Hard Reaction Quotient (Q) Practice Questions

Concept Explanation

The reaction quotient (Q) is a mathematical expression that describes the relative amounts of products and reactants present in a reaction at a given moment in time, regardless of whether the system has reached chemical equilibrium. By comparing the numerical value of Q to the equilibrium constant (K), chemists can predict the direction in which a net reaction will proceed to achieve stability. If Q < K, the reaction shifts toward the products (right); if Q > K, the reaction shifts toward the reactants (left); and if Q = K, the system is at equilibrium. This concept is a fundamental application of Le Chatelier's Principle, which governs how systems respond to changes in concentration, pressure, or temperature.

Calculating Q involves the same formula as the equilibrium constant: the product of the concentrations (or partial pressures) of the products raised to their stoichiometric coefficients, divided by the product of the concentrations of the reactants. For a generic reaction \(aA + bB \rightleftharpoons cC + dD\), the expression is:

\(Q_c = \frac{[C]^c [D]^d}{[A]^a [B]^b}\)

In advanced chemistry, understanding the reaction quotient is essential for mastering topics like hard Ka and Kb calculations and complex solubility equilibria. Unlike K, which is constant for a specific temperature, Q changes as the reaction progresses. It is a snapshot of the current state of a chemical system, providing a quantitative basis for predicting spontaneity when combined with thermodynamic data like Gibbs free energy.

Solved Examples

1. Example 1: Predicting Reaction Direction
   For the reaction \(N_2(g) + 3H_2(g) \rightleftharpoons 2NH_3(g)\), the equilibrium constant \(K_c\) is 0.50 at 400 K. A 2.0 L flask contains 0.10 mol \(N_2\), 0.30 mol \(H_2\), and 0.20 mol \(NH_3\). Determine the value of Q and the direction of the reaction.

   1. Calculate molar concentrations: \([N_2] = 0.05 M\), \([H_2] = 0.15 M\), \([NH_3] = 0.10 M\).

   2. Set up the Q expression: \(Q_c = \frac{[NH_3]^2}{[N_2][H_2]^3}\).

   3. Substitute values: \(Q_c = \frac{(0.10)^2}{(0.05)(0.15)^3} = \frac{0.01}{0.00016875} \approx 59.26\).

   4. Compare Q to K: Since \(Q (59.26) > K (0.50)\), the reaction will shift to the left (toward reactants).

2. Example 2: Partial Pressures and Qp
   At a specific temperature, \(K_p = 25\) for \(2NO_2(g) \rightleftharpoons N_2O_4(g)\). If the partial pressures are \(P_{NO_2} = 0.5 \text{ atm}\) and \(P_{N_2O_4} = 5.0 \text{ atm}\), is the system at equilibrium?

   1. Set up the \(Q_p\) expression: \(Q_p = \frac{P_{N_2O_4}}{(P_{NO_2})^2}\).

   2. Substitute values: \(Q_p = \frac{5.0}{(0.5)^2} = \frac{5.0}{0.25} = 20\).

   3. Compare: Since \(Q_p (20) < K_p (25)\), the system is not at equilibrium and will shift right to produce more \(N_2O_4\).

3. Example 3: Complex Stoichiometry
   Consider \(2A(g) + B(s) \rightleftharpoons 3C(g)\) with \(K_c = 1.2 \times 10^{-2}\). If \([A] = 0.5 M\) and \([C] = 0.1 M\), find Q.

   1. Identify phases: Solids like \(B(s)\) are excluded from the Q expression.

   2. Set up expression: \(Q_c = \frac{[C]^3}{[A]^2}\).

   3. Substitute values: \(Q_c = \frac{(0.1)^3}{(0.5)^2} = \frac{0.001}{0.25} = 0.004\).

   4. Compare: \(Q (0.004) < K (0.012)\), so the reaction shifts right.

Practice Questions

1. The reaction \(H_2(g) + I_2(g) \rightleftharpoons 2HI(g)\) has \(K_c = 54.3\) at 430°C. If a 5.0 L vessel contains 0.50 mol \(H_2\), 0.50 mol \(I_2\), and 4.0 mol \(HI\), calculate Q and predict the shift.

2. For the decomposition of phosphorus pentachloride, \(PCl_5(g) \rightleftharpoons PCl_3(g) + Cl_2(g)\), \(K_c = 0.042\) at 250°C. In a sample, \([PCl_5] = 0.10 M\), \([PCl_3] = 0.05 M\), and \([Cl_2] = 0.05 M\). Determine if the system is at equilibrium.

3. At 1000 K, the reaction \(2SO_2(g) + O_2(g) \rightleftharpoons 2SO_3(g)\) has \(K_p = 3.4\). If the partial pressures are \(P_{SO_2} = 0.45 \text{ atm}\), \(P_{O_2} = 0.20 \text{ atm}\), and \(P_{SO_3} = 0.60 \text{ atm}\), calculate \(Q_p\).

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4. In the reaction \(CO(g) + H_2O(g) \rightleftharpoons CO_2(g) + H_2(g)\), \(K_c = 4.0\) at 500 K. If the concentrations are all \(0.20 M\), what is the value of Q and which way does the reaction shift?

5. A mixture of 2.0 mol \(N_2O_4\) and 4.0 mol \(NO_2\) is placed in a 10.0 L container at 373 K. If \(K_c = 0.36\) for \(N_2O_4(g) \rightleftharpoons 2NO_2(g)\), calculate Q and determine the direction of net change.

6. For the heterogeneous reaction \(CaCO_3(s) \rightleftharpoons CaO(s) + CO_2(g)\), \(K_p = 1.16\) at 800°C. If the partial pressure of \(CO_2\) in a kiln is 0.50 atm, calculate Q and predict the behavior of the solid calcium carbonate.

7. The synthesis of methanol \(CO(g) + 2H_2(g) \rightleftharpoons CH_3OH(g)\) has \(K_c = 10.5\) at a high temperature. Concentrations are \([CO] = 0.2 M\), \([H_2] = 0.1 M\), and \([CH_3OH] = 0.05 M\). Calculate Q.

8. In the reaction \(2NO(g) + Cl_2(g) \rightleftharpoons 2NOCl(g)\), \(K_c = 6.5 \times 10^4\). If \([NO] = 1.0 \times 10^{-2} M\), \([Cl_2] = 2.0 \times 10^{-2} M\), and \([NOCl] = 5.0 M\), calculate Q and predict the shift.

Answers & Explanations

1. Q = 64. \([H_2] = 0.1, [I_2] = 0.1, [HI] = 0.8\). \(Q = (0.8)^2 / (0.1 \times 0.1) = 0.64 / 0.01 = 64\). Since \(Q (64) > K (54.3)\), reaction shifts left.

2. Q = 0.025. \(Q = (0.05 \times 0.05) / 0.10 = 0.0025 / 0.10 = 0.025\). Since \(Q (0.025) < K (0.042)\), the system is not at equilibrium; it shifts right.

3. Qp = 8.89. \(Q_p = (0.60)^2 / (0.45^2 \times 0.20) = 0.36 / (0.2025 \times 0.20) = 0.36 / 0.0405 = 8.888\).

4. Q = 1.0. \(Q = (0.2 \times 0.2) / (0.2 \times 0.2) = 1.0\). Since \(Q (1.0) < K (4.0)\), the reaction shifts right.

5. Q = 0.80. \([N_2O_4] = 0.2 M\), \([NO_2] = 0.4 M\). \(Q = (0.4)^2 / 0.2 = 0.16 / 0.2 = 0.80\). Since \(Q (0.80) > K (0.36)\), the reaction shifts left.

6. Q = 0.50. For this reaction, \(Q_p = P_{CO_2}\). Since \(Q (0.50) < K (1.16)\), the reaction shifts right, meaning more \(CaCO_3\) will decompose.

7. Q = 25. \(Q = 0.05 / (0.2 \times 0.1^2) = 0.05 / (0.2 \times 0.01) = 0.05 / 0.002 = 25\). Reaction shifts left as \(Q > K\).

8. Q = 1.25 x 10^7. \(Q = (5.0)^2 / ((10^{-2})^2 \times 2 \times 10^{-2}) = 25 / (10^{-4} \times 2 \times 10^{-2}) = 25 / (2 \times 10^{-6}) = 1.25 \times 10^7\). Since \(Q > K\), it shifts left.

Quick Quiz

Frequently Asked Questions

What is the main difference between Q and K?

The equilibrium constant K is a fixed value at a specific temperature representing the system at equilibrium, while the reaction quotient Q describes the system at any point in time. Comparing the two allows chemists to determine which direction the reaction must move to reach equilibrium.

Can Q be a negative value?

No, the reaction quotient Q cannot be negative because it is calculated using concentrations or partial pressures, which are always zero or positive. A value of Q = 0 indicates that no products are currently present in the system.

How does temperature affect the value of Q?

Temperature does not directly change the value of Q for a specific set of concentrations, but it does change the value of K. This shift in K is what determines the new equilibrium position, as explained in studies of hard enthalpy change practice questions and thermodynamics.

Why are solids excluded from the Q expression?

The activity of a pure solid or liquid is defined as 1 because its concentration (density divided by molar mass) remains constant regardless of how much of the substance is present. Therefore, they do not affect the ratio in the reaction quotient expression.

How is Q used in industrial chemistry?

In industrial processes like the Haber process, engineers monitor concentrations to ensure Q remains lower than K, forcing the reaction to continuously produce desired products. This often involves removing products as they form, a practical application of maintaining a specific Q/K ratio.

Can Q be used for reactions that are not in the gas or aqueous phase?

Q is applicable to any reversible chemical reaction where activities can be defined, though it is most commonly used for gaseous and aqueous systems. For more complex electrochemical systems, Q is used in the Nernst equation to calculate cell potential under non-standard conditions.

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