Consider an ionic solid $$MX$$ with $$NaCl$$ structure. Construct a new structure $$(Z)$$ whose unit cell is constructed from the unit cell of $$MX$$ following the sequential instructions given below. Neglect the charge balance.
$$(i)\,\,\,\,\,$$ Remove all the anions $$(X)$$ except the central one

$$(ii)\,\,\,\,$$ Replace all the face centered cations $$(M)$$ by anions $$(X)$$

$$(iii)\,\,$$ Remove all the corner cations $$(M)$$

$$(iv)\,\,\,\,$$ Replace the central anion $$(X)$$ with cation $$(M)$$

The value of $$\,\,\left( {{{number\,\,of\,\,anions} \over {number\,\,of\,\,cations}}} \right)\,\,$$ in $$Z$$ is ___________.

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 $$T$$)

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

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 ___________.