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

Correct Answer: 150

The relationship between enthalpy change at constant pressure (\( \Delta H \)) and internal energy change at constant volume (\( \Delta U \)) is given by the equation:

\( \Delta H = \Delta U + \Delta n_g RT \)

For the combustion of benzoic acid:

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

The change in moles of gas (\( \Delta n_g \)) is calculated as:

\( \Delta n_g = 7 - \frac{15}{2} = -\frac{1}{2} \). Upon substitution into the equation:

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

Using \( R \approx 8.314 \, \text{J/mol.K} \), the result of the calculation is:

\( x = 150 \)