Reaction Equilibrium — Hard Practice Quiz

A Chemistry cheat sheet for Reaction Equilibrium — every key formula with its symbols defined — plus a hard-level practice quiz to test recall.

Formulas & key concepts

Equilibrium Constant (Concentration): Ratio of product concentrations to reactant concentrations at equilibrium, raised to stoichiometric coefficients.

$$K_c = \frac{[D]^d[E]^e}{[A]^a[B]^b}$$

Where: \(K_c\) = equilibrium constant

Haber Process Equilibrium: Specific equilibrium constant expression for \(N_2 + 3H_2 \rightleftharpoons 2NH_3\).

$$K_c = \frac{[NH_3]^2}{[N_2][H_2]^3}$$

Equilibrium Constant (Pressure): Ratio of product partial pressures to reactant partial pressures at equilibrium.

$$K_p = \frac{(P_D)^d(P_E)^e}{(P_A)^a(P_B)^b}$$

Where: \(K_p\) = equilibrium constant (pressure)

Pressure-Concentration Relation: Relates partial pressure of a gas to its molar concentration.

$$P_A = [A]RT$$

Where: \(P\) = pressure, \([A]\) = concentration, \(R\) = gas constant, \(T\) = temperature

Kp-Kc Relationship: Relates equilibrium constants based on pressure and concentration.

$$K_p = K_c(RT)^{\Delta n}$$

Where: \(\Delta n\) = change in moles of gas

Change in Moles: Difference between sum of gaseous product coefficients and gaseous reactant coefficients.

$$\Delta n = (d+e) - (a+b)$$

Reaction Quotient: Same expression as \(K_c\) but calculated with current concentrations, not necessarily at equilibrium.

$$Q_c = \frac{[D]^d[E]^e}{[A]^a[B]^b}$$

Where: \(Q_c\) = reaction quotient

Endothermic Reaction: Heat acts as a reactant; increasing temperature shifts equilibrium to products (right).

$$\text{Reactants} + \text{Heat} \rightleftharpoons \text{Products}$$

Exothermic Reaction: Heat acts as a product; increasing temperature shifts equilibrium to reactants (left).

$$\text{Reactants} \rightleftharpoons \text{Products} + \text{Heat}$$

Practice quiz

  1. For the Haber process, $N_2(g) + 3H_2(g) \rightleftharpoons 2NH_3(g)$, if the equilibrium constant $K_c$ is $0.50 \text{ M}^{-2}$ at $400 \text{ K}$, what is the value of $K_p$ at the same temperature? Use $R = 0.0821 \text{ L} \cdot \text{atm} \cdot \text{mol}^{-1} \cdot \text{K}^{-1}$.

    • $0.00046$
    • $16.42$
    • $0.50$
    • $0.000014$

    Answer: $0.00046$

  2. Consider the reaction $2SO_2(g) + O_2(g) \rightleftharpoons 2SO_3(g)$. If the volume of the reaction vessel is suddenly halved at constant temperature, what is the immediate effect on the values of $K_c$ and $K_p$?

    • Both $K_c$ and $K_p$ will increase.
    • Both $K_c$ and $K_p$ will decrease.
    • $K_c$ will increase, but $K_p$ will remain unchanged.
    • Both $K_c$ and $K_p$ will remain unchanged.

    Answer: Both $K_c$ and $K_p$ will remain unchanged.

  3. For the reaction $A(g) + B(g) \rightleftharpoons 2C(g)$, the equilibrium constant $K_c$ is $4.0$ at a specific temperature. If the initial concentrations are $[A] = 0.1 \text{ M}$, $[B] = 0.1 \text{ M}$, and $[C] = 0.3 \text{ M}$, in which direction will the reaction proceed to reach equilibrium?

    • The reaction will proceed to the right (towards products).
    • The reaction will proceed to the left (towards reactants).
    • The reaction is already at equilibrium.
    • The direction cannot be determined without knowing the temperature.

    Answer: The reaction will proceed to the left (towards reactants).

  4. For the reaction $2X(g) \rightleftharpoons Y(g) + Z(g)$, the equilibrium constant $K_p$ is $0.25$ at $300 \text{ K}$. What is the value of $K_c$ at this temperature? Use $R = 0.0821 \text{ L} \cdot \text{atm} \cdot \text{mol}^{-1} \cdot \text{K}^{-1}$.

    • $K_c = 0.25$
    • $K_c = 0.25 \times (0.0821 \times 300)$
    • $K_c = \frac{0.25}{(0.0821 \times 300)^2}$
    • $K_c = \frac{0.25}{(0.0821 \times 300)}$

    Answer: $K_c = 0.25$

  5. Consider the exothermic reaction $2NO_2(g) \rightleftharpoons N_2O_4(g) + \text{Heat}$. If the temperature of the system is increased, what will be the effect on the equilibrium constant $K_c$ and the position of equilibrium?

    • $K_c$ will increase, and the equilibrium will shift to the right.
    • $K_c$ will decrease, and the equilibrium will shift to the left.
    • $K_c$ will remain unchanged, but the equilibrium will shift to the left.
    • $K_c$ will decrease, and the equilibrium will shift to the right.

    Answer: $K_c$ will decrease, and the equilibrium will shift to the left.

  6. For the gaseous reaction $A(g) \rightleftharpoons 2B(g)$, derive the relationship between $K_p$ and $K_c$ using the ideal gas law relation $P_i = [i]RT$.

    • $K_p = K_c(RT)^{-1}$
    • $K_p = K_c(RT)$
    • $K_p = K_c(RT)^2$
    • $K_p = K_c$

    Answer: $K_p = K_c(RT)$

  7. For a reversible reaction at $298 \text{ K}$, the equilibrium constant $K_p$ is $1.0 \times 10^{-3}$ and $K_c$ is $4.0 \times 10^{-5}$. What is the value of $\Delta n$ (change in moles of gas) for this reaction? Use $R = 0.0821 \text{ L} \cdot \text{atm} \cdot \text{mol}^{-1} \cdot \text{K}^{-1}$.

    • $\Delta n = -1$
    • $\Delta n = 0$
    • $\Delta n = 1$
    • $\Delta n = 2$

    Answer: $\Delta n = 1$

  8. Consider the reaction $A(g) + B(g) \rightleftharpoons C(g)$. What is the effect of adding an inert gas, such as Argon, to this system at constant temperature?

    • Adding inert gas at constant volume shifts the equilibrium to the right, while adding it at constant pressure has no effect.
    • Adding inert gas at constant volume has no effect, while adding it at constant pressure shifts the equilibrium to the left.
    • Adding inert gas at constant volume shifts the equilibrium to the left, while adding it at constant pressure shifts it to the right.
    • Adding inert gas at constant volume has no effect, and adding it at constant pressure also has no effect.

    Answer: Adding inert gas at constant volume has no effect, while adding it at constant pressure shifts the equilibrium to the left.

  9. For the reaction $H_2(g) + I_2(g) \rightleftharpoons 2HI(g)$, the equilibrium constant $K_c$ is $64$ at $450 \text{ K}$. If $0.10 \text{ mol}$ of $H_2$ and $0.10 \text{ mol}$ of $I_2$ are initially placed in a $1.0 \text{ L}$ vessel, what is the equilibrium concentration of $HI$?

    • $0.02 \text{ M}$
    • $0.08 \text{ M}$
    • $0.16 \text{ M}$
    • $0.20 \text{ M}$

    Answer: $0.16 \text{ M}$

  10. Consider an endothermic reaction $A(g) \rightleftharpoons B(g) + C(g)$. If the temperature of the system is increased and the total pressure is simultaneously decreased, what will be the overall effect on the equilibrium position and the value of $K_c$?

    • Equilibrium shifts to the left, and $K_c$ decreases.
    • Equilibrium shifts to the right, and $K_c$ increases.
    • Equilibrium shifts to the right, but $K_c$ remains unchanged.
    • Equilibrium shifts to the left, and $K_c$ increases.

    Answer: Equilibrium shifts to the right, and $K_c$ increases.

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