States of Matter Solid, Liquid and Gas MCQ Questions & Answers in Physical Chemistry | Chemistry

Molecules move very fast in all directions in a straight line by colliding with each other but with different velocity.

When $$Z > 1,$$  real gases are difficult to compress because the forces of attraction between the molecules are very feeble.

$$\eqalign{ & {\text{Under}}\,{\text{indential}}\,{\text{conditions,}}\,\frac{{{r_1}}}{{{r_2}}} = \sqrt {\frac{{{M_2}}}{{{M_1}}}} \cr & {\text{As rate of diffusion is also inversely proportional to}} \cr & {\text{time,}}\,{\text{we}}\,{\text{will}}\,{\text{have}},\,\frac{{{t_2}}}{{{t_1}}} = \sqrt {\frac{{{M_2}}}{{{M_1}}}} \cr & \left( {\text{A}} \right)\,{\text{Thus,}}\,{\text{For}}\,He,\,\,{t_2} = \sqrt {\frac{4}{2}} \left( {5s} \right) = 5\sqrt {2s} \ne 10s; \cr & \left( {\text{B}} \right)\,{\text{For}}\,{O_2},\,\,{t_2} = \sqrt {\frac{{32}}{2}} \left( {5s} \right) = 20s \cr & \left( {\text{C}} \right)\,{\text{For}}\,CO,\,\,{t_2} = \sqrt {\frac{{28}}{2}} \left( {5s} \right) \ne 25s\,; \cr & \left( {\text{D}} \right)\,{\text{For}}\,C{O_2},\,\,{t_2} = \sqrt {\frac{{44}}{2}} \left( {5s} \right) \ne 55s \cr} $$

$$\eqalign{ & {\text{Given conditions}} \cr & {V_1} = 16.4\,L,\,{V_2} = 5\,L \cr & {P_1} = 1.5\,atm,\,{P_2} = 4.1\,atm \cr & {T_1} = 273 + 27 = 300\,K, \cr & {T_2} = 273 + 227 = 500\,K \cr & {\text{Applying gas equation,}}\,\frac{{{P_1}{V_1}}}{{{P_2}{V_2}}} = \frac{{{n_1}{T_1}}}{{{n_2}{T_2}}} \cr & \frac{{{n_1}}}{{{n_2}}} = \frac{{{P_1}{V_1}{T_1}}}{{{P_2}{V_2}{T_2}}} \cr & \therefore \,\,\frac{{1.5 \times 16.4 \times 500}}{{4.1 \times 5 \times 300}} = \frac{2}{1} \cr} $$

All the gases occupy the available volume and will form homogeneous mixture.

The compressibility factor of a gas is defined as $$Z = \frac{{p{V_m}}}{{RT}}$$
For an ideal gas, $$p{V_m} = RT.$$
Hence $$Z = 1$$

$$\frac{{{V_1}}}{{{T_1}}} = \frac{{{V_2}}}{{{T_2}}};{V_1} = 2\,L,$$     $${T_1} = 35 + 273 = 308\,K$$
$${V_2} = ?,{T_2} = 45 + 273 = 318\,K;$$       $${V_2} = \frac{2}{{308}} \times 318 = 2.06\,L$$
$${\text{Capacity of flask}} = 2\,L$$
$${\text{Volume of air escaped}}$$     $$ = 2.06 - 2 = 0.06\,L\,\,{\text{or}}\,\,60\,mL$$

$$\eqalign{ & n = \frac{m}{M} \cr & \,\,\,\,\, = \frac{{2.8}}{{28}} \cr & \,\,\,\,\, = 0.1 \cr & V = \frac{{nRT}}{P} \cr & \,\,\,\,\,\, = \frac{{0.1 \times 0.0821 \times 300}}{{0.821}} \cr & \,\,\,\,\,\, = 3\,L \cr} $$

$$P = 1\,atm,T = 98 + 273 = 371\,K,$$       $$M = 78\,\,g\,\,mo{l^{ - 1}}$$
$$R = 0.0821\,\,L\,\,atm\,\,{K^{ - 1}}\,\,mo{l^{ - 1}}$$
$$PM = dRT\,\,{\text{or}}\,\,d = \frac{{PM}}{{RT}}$$     $$ = \frac{{1 \times 78}}{{0.0821 \times 371}} = 2.56\,\,g\,\,{L^{ - 1}}$$

$$\eqalign{ & {\text{Average velocity}} = \sqrt {\frac{{8RT}}{{\pi M}}} \cr & \therefore \,\,{V_{av}} \propto \sqrt T \,\,or\,\,\frac{{{{\left( {{V_{av}}} \right)}_2}}}{{{{\left( {{V_{av}}} \right)}_1}}} \cr & = \sqrt {\frac{{2T}}{T}} \cr & = 1.4 \cr} $$