The standard enthalpy of formation of $\mathrm{H}_2 \mathrm{O}(\mathrm{g})$ at $298 \mathrm{~K}$ is $-241.82 \mathrm{~kJ} \mathrm{~mol}^{-1}$. Estimate its value at $100^{\circ} \mathrm{C}$ given the following values of the molar heat capacities at constant pressure: $\mathrm{H}_2 \mathrm{O}(\mathrm{g}): 33.58 \mathrm{~J} \mathrm{~K}^{-1} \mathrm{~mol}^{-1} ; \mathrm{H}_2(\mathrm{~g}): 28.82 \mathrm{~J} \mathrm{~K}^{-1} \mathrm{~mol}^{-1} ; \mathrm{O}_2(\mathrm{~g})$ : $29.36 \mathrm{~J} \mathrm{~K}^{-1} \mathrm{~mol}^{-1}$. Assume that the heat capacities are independent of temperature.
The reaction is $\mathrm{H}_2(\mathrm{~g})+\frac{1}{2} \mathrm{O}_2(\mathrm{~g}) \rightarrow \mathrm{H}_2 \mathrm{O}(\mathrm{g})$, so
$$
\Delta_{\mathrm{r}} C_p^{\ominus}=C_{p, \mathrm{~m}}^{\ominus}\left(\mathrm{H}_2 \mathrm{O}, \mathrm{g}\right)-\left\{C_{p, \mathrm{~m}}^{\ominus}\left(\mathrm{H}_2, \mathrm{~g}\right)+\frac{1}{2} C_{p, \mathrm{~m}}^{\ominus}\left(\mathrm{O}_2, \mathrm{~g}\right)\right\}=-9.92 \mathrm{~J} \mathrm{~K}^{-1} \mathrm{~mol}^{-1}
$$
It then follows that
$$
\Delta_{\mathrm{r}} H^{\ominus}(373 \mathrm{~K})=-241.82 \mathrm{~kJ} \mathrm{~mol}^{-1}+(75 \mathrm{~K}) \times\left(-9.92 \mathrm{~J} \mathrm{~K}^{-1} \mathrm{~mol}^{-1}\right)=-242.6 \mathrm{~kJ} \mathrm{~mol}^{-1}
$$
