At 700 K, the equilibrium constant for the reaction CCl₄(𝑔) ⇌ C(𝑠) + 2 Cl₂(𝑔) is 𝐾_𝑝= 0.76. A flask is charged with 2.00 atm of CCl₄, which then reaches equilibrium at 700 K. (a) What fraction of the CCl₄ is converted into C and Cl₂?

검증된 단계별 안내

Start by writing the balanced chemical equation for the reaction: CCl4(g) ⇌ C(s) + 2 Cl2(g). Note that C(s) is a solid and does not appear in the expression for the equilibrium constant Kp.

Express the equilibrium constant Kp in terms of the partial pressures of the gases involved. Since Kp = 0.76, we have: Kp = (P_Cl2)^2 / P_CCl4.

Define the change in pressure for the reaction. Let x be the change in pressure of CCl4 that is converted to products. At equilibrium, the pressure of CCl4 will be (2.00 - x) atm, and the pressure of Cl2 will be 2x atm.

Substitute the equilibrium pressures into the expression for Kp: 0.76 = (2x)^2 / (2.00 - x).

Solve the equation for x to find the change in pressure. The fraction of CCl4 converted is x / 2.00. This will give you the fraction of the initial CCl4 that is converted to C and Cl2 at equilibrium.

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주요 개념

질문에 올바르게 답하기 위해 반드시 이해해야 하는 핵심 개념들은 다음과 같습니다.

Equilibrium Constant (Kp)

The equilibrium constant (Kp) is a dimensionless value that expresses the ratio of the concentrations of products to reactants at equilibrium for a given reaction at a specific temperature. For gaseous reactions, Kp is calculated using partial pressures. In this case, Kp = 0.76 indicates the relationship between the partial pressures of CCl4, C, and Cl2 when the system reaches 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. This principle helps predict how changes in concentration, pressure, or temperature will affect the position of equilibrium, which is essential for understanding how the reaction will shift when CCl4 is introduced into the flask.

Stoichiometry of the Reaction

Stoichiometry involves the quantitative relationships between the reactants and products in a chemical reaction. For the reaction CCl4(g) ⇌ C(s) + 2 Cl2(g), the stoichiometry indicates that one mole of CCl4 produces one mole of solid carbon and two moles of chlorine gas. Understanding stoichiometry is crucial for calculating the fraction of CCl4 converted to products at equilibrium based on the initial concentration and the equilibrium constant.

At 700 K, the equilibrium constant for the reaction CCl4(𝑔) ⇌ C(𝑠) + 2 Cl2(𝑔) is 𝐾𝑝 = 0.76. A flask is charged with 2.00 atm of CCl4, which then reaches equilibrium at 700 K. (a) What fraction of the CCl4 is converted into C and Cl2?