Relationship between Kc and Kp - UNSOLVED PRACTICE SET

Q7. Derive the relationship between Kp and Kc for a general gaseous reaction. Define Δn clearly.

Q8. For the reaction H₂(g) + Cl₂(g) ⇌ 2HCl(g), show that Kp = Kc at all temperatures. Explain why.

Q9. For the reaction 2NH₃(g) ⇌ N₂(g) + 3H₂(g), predict whether Kp will be greater than, less than, or equal to Kc. Justify your answer.

Q10. At 298 K, Kc for a reaction is 2.5 × 10⁻³. If Δn = –2, calculate Kp for this reaction. (R = 0.0821 L·atm/K·mol)

Q11. Explain why Kp and Kc have different units for reactions where Δn ≠ 0, but the same numerical value when Δn = 0.

Q12. A reaction has Kc = 0.50 at 400 K and Δn = +1. Without calculating, predict whether Kp will be greater or smaller than Kc. Explain your reasoning.

Q13. (a) Derive the general relationship Kp = Kc(RT)^Δn starting from the definitions of Kp and Kc.

(b) For each of the following reactions, calculate Δn and predict whether Kp > Kc, Kp < Kc, or Kp = Kc:

(i) 2SO₂(g) + O₂(g) ⇌ 2SO₃(g)

(ii) H₂(g) + CO₂(g) ⇌ H₂O(g) + CO(g)

(iii) N₂O₄(g) ⇌ 2NO₂(g)

(c) At what temperature will Kp = Kc for a reaction where Δn = –1?

Q14. (a) Explain the physical significance of the relationship Kp = Kc(RT)^Δn. What does it tell us about the effect of temperature on the ratio Kp/Kc?

(b) For the reaction: CO(g) + 2H₂(g) ⇌ CH₃OH(g), Kp = 2.25 × 10⁻⁴ at 500 K. Calculate Kc at this temperature.

(c) If the temperature is increased to 600 K, will the ratio Kp/Kc increase, decrease, or remain the same? Explain.

Q15. (a) For the decomposition of calcium carbonate: CaCO₃(s) ⇌ CaO(s) + CO₂(g), derive the relationship between Kp and Kc.

(b) What is the value of Kp for this reaction in terms of the partial pressure of CO₂?

(c) A student argues that since solids are not included in Kc, Kp must also not include any pressure terms for solids. Is the student correct? Explain the correct expression for Kp.

Q16. For the following reactions at 500 K, calculate Kp from the given Kc values:

(a) N₂(g) + O₂(g) ⇌ 2NO(g); Kc = 4.0 × 10⁻⁴

(b) 2SO₂(g) + O₂(g) ⇌ 2SO₃(g); Kc = 2.5 × 10²

(c) N₂O₄(g) ⇌ 2NO₂(g); Kc = 1.5 × 10⁻²

(R = 0.0821 L·atm/K·mol)

For each reaction, state whether Kp > Kc, Kp < Kc, or Kp = Kc, and explain the physical reason behind your observation.

Q16. For the following reactions at 500 K, calculate Kp from the given Kc values:

(a) N₂(g) + O₂(g) ⇌ 2NO(g); Kc = 4.0 × 10⁻⁴

(b) 2SO₂(g) + O₂(g) ⇌ 2SO₃(g); Kc = 2.5 × 10²

(c) N₂O₄(g) ⇌ 2NO₂(g); Kc = 1.5 × 10⁻²

(R = 0.0821 L·atm/K·mol)

For each reaction, state whether Kp > Kc, Kp < Kc, or Kp = Kc, and explain the physical reason behind your observation.

Q18. In the Indian fertiliser industry, the production of urea requires ammonia, which is produced by the Haber process:

N₂(g) + 3H₂(g) ⇌ 2NH₃(g)

(a) Calculate Δn for this reaction.

(b) At 450°C (723 K), Kc = 0.040. Calculate Kp at this temperature.

(c) An engineer wants to compare the equilibrium composition calculated using Kc versus Kp. If the total pressure in the reactor is 200 atm, explain which constant (Kc or Kp) would be more convenient to use for calculating equilibrium partial pressures, and why.

(d) At a higher temperature of 800 K, Kp = 2.5 × 10⁻⁷. Calculate Kc at 800 K and comment on the effect of temperature on the equilibrium position.