Chemical Equilibria: Kc and Kp: Practice Questions

For a reversible chemical reaction at equilibrium in a closed system, which of the following changes will result in a change to the numerical value of the equilibrium constant, \( K_c \)?

Nitrogen and hydrogen react to form ammonia according to the following equation:
\( \text{N}_2(g) + 3\text{H}_2(g) \rightleftharpoons 2\text{NH}_3(g) \)
At a certain temperature, an equilibrium mixture contains the following partial pressures: \( P(\text{N}_2) = 2.0 \text{ atm} \), \( P(\text{H}_2) = 1.0 \text{ atm} \), and \( P(\text{NH}_3) = 0.50 \text{ atm} \). Calculate the value of the equilibrium constant, \( K_p \), at this temperature.

Consider the gas-phase dissociation equilibrium:
\( \text{A}(g) \rightleftharpoons 2\text{B}(g) \)
If 20% of \( \text{A} \) dissociates at equilibrium at a constant total pressure \( P \), what is the correct expression for the equilibrium constant \( K_p \) in terms of \( P \)?

For the gaseous equilibrium system:
\( 2\text{SO}_2(g) + \text{O}_2(g) \rightleftharpoons 2\text{SO}_3(g) \)
What is the effect of increasing the total pressure on the system at a constant temperature?

In a closed system at a constant temperature, the following equilibrium is established in a \( 2.0 \text{ dm}^3 \) container:
\( \text{H}_2(g) + \text{I}_2(g) \rightleftharpoons 2\text{HI}(g) \)
At equilibrium, the mixture contains \( 0.40 \text{ mol} \) of \( \text{H}_2 \), \( 0.40 \text{ mol} \) of \( \text{I}_2 \), and \( 1.60 \text{ mol} \) of \( \text{HI} \). Calculate the value of the equilibrium constant, \( K_c \).

The reversible gas-phase reaction is given by:
\(2\text{NO}_2(g) \rightleftharpoons \text{N}_2\text{O}_4(g)\)    \(\Delta H = -57.2 \text{ kJ mol}^{-1}\)
Explain, using the relationship \(\Delta S_{\text{total}} = R \ln K\), how an increase in temperature affects the numerical value of the equilibrium constant, \(K\).

At \(700\text{ K}\), an equilibrium mixture for the reaction \(\text{CO}(g) + 2\text{H}_2(g) \rightleftharpoons \text{CH}_3\text{OH}(g)\) has partial pressures of \(p(\text{CO}) = 5.0\text{ atm}\), \(p(\text{H}_2) = 12.0\text{ atm}\), and \(p(\text{CH}_3\text{OH}) = 1.8\text{ atm}\).
Calculate the value of \(K_p\) under these conditions, including its units.