The reaction (s) leading to the formation of $$1,3,5$$-trimethylbenzene is (are)

Liquids A and B form ideal solution over the entire range of composition. At temperature $$T,$$ equimolar binary solution of liquids $$A$$ and $$B$$ has vapor pressure $$45$$ $$Torr.$$ At the same temperature, a new solution of $$A$$ and $$B$$ having mole fractions $${X_A}$$ and $${X_B}$$, respectively, has vapour pressure of $$22.5$$ $$Torr.$$ The value of $${x_A}/{x_B}$$ in the new solution is ___________.

(given that the vapor pressure of pure liquid $$A$$ is $$20$$ $$Torr$$ at temperature $$T$$)

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

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 ______________.