Question

The standard enthalpy of formation of gaseous $H_{2}O$ at $\text{298} \, \text{K}$ is $- \text{241} \text{.82} \, \text{kJ}$ $\text{mo}\text{l}^{- 1}$ . Calculate $\text{ΔH}_{\text{f}}^{\text{o}}$ at $\text{373} \, \text{K,}$ given the following values of the molar heat capacities at constant pressure.
Molar heat capacity of $\left(\text{H}\right)_{2} \text{O} \left(\text{g}\right) = 33.58 \left(\text{JK}\right)^{- 1} \left(\text{mol}\right)^{- 1}$
Molar heat capacity of $H_{2}\left(g\right)=28.84\text{ J}\left(\text{K}\right)^{- 1}mol^{- 1}$
Molar heat capacity of $O_{2}\left(g\right)=29.37\text{ J}\left(\text{K}\right)^{- 1}mol^{- 1}$
Assume that the heat capacities are independent of temperature.

• A. $-242.6\text{ kJ }mol^{- 1}$
• B. $-485.2\text{ kJ }mol^{- 1}$
• C. $-121.3\text{ kJ }mol^{- 1}$
• D. $-286.4\text{ kJ }mol^{- 1}$

Answer 1

Answer: (A)

The reaction is $H_{2}\left(g\right)+\frac{1}{2}O_{2}\left(g\right) \rightarrow H_{2}O\left(g\right)$
$\Delta C_{p}^{o}=C_{p , m}^{o}\left(H_{2} O , g\right)-\left\{C_{p , m}^{o} \left(H_{2} , g\right) + \frac{1}{2} C_{p , m}^{o} \left(O_{2}\right)\right\}$
$=33.58-\left\{28.84 + \frac{1}{2} \left(29.37\right)\right\}$
$=-9.94\text{ JK}^{- 1}mol^{- 1}$
Using Kirchhoff's equation,
$\Delta H^\circ \left(373 \, K\right)=\Delta H^\circ \left(298 \, K\right)+\left(T_{2} - T_{1}\right)\Delta C_{p}^{o}$
$=-241.82+\left(373 - 298\right)\times \left(- 9.94\right)$
$=-242.6\text{ kJ mo}\text{l}^{- 1}$