Using data from Appendix C, write the equilibrium-constant expression and calculate the value of the equilibrium constant and the free-energy change for these reactions at 298 K: (b) 2 HBr(g) + Cl2(g) ⇌ 2 HCl(g) + Br2(g) (c) 2 SO2(g) + O2(g) ⇌ 2 SO3(g)

Verified step by step guidance

Step 1: Write the equilibrium-constant expression for each reaction. For a general reaction aA + bB ⇌ cC + dD, the equilibrium constant expression Kc is given by \( K_c = \frac{[C]^c[D]^d}{[A]^a[B]^b} \). Apply this to each reaction.

Step 2: For reaction (b) 2 HBr(g) + Cl2(g) ⇌ 2 HCl(g) + Br2(g), the equilibrium-constant expression is \( K_c = \frac{[HCl]^2[Br_2]}{[HBr]^2[Cl_2]} \).

Step 3: For reaction (c) 2 SO2(g) + O2(g) ⇌ 2 SO3(g), the equilibrium-constant expression is \( K_c = \frac{[SO_3]^2}{[SO_2]^2[O_2]} \).

Step 4: Use the standard Gibbs free energy change equation \( \Delta G^\circ = -RT \ln K \) to relate the equilibrium constant to the free energy change. Here, R is the gas constant (8.314 J/mol·K) and T is the temperature in Kelvin (298 K).

Step 5: Calculate \( \Delta G^\circ \) for each reaction using \( \Delta G^\circ = \sum \Delta G^\circ_{\text{products}} - \sum \Delta G^\circ_{\text{reactants}} \) with values from Appendix C, then solve for K using \( K = e^{-\Delta G^\circ / RT} \).

Key Concepts

Here are the essential concepts you must grasp in order to answer the question correctly.

Equilibrium Constant (K)

The equilibrium constant (K) is a numerical value that expresses the ratio of the concentrations of products to reactants at equilibrium for a given reaction at a specific temperature. It is derived from the balanced chemical equation and is calculated using the formula K = [products]^[coefficients] / [reactants]^[coefficients]. A large K value indicates that products are favored at equilibrium, while a small K value suggests that reactants are favored.

Gibbs Free Energy (ΔG)

Gibbs free energy (ΔG) is a thermodynamic quantity that indicates the spontaneity of a reaction at constant temperature and pressure. It is calculated using the equation ΔG = ΔG° + RT ln(Q), where ΔG° is the standard free energy change, R is the universal gas constant, T is the temperature in Kelvin, and Q is the reaction quotient. A negative ΔG indicates a spontaneous reaction, while a positive ΔG suggests non-spontaneity.

Reaction Quotient (Q)

The reaction quotient (Q) is a measure of the relative concentrations of products and reactants at any point in a reaction, not necessarily at equilibrium. It is calculated similarly to the equilibrium constant but uses the current concentrations instead of equilibrium concentrations. Comparing Q to K helps predict the direction in which a reaction will proceed to reach equilibrium: if Q < K, the reaction will shift to the right (toward products), and if Q > K, it will shift to the left (toward reactants).

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Reaction Quotient Q

Related Practice

Textbook Question

Isomers are molecules that have the same chemical formula but different arrangements of atoms, as shown here for two isomers of pentane, C₅H₁₂.

(b) Which isomer do you expect to have the higher standard molar entropy? Explain.

Textbook Question

The accompanying diagram shows how ΔH (red line) and TΔS (blue line) change with temperature for a hypothetical reaction.

(b) In what temperature range is this reaction spontaneous?

Textbook Question

Consider a reaction A₂(𝑔) + B₂(𝑔) ⇌ 2 AB(𝑔), atoms of A shown in red in the diagram and atoms of B shown in blue. (a) If 𝐾_𝑐 = 1, which box represents the system at equilibrium?

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Textbook Question

Consider a reaction A₂(𝑔) + B₂(𝑔) ⇌ 2 AB(𝑔), atoms of A shown in red in the diagram and atoms of B shown in blue. (b) If 𝐾_𝑐= 1, which box represents the system at 𝑄 < 𝐾_𝑐?

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