The equation of state for one mole of a gas is , where is a constant, independent of temperature. Th — Thermodynamics and Thermochemistry Chemistry Question
Question
The equation of state for one mole of a gas is $PV = RT + BP$, where $B$ is a constant, independent of temperature. The internal energy of fixed amount of gas is function of temperature only. If one mole of the above gas is isothermally expanded from 12 L to 22 L at a constant external pressure of 1 bar at 400 K, then the change in enthalpy of the gas is approximately ($B = 2 \text{ L/mol}$)
💡 Solution & Explanation
$\Delta H = \Delta U + \Delta(PV)$. Since $T$ is constant, $\Delta U = 0$ and $\Delta(RT) = 0$. $\Delta(PV) = \Delta(BP) = B(P_2 - P_1)$. $P_1 = \frac{RT}{V_1-B} = \frac{0.08314 \times 400}{12-2} = 3.3256 \text{ bar}$. $P_2 = \frac{RT}{V_2-B} = \frac{33.256}{20} = 1.6628 \text{ bar}$. $\Delta H = 2 \text{ L/mol} \times (1.6628 - 3.3256) \text{ bar} = -3.3256 \text{ bar L} \approx -332.6 \text{ J}$.