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:
Correct Answer: 150
Solution and Explanation
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:
\( x = 150 \)
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