The enthalpy change for the complete combustion of 1 mol of methane at 1 bar and 298 K is - 890.3 kJ mol^-1.
Calculate $\Delta_{\mathrm{c}} H^{\circ}$ at 335 K.
Mean C_p / J K^-1 mol^-1: CH₄ (g) 35.7; O₂ (g) 29.4; CO₂ (g) 37.1; H₂O (l) 75.3.

Question

The enthalpy change for the complete combustion of 1 mol of methane at 1 bar and 298 K is - 890.3 kJ mol^-1.
Calculate

\Delta_{\mathrm{c}} H^{\circ}

at 335 K.
Mean C_p / J K^-1 mol^-1: CH₄ (g) 35.7; O₂ (g) 29.4; CO₂ (g) 37.1; H₂O (l) 75.3.

Quizplus · Accepted Answer

We can use the following formula to calculate the change in enthalpy at a different temperature:

$\Delta_{\mathrm{c}} H_2^{\circ} = \Delta_{\mathrm{c}} H_1^{\circ} + \sum n_i C_{\mathrm{p},i} \Delta T$

Where:
$\Delta_{\mathrm{c}} H_1^{\circ}$ is the enthalpy change at temperature T1
$\Delta_{\mathrm{c}} H_2^{\circ}$ is the enthalpy change at temperature T2
$n_i$ is the stoichiometric coefficient of component i
$C_{\mathrm{p},i}$ is the molar heat capacity of component i
$\Delta T = T_2 - T_1$

Substituting the given values, we get:

$\Delta_{\mathrm{c}} H_2^{\circ} = -890.3 \, \mathrm{kJ \, mol^{-1}} + (1\times 35.7 + 2\times 29.4 + 1\times 37.1 + 2\times 75.3) \, \mathrm{J \, K^{-1} \, mol^{-1}} \times (335-298) \, \mathrm{K}$

$\Delta_{\mathrm{c}} H_2^{\circ} = -886.9 \, \mathrm{kJ \, mol^{-1}}$

Therefore, the best choice is D.

The Enthalpy Change for the Complete Combustion of 1 Mol ΔcH∘\Delta_{\mathrm{c}} H^{\circ}Δc​H∘

The Enthalpy Change for the Complete Combustion of 1 Mol $\Delta_{\mathrm{c}} H^{\circ}$