Chapter 12

During \(200 \mathrm{~J}\) work done on the system, \(140 \mathrm{~J}\) of heat is given out. Calculate the change in internal energy.

A system does \(40 \mathrm{~J}\) work on surrounding as well as gives out \(20 \mathrm{~J}\) energy. Calculate the change in internal energy.

A system does \(100 \mathrm{~J}\) work on surroundings by absorbing \(150 \mathrm{~J}\) of heat. Calculate the change in internal energy.

Calculate the work done during the process when one mole of gas is allowed to expand freely into vacuum.

Two litre of \(\mathrm{N}_{2}\) at \(0^{\circ} \mathrm{C}\) and 5 atm pressure are expanded isothermally against a constant external pressure of 1 atm until the pressure of gas reaches 1 atm. Assuming gas to be ideal, calculate work of expansion.

For the water gas reaction : $$ \mathrm{C}_{(\mathrm{s})}+\mathrm{H}_{2} \mathrm{O}_{(\mathrm{g})} \rightleftharpoons \mathrm{CO}_{(\mathrm{g})}+\mathrm{H}_{2(\mathrm{~g})} $$ the standard Gibbs energy of reaction (at \(1000 \mathrm{~K}\) ) is \(-8.1 \mathrm{~kJ} \mathrm{~mol}^{-\mathrm{i}}\). Calculate its equilibrium constant.

Find out whether it is possible to reduce \(\mathrm{MgO}\) using carbon at \(298 \mathrm{~K}\). If not, at what temperature it becomes spontaneous. For reaction, \(\mathrm{MgO}(s)+\mathrm{C}(s) \longrightarrow \mathrm{Mg}(s)+\mathrm{CO}(g), \Delta H^{\circ}=+491.18 \mathrm{~kJ} \mathrm{~mol}^{-1}\) and \(\Delta S^{0}=197.67 \mathrm{JK}^{-1} \mathrm{~mol}^{-1}\)

Calculate the change of entropy, \(\Delta_{r} S^{\circ}\) at \(298 \mathrm{~K}\) for the reaction in which urea is formed from \(\mathrm{NH}_{3}\) and \(\mathrm{CO}_{2}\). \(2 \mathrm{NH}_{3}(g)+\mathrm{CO}_{2}(g) \longrightarrow \mathrm{NH}_{2} \mathrm{CONH}_{2}(a q)+\mathrm{H}_{2} \mathrm{O}(l) .\) The standard entropy of \(\mathrm{NH}_{2} \mathrm{CONH}_{2}(a q), \mathrm{CO}_{2}(g), \mathrm{NH}_{3}(g)\) and \(\mathrm{H}_{2} \mathrm{O}(l)\) are \(174.0\), \(213.7,192.3\) and \(69.9 \mathrm{JK}^{-1} \mathrm{~mol}^{-1}\) respectively.

Calculate the equilibrium constant \(K_{\mathrm{p}}\) for the reaction given below if \(\Delta G^{\circ}=-10.632 \mathrm{~kJ}\) at \(300 \mathrm{~K}\) $$ \mathrm{CO}_{2(\mathrm{~g})}+\mathrm{H}_{2(\mathrm{~g})} \rightleftharpoons \mathrm{CO}_{(\mathrm{g})}+\mathrm{H}_{2} \mathrm{O}_{(\mathrm{g})} $$

The enthalpy of vaporisation of liquid diethyl ether \(-\left(\mathrm{C}_{2} \mathrm{H}_{5}\right)_{2} \mathrm{O}\), is \(26.0 \mathrm{~kJ} \mathrm{~mol}^{-1}\) at its boiling point \(\left(35.0^{\circ} \mathrm{C}\right)\). Calculate \(\Delta S\) for conversion of : (a) liquid to vapour, and \(\quad\) (b) vapour to liquid at \(35^{\circ} \mathrm{C}\).