Question

The heat of combustion of solid benzoic acid at constant volume is $-321.30 \, \text{kJ}$ at $27^\circ \text{C}$. The heat of combustion at constant pressure is $(-321.30 - xR)\, \text{kJ}$. The value of $x$ is:

Answer 1

The relation between heat at constant pressure ($\Delta H$) and at constant volume ($\Delta U$) is:

$\Delta H = \Delta U + \Delta n_g RT$

For benzoic acid:

$C_6H_5COOH(s) + \frac{15}{2} O_2(g) \rightarrow 7CO_2(g) + 3H_2O(l)$

$\Delta n_g = 7 - \frac{15}{2} = -\frac{1}{2}$. Substituting:

$\Delta H = -321.30 - \frac{1}{2} R \times 300$

Here, $R \approx 8.314 \, \text{J/mol.K}$. Solving gives:

$x = 150$