Calculate the heat of reaction at for if the heat of reaction at is . The molar heat capacities at c — Thermodynamics and Thermochemistry Chemistry Question
Question
Calculate the heat of reaction at $77^\circ \text{C}$ for $\frac{1}{2}H_2(g) + \frac{1}{2}Cl_2(g) \rightarrow HCl(g)$ if the heat of reaction at $27^\circ \text{C}$ is $-22.1 \text{ kcal}$. The molar heat capacities at constant pressure ($C_p$) at $27^\circ \text{C}$ for $H_2$, $Cl_2$, and $HCl$ are $6.82$, $7.70$, and $6.80 \text{ cal K}^{-1} \text{ mol}^{-1}$ respectively.
💡 Solution & Explanation
According to Kirchhoff's equation, $\Delta H_{T_2} = \Delta H_{T_1} + \Delta C_p(T_2 - T_1)$. Here, $\Delta C_p = C_p(HCl) - [\frac{1}{2}C_p(H_2) + \frac{1}{2}C_p(Cl_2)] = 6.80 - [\frac{1}{2}(6.82) + \frac{1}{2}(7.70)] = 6.80 - [3.41 + 3.85] = 6.80 - 7.26 = -0.46 \text{ cal K}^{-1} \text{ mol}^{-1}$. The change in temperature is $\Delta T = 350 \text{ K} - 300 \text{ K} = 50 \text{ K}$. $\Delta H_{350} = -22.1 \text{ kcal} + \frac{-0.46 \times 50}{1000} \text{ kcal} = -22.1 - 0.023 = -22.123 \text{ kcal}$.