A closed tank has two compartments $$A$$ and $$B,$$ both filled with oxygen (assumed to be ideal gas). The partition separating the two compartments is fixed and is a perfect heat insulator (Figure $$1.$$). If the old partition is replaced by a new partition which can slide and conduct heat but does NOT allow the gas to leak across (Figure $$2$$), the volume (in $${m^3}$$) of the compartment A after the system attains equilibrium is ______________.

The plot given below shows $$P-T$$ curves (where $$P$$ is the pressure and $$T$$ is the temperature) for two solvents $$X$$ and $$Y$$ and isomolal solutions of $$NaCl$$ in these solvents. $$NaCl$$ completely dissociates in both the solvents.



On addition of equal number of moles of a non-volatile solute $$S$$ in equal amount (in $$kg$$) of these solvents, the elevation of boiling point of solvent $$X$$ is three times that of solvent $$Y$$. Solute $$S$$ is known to undergo dimerization in these solvents. If the degree of dimerization is $$0.7$$ in solvent $$Y$$, the degree of dimerization in solvent $$X$$ is ___________.

An organic acid P $$\left( {{C_{11}}{H_{12}}{O_2}} \right)$$ can easily be oxidized to a dibasic acid which reacts with ethylene glycol to produce a polymer dacron. Upon ozonolysis, P gives an aliphatic ketone as one of the products. P undergoes the following reaction sequences to furnish R via Q. The compound P also undergoes another set of reactions to produce S.



The compound R is

Treatment of benzene with $$CO/HCl$$ in the presence of anhydrous $$AlC{l_3}/CuCl$$ followed by reaction with $$A{c_2}O/NaOAc$$ gives compound $$X$$ as the major product. Compound $$X$$ upon reaction with $$B{r_2}/N{a_2}C{O_3},$$ followed by heating at $$473$$ $$K$$ with moist $$KOH$$ furnishes $$Y$$ as the, major product. Reaction of $$X$$ with $${H_2}/Pd$$-$$C,$$ followed by $${H_3}P{O_4}$$ treatment gives $$Z$$ as the major product.

The compound $$Y$$ is