In a container at , is at a pressure of and is attempting to reach equilibrium with an excess of sol — Chemical Equilibrium Chemistry Question
Question
In a $20\text{ L}$ container at $400\text{ K}$, $CO_2(g)$ is at a pressure of $0.4\text{ atm}$ and is attempting to reach equilibrium with an excess of solid $SrO$ and $SrCO_3$ according to $SrCO_3(s) \rightleftharpoons SrO(s) + CO_2(g)$. The equilibrium constant $K_p$ is $1.6\text{ atm}$. The volume of the container is slowly decreased by a movable piston. What is the maximum volume in liters at which the pressure of $CO_2$ just attains its equilibrium value?
💡 Solution & Explanation
At equilibrium, $P_{CO_2} = K_p = 1.6\text{ atm}$. Initially, the pressure is $0.4\text{ atm}$ at $20\text{ L}$, which means $Q_p < K_p$ and no $SrCO_3$ is forming yet (gas is simply being compressed). Using Boyle's Law ($P_1 V_1 = P_2 V_2$) before the equilibrium threshold is crossed: $0.4 \times 20 = 1.6 \times V_2$. Solving yields $V_2 = 8 / 1.6 = 5\text{ L}$. Any further compression will cause $CO_2$ to precipitate as $SrCO_3$ to maintain $1.6\text{ atm}$.