21.
A 5-litre cylinder contained $$10\,moles$$ of oxygen gas at $$27{\,^ \circ }C.$$ Due to sudden leakage through the hole, all the gas escaped into the atmosphere and the cylinder got empty. If the atmospheric pressure is 1.0 atmosphere, calculate the work done by the gas.
22.
The molar heat capacity $$\left( {{C_p}} \right)$$ of $$C{D_2}O$$ is $$10\,cals$$ at $$1000\,K.$$ The change in entropy associated with cooling of $$32\,g$$ of $$C{D_2}O$$ vapour from $$1000\,K$$ to $$100\,K$$ at constant pressure will be : ( $$D =$$ deuterium, atomic mass $$= 2$$ $$u$$ )
23.
One mole of an ideal gas is expanded isothermally and reversibly to half of its initial pressure. $$\Delta S$$ for the process in $$J\,{K^{ - 1}}\,mo{l^{ - 1}}$$ is $$\left[ {\ell n\,\,2 = 0.693\,{\text{and}}\,R = 8.314,J/\left( {mol\,K} \right)} \right]$$
24.
The $$\left( {{S^ \circ }} \right)$$ of the following substances are :
$$\eqalign{
& C{H_4}\left( g \right)\,\,186.2\,J{K^{ - 1}}\,mo{l^{ - 1}} \cr
& {O_2}\left( g \right)\,\,205.2\,J{K^{ - 1}}\,mo{l^{ - 1}} \cr
& C{O_2}\left( g \right)\,\,213.6\,J{K^{ - 1}}\,mo{l^{ - 1}} \cr
& {H_2}O\left( g \right)\,\,69.9.\,J{K^{ - 1}}\,mo{l^{ - 1}} \cr} $$
The entropy change $$\left( {\Delta {S^ \circ }} \right)$$ for the reaction $$C{H_4}\left( g \right) + 2{O_2}\left( g \right) \to C{O_2}\left( g \right) + 2{H_2}O\left( l \right)$$ is :
25.
For a particular reversible reaction at temperature $$T,$$ $$\Delta H$$ and $$\Delta S$$ were found to be both $$+ve.$$ If $${T_e}$$ is the temperature at equilibrium, the reaction would be spontaneous when
$$\eqalign{
& {\text{At}}\,{\text{equilibrium}}\,\,\Delta G = 0 \cr
& {\text{Hence}},\,\Delta G = \Delta H - {T_e}\Delta S = 0 \cr
& \therefore \,\,\Delta H = {T_e}\Delta S\,\,or\,\,{T_e} = \frac{{\Delta H}}{{\Delta S}} \cr} $$
For a spontaneous reaction
$$\Delta G$$ must be negative which is possible only if $$\Delta H < T\Delta S$$
$$or\,T > \frac{{\Delta H}}{{\Delta S}};\,\,\,{T_e} < T$$
26.
What will be the enthalpy change of conversion of graphite into diamond ?
$$\eqalign{
& {\text{[Given}}\,\,{C_{{\text{graphite}}}},{\Delta _{{\text{comb}}}}H = - 391.25\,kJ; \cr
& {C_{{\text{diamond}}}},{\Delta _{{\text{comb}}}}H = - 393.12\,kJ] \cr} $$
Mathematical expression of the thermodynamic equilibrium is
$$\Delta G = \Delta {G^ \circ } + 2.303RT\,\,{\text{log}}\,\,Q$$
At equilibrium when $$\Delta G = 0$$ and $$Q = K$$
then $$\Delta G = \Delta {G^ \circ } + 2.303\,RT\,\,{\text{log}}\,\,K = 0$$
$$\,\,\,\,\,\,\,\,\,\Delta {G^ \circ } = - 2.303\,RT\,\,{\text{log}}\,\,K$$
28.
What is the entropy change $$\left( {{\text{in}}\,J{K^{ - 1}}\,mo{l^{ - 1}}} \right)$$ when one mole of ice is converted into water at $${0^ \circ }C?$$ ( The enthalpy change for the conversion of ice to liquid water is $$6.0\,kJ\,mo{l^{ - 1}}$$ at $${0^ \circ }C$$ )
29.
Bond energies of $$H-H$$ and $$Cl-Cl$$ are $$430\,kJ\,mo{l^{ - 1}}$$ and $$242\,kJ\,mo{l^{ - 1}}$$ respectively. $$\Delta {H_f}$$ for $$HCl$$ is $$91\,kJ\,mo{l^{ - 1}}.$$ What will be the bond energy of $$H - Cl?$$
30.
A gaseous system is initially characterised by
$$500\,mL$$ volume and $$1\,atm$$ pressure at $$298\,K.$$ This system is allowed to do work as follows :
(i) in isobaric conditions, it expands to $$800\,mL$$ resulting a decrease in pressure and temperature to $$0.6\,atm$$ and $$273\,K$$ respectively.
(ii) in adiabatic conditions, it is allowed to expand upto $$800\,mL$$ and results a decrease in pressure and temperature to $$0.6\,atm$$ and $$273\,K$$ respectively.
If Gibbs energy change in (i) is $$\Delta {G_a}$$ and in (ii) is $$\Delta {G_b}$$ then what will be the ratio of $$\frac{{\Delta {G_a}}}{{\Delta {G_b}}}?$$