had never been used in their operations. After talking with 3M they asked me to send a picture, which I did. After looking at the picture the 3M lab told me that they did not believe the test to be positive for lead but didn't explain the color I observed.
I realized I had cleaned the floors with a cleaner which contained silver citrate as a preservative. Would the silver ions have reacted with the rhodizonic acid? What color would this have produced? I observed a pinkish color (definitely not red. More pink/purple) in some areas I tested.
I can include a picture if it would help.

$\ce{Ag+}$ reacts with Sodium Rhodizonate to form a Black colored compound - but only in a neutral or weak-acidic environment.
$\ce{Pb^{2+}}$ should give you a Blue-Violet color (or Scarlet if we're dealing with a weak-acidic environment); therefore, I don't think you're dealing with a lead contamination.
Reference: Feigl, F.; Suter, H. A. Analytical Use of Sodium Rhodizonate. Ind. Eng. Chem. Anal. Ed. 1942, 14 (10), 840–842. DOI: 10.1021/i560110a034.

I investigated silver rhodizonate, among other ions, in my master's thesis. Being a high symmetry oxocarbon $(D_\mathrm{6h}),$ it exhibits many interesting spectroscopic properties. The results are published in the Journal of Raman Spectroscopy.[1] It indeed forms a dark substance, whose absorption spectrum can be altered if the sample is ground. This phenomenon deserves further study!
Reference: 1. Gonçalves, N. S.; Santos, P. S. Resonance Raman spectroscopy of rhodizonates: Evidence of low-energy transitions in the solid state. J. Raman Spectrosc. 1995, 26 (5), 363–372. DOI: 10.1002/jrs.1250260507.


text:
knowing that a strong base is a strong electrolyte, when we add a weak acid in water, will its conjugate strong base be a strong electrolyte too?
I am not sure if the questions makes sense. What i am trying to say is that, if weak acids form strong conjugate bases, why aren't they strong electrolytes?  Thank you in advance.

Hi and welcome to chemistry.stackexchange.com. Feel free to take a [tour] of the site. Note that your question should ideally be posted in the body of your post. You can [edit] it in.

You know that basicity/acidity and conductivity are unrelated topics?

A strong acid is a strong electrolyte and a weak acid is a weak electrolyte no?

Not necessarily. Sulphuric acid is a very strong acid, but $96~%\ \ce{H2SO4}$ is a lousy electrolyte.

that explains a lot. i mixed up some concepts thank you for your help.


text:
Why is charcoal useful as a fuel compared to wood? Don't we lose energy by making it?
Charcoal is produced by partially burning wood. However, as the wood is burned, some of its energy is lost. Why is it that charcoal is still preferred as a fuel instead of wood in many cases?
Doesn't charcoal contain less energy than wood? Is the main reason that wood contains a lot of water which would form unwanted vapor?

Energy density is important

True, some of the energy is lost. But some of the mass is lost too.

As I understand it, charcoal --mostly carbon, plus some amount of inorganic ash-- burns cleaner - and hotter - than wood, and has more energy content per unit of weight than wood. The process of making charcoal involves heating the wood in the absence of air or with limited contact with air - driving off water and low molecular weight oils and odor components that produce a lot of the smoke from burning wood, and converting cellulose (a major component of wood) into carbon plus water.

It is kind of like the difference between coke and coal - by getting the water and high-vapor pressure stuff out, you are left with a more repeatable product.


text:
Predicting major product of a reaction with nitrous acid
$\hspace{4.5cm}$
For the above reaction I am asked to predict $\ce{X}$, the major product.
Of the options given, I thought product (1) would be correct, seeing as how it has the most stable intermediate cation (tertiary) and a highly substituted double bond.
$\hspace{3.9cm}$
The answer however states that product (2) is the major product.
I can't understand why the second product would be favored over the first. There's no obvious stabilizing factor here in product (2).

Oxonium cations are more stable than tertiary.

Isn't a secondary carbocation the intermediate and not an oxonium ion for product 2?I mean, after N2 is eliminated and a hydride transer occurs from the carbonyl carbon to the carbocation, isnt a secondary carbocation formed next to electronegative oxygen?

...Which is a protonated carbonyl - oxonium cation. Somehow this powerful mesomeric stabilisation is often omitted

(2) cannot be the major product as of the images you are supplying now unless a carbon source is added. The carbon atoms don’t add up.

I think (2) is correct, but either your or your book erred in writing it. This is what the mechanism (and major product) should be:


text:
Why do acids mix in water faster than bases?
I have $100\ \mathrm{L}$ of water in a tank with an mixer inside and want to know how fast the tank mixes at a given rpm-setting.
I am adding $50\ \mathrm{mL}$ of $2\ \mathrm{N}\ \ce{HCl}$ and see how long the $\ce{pH}$ goes to down to an equilibrium.
Then I add $50\ \mathrm{mL}$ of $2\ \mathrm{N}\ \ce{NaOH}$ to the solution and wait for the $\ce{pH}$ to come to an equilibrium $\ce{pH}$.
I feel like the 2 times should be the same, but acid mixes much faster than base in all cases. Why?
The time for $\ce{pH}$ to change from $7$ to $4$ is always less than time for $\ce{pH}$ to change from $4$ to $7$ in the same tank at the same rpm.
Any theories regarding why?

How do you test the pH change? Also, what is "eve"?

pH probes are being used fr monitoring pH.. Not sure what you mean by "eve" .. RPM= rotations per min of the impeller/mixer

You had "eve" as one of your tags. It has apparently been edited out. If you were doing chemical analysis of pH, I would have guessed a slower base reaction than acid reaction. Don't know enough about pH meters to know if that's a possibility.

The analysis is slightly skewed. Please do the confirmation experiment of adding $50~\mathrm{ml}\ 2~\mathrm{M}\ \ce{NaOH}$ to $100~\mathrm{ml}$ of water and compare that time to adding $50~\mathrm{ml}\ 2~\mathrm{M}\ \ce{HCl}$.

Could it simply be that you are adding 50 mls of acid to 100 mls of water and then 50 mls of base to 150 mls of solution? Time for mixing in a larger volume? Do as @Jan says, and time base into water, followed by acid into the solution and compare your times..

The volume is 100 litres, not 100 millilitres.

@aventurin oops! Time to visit the opticians! So Suresh ignore the 1st part of my previous comment, but Jan's comment still needs to tried out.

You cannot compare the rate of first mixing acid with water with the rate of mixing the base with the diluted acid. You should compare the rate of mixing the acid with water with the rate of mixing the base with water instead.
The reason is that adding the base to the diluted acid will neutralize portions of the base during the mixing process resulting in lower concentration gradients that make the mixing slower.
A simple gedankenexperiment will show this. Consider a cylindrical tank with water of volume 1 with a mixing rod along the axis. Now put an amount of 1 acid into the tank along its axis. When the acid has made half the way to the wall of the tank the concentration in the inner volume is 4. The gradient is 4.
Now think of adding an amount of 1 base to the completely mixed diluted acid. When the base has made half the way to the wall of the tank, 1/4 of the base has already been neutralized. The concentration in the inner volume is 3. The gradient is only 3 compared to 4 before.

For those of us not inclined towards sesquipedalianism, "gedankenexperiment" just means "thought experiment".

Thank you for all the responses. A few important things -- 1. We are adding very little acid/base to a lot of water 2. The mixing is completely impeller driven and not acid/base dispersion driven. We add the acid - it mixes 100% in 5 mins wait for 30 while the impeller turned on, then add the base do the same..


text:
Is it true that all of the physical laws and mathematics needed to describe chemistry are known?
This question comes from a rather famous quote by Paul Dirac which goes like this,

The underlying physical laws necessary for the mathematical theory of a large part of physics and the whole of chemistry are thus completely known, and the difficulty is only that the exact application of these laws leads to equations much too complicated to be soluble. It therefore becomes desirable that approximate practical methods of applying quantum mechanics should be developed, which can lead to an explanation of the main features of complex atomic systems without too much computation.
  -Paul M. Dirac

I have seen this quote a number of times and it never struck me as being peculiar because to my knowledge the actual physical laws describing everything we care about in chemistry are known. However, I was recently at a talk (it was a presentation to one of my classes, but the speaker gave a talk about his research) about density functional theory, and this quote was shown as a sort of introduction for why density functional theory was developed and is applied as a form of approximation. After showing this quote, the speaker said "well that's not strictly speaking true..." and then moved on and didn't say anything else.
I meant to ask what he meant by this after the talk, but I forgot because I was asking about something else.
So, to expand on this:
Are there any physical laws which are unknown (or believed to be unknown) which directly relate to chemistry?
Are there any mathematics which have not been developed which are necessary to fully describe some aspect of known chemistry?

The wave function of a multi-electron atom can not be solved for. That is a pretty basic one.

Electronegativity still doesn't have a solid mathematical description. Electron correlation still has no exact mathematical description.

Need to upvote Jon's comment like 500 more times.

A relevant link from another physicist's point of view. Follow the links inside for more.

Jon Custer's point does not refute Dirac's quote, but is exactly what Dirac meant by it: The fundamental wave equations are known, but solving them exactly even for an atom (except for H) is likely impossible.

@James The fundamental wave equations are not known. Dirac admitted this in 1978. In fact no wave equation can be fundamental because wave theory only applies to pure quantum states.

As I understand it the Schroedinger equation has no satisfying derivation, so in that sense Quantum Mechanics is not understood, so it is quite possible that there are other laws to be discovered. One of this years Nobel Prize winners in physics comments that what he observes is not fully understood, so if QM is incomplete, so is Chemistry.

This sounds an awful lot like something I said at a talk this week, so I feel obligated to answer.
First, in terms of fundamental interactions, yes, excluding a quantum theory of gravity we have a quantum field theory for how the other fundamental forces work (electromagnetic/weak and strong).
@DavePhD mentions that Dirac was wrong at least up to the development of QED. This is true. Dirac could write the non-relativistic molecular Hamiltonian down. He knew that even if he couldn't solve it, all the physics were still there, and so in principle the system was "knowable." This is just like how we can't solve the gravitational many-body problem exactly but we definitely know how Newtonian gravity works.
Anyway, fast forward to today. We can write the QED equations of motion down which account for the time-evolution of all field operators. In principle this contains all the interactions necessary to describe molecules. Computational complexity aside, I think it is important to recognize that we must get rid of several degrees of freedom before we can even define a molecule. Most importantly we have to remove the possibility of electron-positron pair creation, since in QED particle number is not constant. Molecules, after all, are defined (in our chemists' minds) as having a fixed number of electrons. Heck, even "particles" themselves are not really present in QED, they are just excitations of the underlying quantum field.
We do something similar even in non-relativistic QM, where we fix the geometry of molecules via the Born Oppenheimer approximation (and treat nuclei as classical). If we didn't, the Schrodinger equation would describe every possible geometry of a collection of atoms and electrons (Well, geometry is not well defined in a electron-nuclear wave function, but you get the idea).
All this to say, writing the equations that govern a molecule will never be as simple as just "writing down the fundamental interactions", and I think Dirac got that wrong. Approximations will always be necessary as long as we hold onto a conception of a molecule as a fundamental object of study.
Molecular QED today is limited to effective Hamiltonian theories involving photon absorption and emission. But most of the same results can be derived from a classical view of EM fields.
Most of QED is unnecessary for an accurate description of chemistry. Pair creation processes are in energy ranges that we just don't access in the laboratory. The one area which it could excel is relativistic electronic structure theory. Our current attempts are based off of the Dirac equation, which really only holds for one spin-$1/2$ particle. Given the extension to multiple particles, we have to resort to approximate relativistic treatments. The most accurate -- in the sense that it contains the most physics -- relativistic two electron interaction term I've come across is the Breit interaction, but even that is an approximate electron-electron repulsion term. We don't know the exact relativistic term within the structure of relativistic electronic structure theory. But that's okay for now, since even including the Breit term is overkill for most molecular systems.
As far as not knowing all the fundamental interactions relevant for chemistry, let me finish with one example that I find particularly fascinating, and that is the nature of chirality of molecules. One area of study is whether or not one enantiomer of a chiral molecule is energetically more stable than the other. Even if there is a slight difference, over long periods of time it may explain why life tended to evolve using L-amino acids, among other things. This energy difference is hypothesized to be very small, on the order of 10$^{-11}$ J / mol.
Anyway, this theoretical difference in energy of chiral molecules cannot be explained using any theory of electromagnetic interactions, because the  EM interactions are identical in chiral molecules. Instead, the difference in energy (if there is one) must come from a parity-violating term, which shows up only in the electroweak interaction. So this area of study is known as electroweak chemistry. As far as I know, the exact form of this parity violating term is up for debate (and there may be multiple terms), since it necessarily has to couple to some sort of magnetic perturbation, like spin-orbit coupling. Because no one really knows exactly what this term looks like, it makes it difficult for theorists to predict what the possible energy difference between enantiomers should be. Which then makes it very difficult for spectroscopists to know what to probe for.
So this is an example of a fundamental interaction relevant to chemistry (albeit a small one), that we don't really know much about, but would give huge insights into the evolution of life as we know it.

Ha. You probably couldn't have answered in that much detail if I asked after the talk. The part about electroweak interactions is particularly interesting. And thanks for the talk!

Quantum field theory cannot even describe the old Coulomb interaction, let alone all other interactions.
The "QED equations of motion" are not true equations of motion because t in them is not time, but a fictitious parameter with no physical meaning. Furthermore, field theory cannot describe bound states, let alone molecules.
Molecules are defined as having a fixed number of electrons when considered isolated from the rest of the universe.

The excitations from quantum fields are not real particles, they are fictitious objects sometimes called "bare particles".
The Dirac equation is not a valid wave function equation for a spin one-half particle.
The Breit interaction suffers from the problem of continuous dissolution unless modified with positive energy projection operators.
Kudos for mentioning electroweak chemistry.

First, it is one thing to know the basis for a "law", and quite another to mathematically calculate the effects of that law. Consider just carbon, for example... chains may be made of thousands of atoms, with various functional groups attached to each. Though, as Dirac stated, it helps to have "shortcuts" to computation such as Fast Fourier transforms, there are still problems that cannot be solved in a "reasonable" time.
Second, if there are unknown laws, how would we know about it (not to quote Rumsfeld on unknown unknowns)?
And finally, even if all physical laws were known and understood, it would still be impossible to predict everything: Kurt Gödel's incompleteness theorems show that in a complex system (it does not have to be very complex; basic grammar-school mathematics qualifies), questions can be asked that cannot be proved true or false. This extends to chemistry and physics.

Only very recently has mathematical undecidability been rigorously determined for a "reasonable" physical problem. Even then, there was a lot of discussion about the interpretation of the results, which I am nowhere near qualified to relay.

Dirac is probably right but, even if he isn't, it probably isn't important for chemistry.
The issue highlighted by Dirac is that, even if we do understand all the relevant laws of quantum mechanics as far as they determine chemical properties, that doesn't help us turn chemistry into a branch of mathematics. The problem is that while we understand the equations we don't have good ways of solving those equations except for the simples systems. For example, we only have exact solutions to the electron wave function equations (which is what determines most chemical properties) for the simplest possible atoms (one nucleus, one electron). Everything else is an approximation.
This should not be a surprise. The three body problem for Newtonian gravity has no exact solutions (or, more strictly, only a very small number for some very special cases). Quantum wave functions are more complex than that and systems with multiple electrons are not going to have neat mathematical solutions.
What this implies is that we can't reliably predict the chemical properties of anything more complicated than hydrogen atoms from the physical laws they obey even if we completely understand the laws. We can approximate but it is hard to tell if reality deviates from the rules because our approximations are poor or because we don't understand some detail of the rules.
So even if there is some subtle detail of the laws we don't understand, it would be hard to verify the implications for chemistry.
There might be a few areas where obscure parts of quantum mechanics do impact chemistry (though speculation is all we have right now because of the limitation described above). Normally in the quantum mechanics used for chemistry, we are just looking at electromagnetic forces, and that is complicated enough. Some people have speculated that other forces might have small influences that matter for chemistry. For example, there is speculation that some interaction with nuclear forces might explain life's preference for single optical isomers in many living structures. The speculation suggests that optical isomers have very slightly different energies because of a tiny interaction with the asymmetry in non-electromagnetic forces (see this example). But these effects are, if they exist, small compared to the uncertainty in our predictions based on the well-known laws.
So the dominant problem is chemistry is the quality of our approximations not the potential existence of entirely new laws.

I think that the importance of "analytic solutions" as a measuring stick of whether a system is understood or not is overblown, because what makes a solution "analytic" is arbitrarily defined. It sounds much like separating numbers between constructible and non-constructible by virtue of the fact that the former can be produced with a compass and straightedge, while the latter can't. Just an artefact from old Greek geometers.

Non-relativistic quantum mechanics and relativistic Dirac equation have finite accuracy. It means if the error in approximation is smaller than the intrinsic error of the underlying equations,  we are still fine.

@NicolauSakerNeto My distinction isn't about the difference between "analytic" and approximate solutions. It is about the difficulty of even getting good approximate solutions, which is still large. That's why computational chemistry needs lots of computer power.

Electron wave function equations are approximations.

@juanrga True for anything other than an isolated hydrogen atom.

They are approximations even for an isolated H atom, because an electron wavefunction assumes either that the nucleus is entirely classical or that there is no electron-nucleus correlation and $\Psi_{atom}\approx\Psi_{electr}\Psi_{nuclear}$.

As already pointed out in a comment by John Custer, Dirac was 100% correct in

The underlying physical laws necessary for the mathematical theory of a large part of physics and the whole of chemistry are thus completely known, and the difficulty is only that the exact application of these laws leads to equations much too complicated to be soluble. It therefore becomes desirable that approximate practical methods of applying quantum mechanics should be developed, which can lead to an explanation of the main features of complex atomic systems without too much computation.

For light systems, typically thought as H-Kr, non-relativistic quantum mechanics i.e. the Schrödinger equation is sufficient to describe chemistry; for heavier nuclei you need to use relativistic quantum mechanics i.e. the Dirac equation which is a bit more complicated. In many cases we can invoke the Born-Oppenheimer method, and assume that the nuclei are moving in the instantaneous field of the electrons; now all we need to solve is the electronic problem.
We know that the exact solution to the electronic problem in this case is achievable with the full configuration interaction (FCI) a.k.a. exact diagonalization method, in which you describe the electronic many-particle wave function by a weighted sum of electronic configurations a.k.a. Slater determinants as $|\Psi \rangle = \sum_k c_k |\Phi_k\rangle$. These electronic configurations are built by distributing $N$ electrons into $K$ single-particle states a.k.a. orbitals. For the method to be accurate, $K\gg N$, and actually to get the exact solution you need $K \to \infty$.
Now, to find the ground state (as well as any excited states), you just need to diagonalize the many-electron Hamiltonian in the basis of the electron configurations. But, the problem is that the number of the electron configurations grows extremely rapidly.
If we assume that we are looking at a spin singlet state, then you have $N/2$ spin-up and $N/2$ spin-down electrons. For each spin, there are ${K \choose N/2} = \frac {K!} {\frac N 2 ! (K-\frac N 2)!} $ ways to populate the orbitals. The total number of electron configurations for $N$ electrons in $K$ orbitals, typically denoted as ($N$e,$K$o), is then ${K \choose N/2}^2 = \left[ \frac {K!} {\frac N 2 ! (K-\frac N 2)!} \right]^2$.
Even for the case of a very small number of orbitals, $K=N$, the number of configurations quickly becomes huge. (8e,8o) has 4900 configurations, (10e,10o) has 63 504, (12e,12o) has 853 776, (14e,14o) has 11 778 624, (16e,16o) has 165 636 900, (18e,18o) has 2 363 904 400, (20e,20o) has 34 134 779 536, and (22e,22o) has 497 634 306 624.
Although you can still solve the (8e,8o) problem with dense matrix algebra on modern computers, you see that very quickly you have to become very smart in how to diagonalize the matrix. Because the Hamiltonian is a two-particle operator, it is extremely sparse in the basis of the electron configurations: if two configurations differ by the occupation of more than two orbitals, the Hamiltonian matrix element is zero by Slater and Condon's rules. Moreover, for large problem sizes you also want to avoid storing the matrix, which is why you want to use an iterative method. (The famous Davidson method for iterative diagonalization was actually developed exactly for this purpose!)
With smart algorithms, billion-configuration calculations i.e. the (18e,18o) problem have been possible since the early 1990s, see e.g. Chem. Phys. Lett. 169, 463 (1990). However, despite the huge increase in computational power in the last 30 years, the barrier has barely budged: as far as I am aware, the largest FCI problem that has been solved is the (22e,22o) calculation in J. Chem. Phys. 147, 184111 (2017).
The thing to note here is that even the (22e,22o) calculation is not large enough to solve a single atom in an exact fashion: you need a lot more orbitals to achieve quantitative accuracy with experiment. Although a high-lying orbital contributes only very little to the correlation energy, there are A LOT of them.
Exactly as Dirac wrote, approximations are needed. Density-functional approximations are extremely popular in applications, but they are far from exact. On the other hand, high-accuracy studies often employ the coupled-cluster method, which is a reparametrization of the FCI method; however, it, too would exhibit exponential scaling were it not truncated - i.e. approximated.

+1. We found reached close to milli-hartree precision for the total energy of a CAS(54,54) in this one: https://aip.scitation.org/doi/10.1063/1.5063376

Dirac was 100% wrong.
The Schrödinger equation is not sufficient to describe all of chemistry and the Dirac equation is not a valid relativistic generalization. In fact, Dirac finally admitted that he did not obtain a valid formulatino og relativistic quantum mechanics.

[citation missing]

Dirac published that statement in Quantum Mechanics of Many Electron Systems, received 12 March 1929.
In 1948 Verwey and Overbeek demonstrated experimentally that the London dispersion interaction is even weaker than 1/$r^6$ at long distance (say hundreds of Angstroms or more).
Casimir and Polder soon thereafter explained with quantum electrodynamics (QED) that the dependence should be 1/$r^7$ at relatively long distances.
See section 3.1.1 Van der Waals Forces, in Some Vacuum QED Effects
So Dirac was wrong at least up to the development of QED.

The answer to both of your questions is yes. There are unknown physical laws that are directly related to chemistry and there are mathematics that have not yet been developed and are necessary to fully describe some aspect of known chemistry.
But before I expand on my answer, let me add that Dirac wrote what you quote right after he developed the first version of quantum electrodynamics in 1927. Around 50 years later, he changed his mind, admitting that quantum electrodynamics was an incomplete theory and he invited his colleagues to "seek a new relativistic quantum mechanics".
There are several aspects of known chemistry that cannot be explained by current physical laws. I will mention three.
Emergence
Although we knew the fundamental physical laws that apply to matter, this does not mean that the rest of the disciplines are only applications of those laws. As Anderson wrote in his classic "More is different" [1], biology is not applied chemistry, nor is chemistry applied physics. Emergent properties are those that only exist at a certain level of organization of matter and cannot be derived from lower levels.
Structure
Quantum mechanics is incompatible with molecular structure, as pointed out in several articles by Woolley. As explained in [2], the Schrödinger equation cannot differentiate between the following three molecules

Attempts to explain molecular structure introduce generalizations of the Schrödinger equation.
Reactions
The incompatibility between chemical reactions and quantum mechanics was highlighted by Prigogine [3]:

Quantum mechanics, in its orthodox form, corresponds to a deterministic time-reversible description. This is not so for chemistry. Chemical reactions correspond to irreversible processes creating entropy. That is, of course, a very basic aspect of chemistry, which shows that it is not reducible to classical dynamics or quantum mechanics.

He and his group developed extensions of quantum mechanics for irreversible processes.
References

More Is Different: Broken symmetry and the nature of the
hierarchical structure of science. 1972: Science 177(4047)
393–396. Anderson, P. W.
Must a molecule have shape? 1988: New Scientist 120, 53–57. Woolley, Richard Guy.
Chemical Kinetics and Dynamics 2003: Annals of the New York Academy of Sciences 988, 128–132. Prigogine, Ilya.

"The Schrödinger equation cannot differentiate between the following three molecules" - I don't understand how this could be true. Clearly the electric potential field from the positive charges is different because the protons are in different locations.

@NicolauSakerNeto A full quantum mechanical treatment of a collection of nuclei and electrons cannot assign locations to nuclei. The three molecules draw in the article correspond to the same Hamiltonian and are the same quantum system according to the SCH equation.


text:
Why are electrolysis cell plates turning a brown color?
I have been experimenting with electrolysis for producing oxyhydrogen and using potassium carbonate $(\ce{K2CO3})$ as an electrolyte.  After several hours of electrolysis, I noticed that the plates began to tarnish and after 24 hours, are now dark brown. The plates are made of 316 stainless steel and the electrolyte remains clear.
When I chose to use $\ce{K2CO3}$, I thought that it would not decompose during electrolysis but now I suspect that it is decomposing and electroplating the stainless steel plates with carbon. If this is the case, will this have an adverse effect on the plates ability to conduct and produce oxyhydrogen? Also, is $\ce{CO2}$ being produced?

Since the carbonate radical is covalently bonded, it probably is not being decomposed electrolytically. Much more likely is that iron in the stainless steel is being removed and oxidized, leaving a thin film of "rust" on the plates.
A few ways you can prove this:

Immerse the browned plates in oxalic acid, which will slowly dissolve iron oxides, but leave carbon untouched.
Substitute platinum electrodes -- admittedly expensive, but Pt is the "gold" standard for electrodes. They should not discolor.
Spray the browned plates with a solution of potassium ferricyanide. If free iron is present, a blue color ("Prussian blue") appear.

Titanium could also be used for anodes.

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


text:
How can I predict if a reaction will occur between any two (or more) substances?
I am new to chemistry and I find it fascinating. I am trying to learn about chemical reactions and I was wondering if there was an easy way to quickly tell if any combination of chemical substances would produce a reaction and what product(s) if any might be formed.
For example, if I pick any two random substances $\ce{A}$ and $\ce{B}$, can I determine if a reaction will occur and predict the products?
$$\ce{A + B -> \ ?}$$
More specifically, let's say I just learned that chlorine bleach (sodium hypochlorite) can be made by a reaction of sodium hydroxide and chlorine with sodium chloride as a byproduct:
$$\ce{NaOH(aq) + Cl2(g) -> NaOCl(aq) + NaCl(aq)}$$
Is there a way that I could have predicted this reaction (and any other) before I learned about it? I do not want to memorize the outcome of every combination o that I can answer questions about chemical reactions. I am hoping there is a short list of simple rules that govern all chemical reactions that I can commit to memory and then apply to any combination of substances. I might also like to be able to develop a simple computer program built around an algorithm for these reactivity rules that can sample databases of known substances and predict new reactions.

Sometimes yes, we have some hand-waving justified rules for some reaction or we can perform simulation within the available resources; sometimes no, nature is still beyond our current capacity.

check change in gibbs free energy of the raction

@AlphaRomeo - That assumes that we know there is a reaction and what the products are, and then we can know whether the reaction is spontaneous or not. My question is more about knowing if there is a potential chemical change and how to determine what the product might be. For example $\Delta_r G^{\circ}$ values cannot be used to determine the expected major product (or whether anything at all happens) of the following potential reaction: $$\ce{H2O(l) + HCl(aq) + Rh(s) -> ?}$$

Can I predict the products of any chemical reaction?
In theory, yes!
Every substance has characteristic reactivity behavior. Likewise pairs and sets of substances have characteristic behavior. For example, the following combinations of substances only have one likely outcome each:
$$
\ce{HCl + NaOH -> NaCl + H2O} \\[2ex]
\ce{CH3CH2CH2OH->[$1.$ (COCl)2, (CH3)2SO][$2.$ Et3N] CH3CH2CHO}
$$
However, it is not a problem suited to brute force or exhaustive approaches
There are millions or perhaps billions of known or possible substances. Let's take the lower estimate of 1 million substances. There are $999\,999\,000\,000$ possible pairwise combinations. Any brute force method (in other words a database that has an answer for all possible combinations) would be large and potentially resource prohibitive. Likewise you would not want to memorize the nearly 1 trillion combinations.
If more substances are given, the combination space gets bigger. In the second example reaction above, there are four substances combined: $\ce{CH3CH2CH2OH}$, $\ce{(COCl)2}$, $\ce{(CH3)2SO}$, and $\ce{Et3N}$. Pulling four substances at random from the substance space generates a reaction space on the order of $1\times 10^{24}$ possible combinations. And that does not factor in order of addition. In the second reaction above, there is an implied order of addition:

$\ce{CH3CH2CH2OH}$
$\ce{(COCl)2}$, $\ce{(CH3)2SO}$
$\ce{Et3N}$

However, there are $4!=24$ different orders of addition for four substances, some of which might not generate the same result. Our reaction space is up to $24\times 10^{24}$, a bewildering number of combinations. And this space does not include other variables, like time, temperature, irradiation, agitation, concentration, pressure, control of environment, etc. If each reaction in the space could somehow be stored for as little as 100 kB of memory, then the whole space of combinations up to 4 substances would require $2.4 \times 10^{27}$ bytes of data, or $2.4\times 10^7$ ZB (zettabytes) or $2.4\times 10^4$ trillion terabytes. The total digital data generated by the human species was estimated recently (Nov. 2015) to be 4.4 ZB. We need $5.5\times 10^5$ times more data in the world to hold such a database. And that does not even count the program written to search it or the humans needed to populate it, the bandwidth required to access it, or the time investment of any of these steps.
In practice, it can be manageable!
Even though the reaction space is bewilderingly huge, chemistry is an orderly predictable business. Folks in the natural product total synthesis world do not resort to random combinations and alchemical mumbo jumbo. They can predict with some certainty what type of reactions do what to which substances and then act on that prediction.
When we learn chemistry, we are taught to recognize if a molecule belongs to a certain class with characteristic behavior. In the first example above, we can identify $\ce{HCl}$ as an acid and $\ce{NaOH}$ as a base, and then predict an outcome that is common to all acid-base reactions. In the second example above, we are taught to recognize $\ce{CH3CH2CH2OH}$ as a primary alcohol and the reagents given as an oxidant. The outcome is an aldehyde.
These examples are simple ones in which the molecules easily fit into one class predominantly. More complex molecules may belong to many categories. Organic chemistry calls these categories “Functional Groups”. The ability to predict synthetic outcomes then begins and ends with identifying functional groups within a compound's structure. For example, even though the following compound has a more complex structure, it contains a primary alcohol, which will be oxidized to an aldehyde using the same reagents presented above. We can also be reasonably confident that no unpleasant side reactions will occur.

If the reagents in the previous reaction had been $\ce{LiAlH4}$ followed by $\ce{H3O+}$, then more than one outcome is possible since more than one functional group in the starting compound will react. Controlling the reaction to give one of the possible outcomes is possible, but requires further careful thought.
There are rules, but they are not few in number. There are too many classes of compounds to list here. Likewise even one class, like primary alcohols (an hydroxyl group at the end of a hydrocarbon chain) has too many characteristic reactions to list here. If there are 30 classes of compounds (an underestimate) and 30 types of reactions (an underestimate), then there are 900 reaction types (an underestimate). The number of viable reaction types is more manageable than the total reaction space, but would still be difficult to commit to memory quickly. And new reaction types are being discovered all the time.
Folks who learn how to analyze combinations of compounds spend years taking courses and reading books and research articles to accumulate the knowledge and wisdom necessary. It can be done. Computer programs can be (and have been) designed to do the same analysis, but they were designed by people who learned all of the characteristic combinations. There is no shortcut.

Its also important to notice that most reactions, especially those between molecules rich of functional groups, can have many possible outcomes, which will all occur in different frequencies and concurrent, making it simply impossible to predict every single reaction.

The short answer is NO.
There is no single complete theory that is able to predict what products will result from combining a number of reactants. Note that the products of a chemical reaction are not only a function of the reactants, but also of temperature, pressure, catalyst present and several other factors.
You will be hard pressed to find any Chemistry book that even starts to attempt to describe a predictive model.
Because of this huge gap in scientific knowledge the best next thing is to empirically test what happens when reactants are brought together under certain conditions and then find similarities when different reactants of the same general type are used.
For example if empirically you establish that:
$$\ce{CH2=CH2 + HCl -> CH3CH2Cl}\\ \text{and}$$
$$\ce{CH3CH=CH2 + HCl -> CH3CH2CH2Cl}$$
You could predict that in any reaction of the type RCH=CH2 + HCl the following type of product will be found:  RCH2CH2Cl
This is one of the reasons Organic Chemistry books are so thick. Since there a many types of substances, they are grouped together as members of a family that are known to react in a certain manner under certain conditions.
The predictive power of this method is rather weak, since it only applies to a very narrow set of circumstances, but there does not exist a better system today.

The benefits of finding these ground rules that manage reactions (even if you need to put in variables like temp, pressure, etc) are so evident and so big that I would expect some investigation is ongoing. Is there anything in that sense?

I believe in the arena of radical based chemical reactions (aka, radical chemistry) a possibly different answer is appropriate. The answer is, in select context, likely yes based on intuitive combinatorial results with characteristically probabilistic product distribution.
First, it should be noted that radical reactions are best depicted with corresponding forward and reverse reaction rates that are, at least, temperature-dependent. As such, radical on radical reactions are often written with '=' sign given the increased ease of reversibility.
Here is a concrete example where a simple combinatorial approach is actually accurate on the reaction system around chlorine monoxide radical ($\ce{•ClO}$) leading to ozone depletion. The possible set of radical reactions include in a source, for example:
$\ce{•ClO + •ClO = ClOOCl}$
$\ce{ClOOCl + hv -> •Cl + •ClOO}$
$\ce{•ClOO = •Cl + O2}$
$\ce{•OCl + •OCl = •OClO + •Cl}$
And I would add:
$\ce{•Cl + •Cl = Cl2}$
where it is evident that a simple combinatorial approach would likely list possible reactions. However, not all radical reactions are expected to be observed in the equal proportional (so, an interesting statistical product distribution will arise).


text:
What is the lowest temperature tungsten starts sublimating at?
What is the lowest temperature tungsten starts sublimating at? I've tried to search in Google but without any luck.
For example, $\ce{WO3}$ starts sublimating roughly at $\pu{550 °C}$, according to the paper Growth of epitaxial tungsten oxide nanorods.

There is no such thing. Any compound has some vapor pressure at any temperature. Of course, for tungsten at room temperature it would be negligibly low. If you want to know when the pressure hits some particular threshold, define the threshold first.

Let's say 0.001 Pa.

Now that's a sensible question. Wait a sec, I'll check my figures.

Maybe it would be better to share your figures, since I might want to know the temperature at a different pressure... :)

Well, you see, searching online for "vapor pressure at such-and-such temperature" (or conversely, "temperature to get such-and-such pressure") is often fruitless, and unnecessary too, because pretty decent approximations are known. Here is one:
$$\ln\mathfrak p=-{\Delta H\over R}\left({1\over T}-{1\over T_0}\right)$$
where $\mathfrak p$ is your vapor pressure in atmospheres, $\Delta H$ is the enthalpy of vaporization and $T_0$ is the boiling temperature at normal pressure. For tungsten, the latter two are reported as 774 kJ/mol and 6203 K, respectively. Now you may plug in your desired pressure and solve for temperature.
That's a relatively crude approximation, for the enthalpy will hardly remain constant over such a wide range of temperatures. This page may contain better approximations designed for specific ranges.

Kurt J. Lesker has a gigantic table of materials and the temperatures at which they achieve a vapour pressure of $10^{-8}$, $10^{-6}$ and $10^{-4}\  \mathrm{torr}$. For tungsten, these are $2117$, $2407$ and $2757\ \mathrm{ºC}$, respectively. For $\ce{WO3}$, only the highest vapour pressure has a tabulated temperature, at $980\ \mathrm{ºC}$

This answer only works for liquids, not solids.  For sublimation, you need the enthalpy of sublimation and a reference vapor pressure for the solid at some temperature (as you stated, this would be crude as the enthalpy of sublimation would change with T).

@S.Burt True, I forgot to mention that. Well, one may calculate the vapor pressure at melting point to use that as a reference, and simply add together the enthalpies of melting and vaporization... but that would mean building one crude approximation on top of the other. All in all, that's one more reason for resorting to some empirical formula.

I've never seen pressure denoted with a Fraktur character $\mathfrak p$ in non-German texts. Does it mean anything specific?

@andselisk No. Quite a few years ago, my physical chemistry professor used to write it like that, probably for no other reason than his professor did the same before him, and so on.


text:
1H-NMR spectrum for furfural

I was supposed to identify this compound by knowing its molecular formula and the following spectra:
$1\mathrm{H}\ (\mathrm{s},\ 9.67\,\mathrm{ppm})\\
1\mathrm{H}\ (\mathrm{quartet},\ 7.73\,\mathrm{ppm})\\
1\mathrm{H}\ (\mathrm{quartet},\ 7.30\,\mathrm{ppm})\\
1\mathrm{H}\ (\mathrm{quartet},\ 6.63\,\mathrm{ppm})$

My question is: how come we get quartets for the protons on the furan ring? I can see it getting doublets and triplets, but it seems impossible for them to couple with the aldehyde proton (which, in itself, doesn't couple with any of them).

Who decided that these peaks are quartets? Was this provided to you, or was it your interpretation? They will not be (and are not) quartets, but doublets of doublets. On a good day of shimming you will see some coupling to the aldehyde.

This was provided to me by a problem. Indeed, they should've specified it's a doublet doublet which looks like a quartet. therefore, my confusion arised from the fact that the coupling constants would be the same.

The coupling constants are no the same, because then you would indeed see a triplett. If the four peaks are indeed equidistant, then one coupling constant would be twice as large as the other.

It sounds like the problem is really one of terminology: you would expect to see a doublet of doublets for each of the three aromatic protons, and a doublet of doublets (typically) has 4 peaks, but it is not correct to call such a multiplet a quartet.  The integral ratios would be 1:1:1:1 instead of 1:3:3:1 (maybe 1:2:1 if the two inner peaks coalesce).  Sometimes TAs (and even faculty) get sloppy/lazy with their notation.

They are not coupling with the aldehyde proton. Because the three protons around the ring are locked in such close proximity to one another, they will all couple each other. Let us consider these protons:
$\hspace{6cm}$
As by the $(n+1)$ rule of multiplicity, a proton will couple with each nearby, chemically unique proton and be split into $(n+1)$ peaks. These split signals can then also be split into $(n+1)$ more peaks by other nearby, chemically unique proton. Since all three protons are in the same region of space around the ring, they all couple each other, splitting each proton's signal into $(1+1)(1+1)=4$ peaks, making each signal a doublet of doublets (a quartet).
If you'd like a detailed analysis of the NMR of furfanal, you can read about it here.

A doublet of doublets is not a quartett. Even if one coupling constant is twice that of the other, the four peaks still have the same integral each, not 1:3:3:1.


text:
Why most of the atoms with fully filled outer orbits are gaseous?
Most of the elements with fully filled outer orbits are gaseous in nature (He, Ne, Ar, Kr, Xe, Rn) with exception of Uuo (as per Wikipedia its solid).
Why these fully filled outer orbit elements are always gaseous in nature?
I couldn't find a any relevant links in googling. Can someone please explain?
Thanks in advance.

Why, that's simple: they don't form bonds with each other or anything else, because they don't need to. They've already completed their outer levels, and are quite happy on their own.

I'm not sure that enough UUO has been made to identify what the STP phase is?

@JonCuster All such parameters as melting point for such radioactive elements are theoretical computations ignoring their radioactivity.

@Mithoron - And those are sufficiently difficult calculations even for atoms with many fewer electrons that, well, I'll view them with quite a large grain of salt. There are enough other surprises in the periodic table...

Your googling can't have been very thorough. https://en.wikipedia.org/wiki/Noble_gas#Physical_and_atomic_properties

Its all about bonding.
Elements with full outer shells are happy with their electrons and have no desire to either pick up more or shed the ones they have. Elements with incomplete shells strive to fill them by forming bonds with other elements so they can share electrons and achieve a happier state.
For example, chlorine (one electron short) and sodium (one electron too many) can play nice together (both achieve filled shells) when sodium gives up and chlorine gains an electron. The charged atoms that result tend to stick together (electromagnetism is strong) giving crystals of common salt. Other atoms can for different types of bond to share their electrons.
Bonding creates bigger entities than single atoms and bigger entities are more likely to be solids or liquids than a single atom. This is both because of their size but also because molecules have more ways to interact than atoms do. Water molecules have lots of ways to stick together compared to, say, neon although their mass is similar. The bonding in water creates dipoles that attract other water molecules in ways that two atoms of neon don't.
So noble gases don't form many bonds with other atoms and, when other atoms bond they create new entities that are more likely to stick together making it more likely that they will form liquids or solids.

Well, as it's not bad for answer for noobs, it would be nice to get some info like estimate for strength of forces between Xe atoms in pure liquid or sth like that.


text:
Different between molecular and ionic equations
I want to know if ALL equations have to be balanced? Say for example if Hydrogen gas (H2) burns in air (O2) to form water (H2O) I get the following:

H2 + O2 --> H2O. Means that balanced would be 2H2 + O2 --> 2H2O.

I dont understand why this also is not correct:

H2 + O2 --> H2O + O- (anion)

Isnt the above also correct since the Oxygen atom from the reactants is displaced? Doesnt it still abide by the law of conservation?

Yes, all equations have to be balanced, not only in all elements, but in charge as well (which your last equation is not), otherwise they make no sense. Also, welcome to Chem.SE.

See https://en.wikipedia.org/wiki/Charge_conservation

I don't think that the 3rd equation is correct because yes it is balanced but look at the product it yields. In an experiment 2H2 + O2 always produce water with no oxygen anion.
If you draw the lewis structure of the last equation the charge of O is not going to be negative. It will still be neutral because no electrons are added.
Hope that helps.thank you.

It is not balanced, because it does not conserve charge.


text:
Coefficients in K2SO4 electrolysis scheme (textbook)
From a textbook, a scheme of $\ce{K2SO4}$ electrolysis:

I don't understand how the two equations with the coefficients 2 before the water combine into the equation with the coefficient 6. Would not the coefficient before $\ce{H2}$ be 1.5 then?
The text is

When a salt consisting of an active metal and an oxygen-containing acid moiety is subjected to electrolysis, both cathode and anode participate in the electrolytic dissolution of water.

Multiply the first (left) equation by 2.

@IvanNeretin - would not I have then to multiply the second by 2 also, giving me 8H2O in the final reaction?

Nope. Remember, you want the whole thing to be balanced in electrons too.

@IvanNeretin - thank you! I see. The balancing goes around the $\ce{4e^-}$. I thought it was in order to make OH- and H+ to dovetail into water nicely, and forgot about electron balancing.

It seems to me that there is a typo in the first equation. It should be $$\ce{2H2O + 2e^- <=> H2 ^ + 2OH^-}$$

@MaxW - indeed, I had noticed that, but this is a minor typo - the only one that I've found so far in this particular textbook.