For the reaction 2 A(g) ⇌ B(g) + 2 C(g), a reaction vessel initially contains only A at a pressure of PA = 255 mmHg. At equilibrium, PA = 55 mmHg. Calculate the value of Kp. (Assume no changes in volume or temperature.)

Name: Chemistry: A Molecular Approach
Author: Tro
ISBN: 9780134112831

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Identify the initial and equilibrium pressures of A. Initially, the pressure of A is 255 mmHg, and at equilibrium, it is 55 mmHg.

Determine the change in pressure of A. The change in pressure, \( \Delta P_A \), is the initial pressure minus the equilibrium pressure: \( \Delta P_A = 255 \text{ mmHg} - 55 \text{ mmHg} \).

Use the stoichiometry of the reaction to find the changes in pressure for B and C. Since 2 moles of A produce 1 mole of B and 2 moles of C, the change in pressure for B is \( \Delta P_B = \frac{1}{2} \Delta P_A \) and for C is \( \Delta P_C = \Delta P_A \).

Calculate the equilibrium pressures of B and C. Since B and C are initially absent, their equilibrium pressures are equal to their changes in pressure: \( P_B = \Delta P_B \) and \( P_C = \Delta P_C \).

Write the expression for \( K_p \) using the equilibrium pressures: \( K_p = \frac{P_B \cdot P_C^2}{P_A^2} \), and substitute the equilibrium pressures to find \( K_p \).

주요 개념

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Equilibrium Constant (Kp)

The equilibrium constant (Kp) is a numerical value that expresses the ratio of the partial pressures of the products to the reactants at equilibrium for a given reaction. It is calculated using the formula Kp = (P_B * P_C^2) / (P_A^2) for the reaction 2 A(g) ⇌ B(g) + 2 C(g). A higher Kp value indicates a greater concentration of products at equilibrium compared to reactants.

Partial Pressure

Partial pressure is the pressure exerted by a single component of a gas mixture. In the context of the reaction, the partial pressures of A, B, and C at equilibrium are crucial for calculating Kp. The total pressure in the vessel is the sum of the partial pressures of all gases present, and changes in these pressures reflect the progress of the reaction towards equilibrium.

Le Chatelier's Principle

Le Chatelier's Principle states that if a dynamic equilibrium is disturbed by changing the conditions, the system will adjust to counteract the change and restore a new equilibrium. In this reaction, the decrease in the partial pressure of A indicates that the reaction is shifting towards the products (B and C) to reach a new equilibrium state, which is essential for understanding how Kp is affected by changes in concentration or pressure.