Vapour pressure increases with rise in temperature.

$$\eqalign{ & 200 = \sqrt {\frac{{2RT}}{{2 \times {{10}^{ - 3}}}}} ;\,RT = 40 \cr & {\text{Average}}\,K.E. = \frac{3}{2}nRT = \frac{3}{2} \times \frac{8}{2} \times 40 = 240\,J \cr} $$

In unit cell, $$X$$ - atoms at the comers $$ = \frac{1}{8} \times 8 = 1$$
$$Y$$ - atoms at the face centres $$ = \frac{1}{2} \times 6 = 3$$
Ratio of $$X$$ and $$Y$$ = 1 : 3.
Hence, formula is $$X{Y_3}.$$

According to ideal gas equation, $$pV = nRT$$
If $$T$$ is constant and mass is constant, so number of moles $$(n)$$ also constant $$\left[ {n = \frac{{{\text{mass}}}}{{{\text{molar mass}}}}} \right]$$
therefore $$pV = {\text{constant}}$$

Given initial volume $$\left( {{V_1}} \right) = 600\,c.c.;$$    Initial pressure $$\left( {{P_1}} \right) = 750\,mm$$    of $$Hg$$  and final volume $$\left( {{V_2}} \right) = 500\,c.c.$$    according to Boyle’s law,
$$\eqalign{ & {P_1}{V_1} = {P_2}{V_2} \cr & {\text{or}}\,\,750 \times 600 = {P_2} \times 500 \cr & {\text{or}}\,\,{P_2} = \frac{{750 \times 600}}{{500}} \cr & \,\,\,\,\,\,\,\,\,\,\,\,\,\, = 900\,mm\,{\text{of}}\,{\text{Hg}} \cr & {\text{Therefore increase of pressure}} \cr & {\text{ = }}\left( {900 - 750} \right) \cr & = 150\,mm\,{\text{of}}\,{\text{Hg}} \cr} $$

Increase in temperature increases the kinetic energy of the molecules and effectiveness of intermolecular attraction decreases, so surface tension decreases as the temperature is raised.

$$\eqalign{ & {\text{Edge length}}\,\left( a \right) = 2{r^ + } + 2{r^ - } \cr & \,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,a = 2\left( {{r^ + } + {r^ - }} \right) \cr & \,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,a = 508\,pm \cr & \,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,{r^ + } = 110\,pm \cr & \,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\frac{{508}}{2} = {r^ + } + {r^ - } \cr & \,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,254 = 110 + {r^ - } \cr & \,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,{r^ - } = 254 - 110 \cr & \,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\, = 144\,pm \cr} $$

Constant $$b$$  is introduced for correction of volume.

Higher the critical temperature, faster is the liquefaction of the gas. Hence, $$N{H_3}$$  will liquefy first and $${N_2}$$  at last.

Number of moles, temperature and volume are same.