MCAT Equilibrium Practice Questions with Answers

1. Concept Explanation

MCAT Equilibrium refers to the state in a reversible chemical reaction where the rate of the forward reaction equals the rate of the reverse reaction, resulting in no net change in the concentrations of reactants and products over time.

At the heart of this concept is the Law of Mass Action, which states that for a generic reaction $aA + bB \rightleftharpoons cC + dD$, the equilibrium constant $K_{ \neq}$ is expressed as the ratio of the product of the concentrations of the products to the product of the concentrations of the reactants, each raised to the power of their stoichiometric coefficients:

$$K_{ \neq} = \frac{[C]^c [D]^d}{[A]^a [B]^b}$$

Key principles to master for the MCAT include:

• Dynamic Equilibrium: The reaction has not stopped; rather, the forward and reverse processes occur at the same speed.
• Reaction Quotient (Q): This is calculated using the same formula as $K_{ \neq}$ but at any point in time. Comparing $Q$ to $K_{ \neq}$ tells us which direction the reaction will shift to reach equilibrium. If $Q < K_{ \neq}$, the reaction proceeds forward. If $Q > K_{ \neq}$, it proceeds in reverse.
• Le Châtelier’s Principle: This principle predicts how a system at equilibrium responds to external stressors like changes in concentration, pressure, volume, or temperature. The system will shift to counteract the stress.
• Temperature Dependence: Unlike changes in concentration or pressure, which change $Q$ but not $K_{ \neq}$, a change in temperature actually changes the value of $K_{ \neq}$.

Understanding these relationships is vital for medical students who must apply these chemical principles to physiological systems, such as the bicarbonate buffer system in human blood. For more on how to effectively learn these complex rules, consider using retrieval practice as a core study strategy.

2. Solved Examples

Example 1: Calculating the Equilibrium Constant
For the reaction $N_2(g) + 3H_2(g) \rightleftharpoons 2NH_3(g)$, at equilibrium, the concentrations are $[N_2] = 0.5 \text{ M}$, $[H_2] = 0.2 \text{ M}$, and $[NH_3] = 0.4 \text{ M}$. Calculate $K_c$.

1. Write the expression: $K_c = \frac{[NH_3]^2}{[N_2][H_2]^3}$
2. Substitute the values: $K_c = \frac{(0.4)^2}{(0.5)(0.2)^3}$
3. Simplify the numerator: $(0.4)^2 = 0.16$
4. Simplify the denominator: $(0.5) \times (0.008) = 0.004$
5. Final calculation: $K_c = \frac{0.16}{0.004} = 40$

Example 2: Predicting Reaction Direction
A reaction has a $K_{ \neq}$ of $1.5 \times 10^{-2}$. If the current reaction quotient $Q$ is $0.5$, which way will the reaction shift?

1. Compare $Q$ and $K_{ \neq}$. Here, $0.5 > 0.015$.
2. Since $Q > K_{ \neq}$, there are more products and fewer reactants than the equilibrium state requires.
3. The reaction will shift to the left (toward reactants) to reach equilibrium.

Example 3: Le Châtelier’s and Pressure
Consider the endothermic reaction: $PCl_5(g) \rightleftharpoons PCl_3(g) + Cl_2(g)$. What happens if the volume of the container is decreased?

1. Decreasing volume increases the total pressure of the system.
2. Le Châtelier’s Principle states the system will shift to the side with fewer moles of gas to reduce pressure.
3. Reactant side = 1 mole of gas; Product side = 2 moles of gas ($1 + 1$).
4. The reaction shifts to the left.

3. Practice Questions

1. A reaction is at equilibrium. If an inert gas like Helium is added to the container at constant volume, what happens to the equilibrium position?

2. For the exothermic reaction $2SO_2(g) + O_2(g) \rightleftharpoons 2SO_3(g)$, how will increasing the temperature affect the value of $K_{ \neq}$?

3. Calculate the equilibrium concentration of $B$ for the reaction $A(aq) \rightleftharpoons 2B(aq)$ if $K_c = 4.0$ and the equilibrium concentration of $A$ is $0.25 \text{ M}$.

4. In the reaction $CaCO_3(s) \rightleftharpoons CaO(s) + CO_2(g)$, what is the correct expression for $K_p$?

5. If a catalyst is added to a reaction at equilibrium, how will the concentrations of the reactants and products change?

6. Pure water auto-ionizes according to the equation $H_2O(l) + H_2O(l) \rightleftharpoons H_3O^+(aq) + OH^-(aq)$. If the reaction is endothermic, how does the pH of pure water change as temperature increases?

7. A system consists of $A(g) + B(g) \rightleftharpoons C(g)$. If the partial pressures are $P_A = 2 \text{ atm}$, $P_B = 2 \text{ atm}$, and $P_C = 8 \text{ atm}$, and $K_p = 1$, in which direction will the reaction proceed?

8. What is the relationship between $\Delta G^\circ$ and $K_{ \neq}$ when $K_{ \neq} > 1$?

4. Answers & Explanations

1. Answer: No change. Adding an inert gas at constant volume increases the total pressure but does not change the partial pressures of the reacting gases. Since the concentrations (moles/volume) remain the same, the equilibrium position is unaffected.
2. Answer: $K_{ \neq}$ decreases. In an exothermic reaction, heat is a product. Increasing temperature is like adding a product, shifting the reaction to the left. Since $K_{ \neq} = \frac{[Products]}{[Reactants]}$, increasing the denominator and decreasing the numerator results in a smaller $K_{ \neq}$.
3. Answer: $1.0 \text{ M}$. The expression is $K_c = \frac{[B]^2}{[A]}$. Substituting the values: $4.0 = \frac{[B]^2}{0.25}$. Multiplying gives $[B]^2 = 1.0$. Taking the square root, $[B] = 1.0 \text{ M}$.
4. Answer: $K_p = P_{CO2}$. Pure solids and liquids are excluded from the equilibrium expression because their "concentrations" (densities) do not change significantly. Only the gas phase $CO_2$ is included. Refer to Wikipedia's entry on Chemical Equilibrium for more on activity coefficients.
5. Answer: No change. A catalyst lowers the activation energy for both the forward and reverse reactions equally. It helps a system reach equilibrium faster but does not change the final equilibrium concentrations.
6. Answer: pH decreases. Since the reaction is endothermic, increasing temperature shifts the equilibrium to the right, increasing $[H_3O^+]$. Since $pH = -\log[H_3O^+]$, an increase in concentration results in a lower pH value (though the water remains neutral because $[OH^-]$ increases equally).
7. Answer: To the left. Calculate $Q_p = \frac{P_C}{P_A \times P_B} = \frac{8}{2 \times 2} = 2$. Since $Q_p (2) > K_p (1)$, the reaction will shift toward the reactants (left).
8. Answer: $\Delta G^\circ$ is negative. The relationship is defined by $\Delta G^\circ = -RT \ln K_{ \neq}$. If $K_{ \neq} > 1$, then $\ln K_{ \neq}$ is positive, making $\Delta G^\circ$ negative, which indicates a spontaneous reaction under standard conditions.

1. Which of the following will change the value of the equilibrium constant (K)?

• AChanging the concentration of reactants
• BChanging the total pressure of the system
• CChanging the temperature
• DAdding a heterogeneous catalyst

6. Frequently Asked Questions

What is the difference between K and Q?

K is the equilibrium constant, representing the ratio of products to reactants at equilibrium, while Q is the reaction quotient, representing that ratio at any specific point in time. Comparing Q to K allows you to determine the direction in which the reaction will proceed to reach equilibrium.

Does a catalyst affect the equilibrium constant?

No, a catalyst does not change the value of the equilibrium constant or the position of equilibrium. It only increases the rate at which equilibrium is achieved by lowering the activation energy for both the forward and reverse reactions.

How does temperature affect K for an endothermic reaction?

For an endothermic reaction, heat is considered a reactant, so increasing the temperature shifts the equilibrium toward the products. This shift increases the concentration of products relative to reactants, thereby increasing the value of the equilibrium constant K.

Why are liquids and solids omitted from Keq?

Pure solids and liquids are omitted because their molar concentrations are determined by their density, which remains constant regardless of how much of the substance is present. Since their activity is defined as 1 in standard states, they do not change the ratio in the equilibrium expression.

What is the relationship between kinetics and equilibrium?

Kinetics describes the speed of a reaction (how fast it reaches equilibrium), while equilibrium describes the extent of a reaction (how much product is formed at the end). The equilibrium constant K is equal to the ratio of the rate constants of the forward and reverse reactions ($k_f / k_r$).

What happens to equilibrium if you add more reactant?

According to Le Châtelier’s Principle, adding more reactant to a system at equilibrium will cause the reaction to shift toward the products to consume the excess. This results in a temporary state where Q < K until equilibrium is re-established at the same K value.