Sulfur trioxide is manufactured via the equilibrium 2 , SO _2(g)+ O _2(g) 2 , SO…

CHEMISTRY · Multi-part · A Level · Chemistry · Gaseous equilibria (Kp) · Gaseous equilibria (Kp)

Problem

Sulfur trioxide is manufactured via the equilibrium

2\,\text{SO}_2(g)+\text{O}_2(g)\rightleftharpoons2\,\text{SO}_3(g)

700\,\text{K}

the standard enthalpy change for this reaction is

\Delta H^{\circ}_{700} = -197\,\text{kJ}

. The molar heat capacities at constant pressure in the temperature range

700\text{–}900\,\text{K}

are approximately constant with the following values:

\begin{aligned} C_{p}(\text{SO}_2) &= 41.9\,\text{J\,mol}^{-1}\text{K}^{-1} \\ C_{p}(\text{O}_2) &= 29.4\,\text{J\,mol}^{-1}\text{K}^{-1} \\ C_{p}(\text{SO}_3) &= 49.6\,\text{J\,mol}^{-1}\text{K}^{-1} \end{aligned}

The equilibrium constant at

700\,\text{K}

K_p = 1.3\times10^{4}

. A gas mixture at

900\,\text{K}

has initial partial pressures

P_{\text{SO}_2}=0.40\,\text{atm}

P_{\text{O}_2}=0.20\,\text{atm}

, and

P_{\text{SO}_3}=0.10\,\text{atm}

in a container of fixed volume. (a) Estimate the standard enthalpy change

\Delta H^{\circ}_{900}

for the reaction at

900\,\text{K}

using the heat-capacity data provided. (b) Using your result from part (a), calculate the value of

K_p

900\,\text{K}

. (c) Determine

Q_p

for the gas mixture at

900\,\text{K}

and predict the direction in which the system will shift to attain equilibrium. (d) Calculate the equilibrium partial pressures of all species at

900\,\text{K}

. Clearly show the setup of any algebraic expressions used to solve for the equilibrium amounts.