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1. What is your motivation for studying mathematics?

I believe pure math is an art form very much like music and painting. As G H Hardy said (don't remember exact phrase) "May Math never be of any use." Very sad to see no number theory subforum on this website dedicated to science. Physics, chemistry and other subjects simply use math as a tool, for their own development and contribute nothing to math itself.
2. Reaction in a buffer medium (Level ****)

An organic nitro compound is electrolytically reduced in an aqueous acetate buffer solution having total acetate (HOAc+OAc-) 0.500 M and pH=5.0. 300 ml of the buffered solution containing 0.01M RNO2 was reduced completely. The dissociation constant of acetic acid is $1.75 \times 10^{-5}$ at 298 K. The reaction is $RNO_2 + 4H^+ + 4e^- \rightarrow RNHOH + H_2O$ Calculate the pH of the solution on completion of the reduction.
3. nucleophilic aromatic substitution

Say im reacting a base with a halobenzene with strong electron withdrawing groups at o- and p- positions. My textbook says this reaction will take place, albeit slowly, as the e- withdrawing groups will delocalize the charge on the intermediate carbanion. But my doubt is, won't the charge be on the carbon meta to these groups, so that the -M effect won't affect the charge at all?
4. SOCl2 reaction stereochemistry

In an inert solvent, retention of configuration of the substrate is observed, whereas in the presence of certain other compounds, like pyridine for instance, inversion of configuration is observed. This is because the pyridine complexes with the HCl formed initially, and this makes the chloride ion free, and the chloride attacks from the back side of the leaving group (SO2 in this case) In the first case, after elimination of HCl, the Cl directly attacks the electrophilic carbon from the same side as the leaving group.
5. Aromatic Compounds

Oxepin is an antiaromatic compound. Antiaromaticity It has a planar ring, which shows resonance, similar to an aromatic compound. But the only thing that makes it different from an aromatic compound is that it fails Huckel's Rule, as it has 8 pi electrons as you correctly mentioned. Only one of the 2 lone pairs of the oxygen are delocalized within the ring.
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