Chapter 13

The integral enthalpy of solution in \(\mathrm{kJ}\) of one mole of \(\mathrm{H}_{2} \mathrm{SO}_{4}\) dissolved in \(n\) mole of water is given by: $$ \Delta H_{s}=\frac{75.6 \times n}{n+1.8} $$ Calculate \(\Delta H\) for the following process: (a) 1 mole of \(\mathrm{H}_{2} \mathrm{SO}_{4}\) dissolved in \(2 \mathrm{~mole}\) of \(\mathrm{H}_{2} \mathrm{O}\). (b) 1 mole of \(\mathrm{H}_{2} \mathrm{SO}_{4}\) dissolved in 7 mole of \(\mathrm{H}_{2} \mathrm{O}\). (c) 1 mole of \(\mathrm{H}_{2} \mathrm{SO}_{4}\) dissolved in 5 mole of \(\mathrm{H}_{2} \mathrm{O}\). (d) solution (a) dissolved in 5 mole of \(\mathrm{H}_{2} \mathrm{O}\). (e) 1 mole of \(\mathrm{H}_{2} \mathrm{SO}_{4}\) dissolved in excess of \(\mathrm{H}_{2} \mathrm{O}\).

The heat of solution of \(\mathrm{NH}_{4} \mathrm{NO}_{3}\) in water was determined by measuring the amount of electrical work needed to compensate for the cooling which would otherwise óccur when the salt dissolves. After the \(\mathrm{NH}_{4} \mathrm{NO}_{3}\) was added to the water, electrical energy was provided by passage of current through a resistance coil until the temperature of the solution reached the value it had prior to the addition of salt. In a typical experiment, \(4.4 \mathrm{~g}\) of \(\mathrm{NH}_{4} \mathrm{NO}_{3}\) was added to \(200 \mathrm{~g}\) water. A current of \(0.75\) ampere was provided through the heater coil, and the voltage across the terminals was \(6.0 \mathrm{~V}\). The current was applied for \(5.2\) minute. Calculate \(\Delta H\) for the solution of \(1.0\) mole \(\mathrm{NH}_{4} \mathrm{NO}_{3}\) in enough water to give same concentration as was attained in the above experiment.

The commercial production of water gas utilizes the reaction under standard conditions: \(\mathrm{C}+\mathrm{H}_{2} \mathrm{O}(\mathrm{g}) \rightarrow \mathrm{H}_{2}+\mathrm{CO}\). The heat required for this endothermic reaction may be supplied by adding a limited amount of air and burning some carbon to \(\mathrm{CO}_{2}\). How many \(\mathrm{g}\) of carbon must be burnt to \(\mathrm{CO}_{2}\) to provide enough heat for the water gas conversion of \(100 \mathrm{~g}\) carbon? Neglect all heat losses to the environment. Also \(\Delta H_{\mathrm{f}}^{2}\) of \(\mathrm{CO}, \mathrm{H}_{2} \mathrm{O}_{(\mathrm{g})}\) and \(\mathrm{CO}_{2}\) are \(-110.53\), \(-241.81\) and \(-393.51 \mathrm{~kJ} / \mathrm{mol}\) respectively.

\(1.00\) litre sample of a mixture of \(\mathrm{CH}_{4(\mathrm{~g})}\) and \(\mathrm{O}_{2(\mathrm{~g})}\) measured at \(25^{\circ} \mathrm{C}\) and 740 torr was allowed to react at constant pressure in a calorimeter which together with its contents had a heat capacity of \(1260 \mathrm{cal} / \mathrm{K}\). The complete combustion of the methane to \(\mathrm{CO}_{2}\) and \(\mathrm{H}_{2} \mathrm{O}\) caused a temperature rise in the calorimeter of \(0.667 \mathrm{~K}\). What was the mole per cent of \(\mathrm{CH}_{4}\) in the original mixture? \(\Delta H_{\text {comb }}^{\circ}\left(\mathrm{CH}_{4}\right)=-215 \mathrm{k}\) cal \(\mathrm{mol}^{-1}\).

The standard enthalpy of formation of \(\mathrm{FeO}\) and \(\mathrm{Fe}_{2} \mathrm{O}_{3}\) is \(-65 \mathrm{kcal}\) \(\mathrm{mol}^{-1}\) and \(-197\) kcal mol \(^{-1}\) respectively. A mixture of two oxides contains \(\mathrm{FeO}\) and \(\mathrm{Fe}_{2} \mathrm{O}_{3}\) in the mole ratio \(2: 1 .\) If by oxidation, it is changed into a \(1: 2\) mole ratio mixture, how much of thermal energy will be released per mol of initial mixture.

\begin{aligned} &\text { The heat of dissociation of } \mathrm{H}_{2} \text { is } 435 \mathrm{~kJ} \mathrm{~mol}^{-1} \text { . If } \mathrm{C}_{(\mathrm{s})} \longrightarrow \mathrm{C}_{(\mathrm{g})} \text { ; }\\\ &\Delta H=720 \mathrm{~kJ} \mathrm{~mol}^{-1}, \text { calculate the bond energy per mol of the } \mathrm{C}-\mathrm{H} \text { bond }\\\ &\text { in } \mathrm{CH}_{4} \text { molecule. } \Delta H_{\mathrm{f}} \text { for } \mathrm{CH}_{4}=-75 \mathrm{~kJ} \mathrm{~mol}^{-1} \text { . } \end{aligned}