Consider the reaction: SO₂Cl₂(g) ⇌ SO₂(g) + Cl₂(g) K_p = 2.91⨉10³ at 298 K In a reaction at equilibrium, the partial pressure of SO₂ is 137 torr and that of Cl₂ is 285 torr. What is the partial pressure of SO₂Cl₂in this mixture?

검증된 단계별 안내

Identify the equilibrium expression for the reaction. For the given reaction, SO2Cl2(g) ⇌ SO2(g) + Cl2(g), the equilibrium constant expression (Kp) is given by Kp = \( \frac{P_{SO2} \times P_{Cl2}}{P_{SO2Cl2}} \).

Substitute the known values of the partial pressures of SO2 and Cl2 into the equilibrium expression. Given that P_{SO2} = 137 torr and P_{Cl2} = 285 torr, the expression becomes Kp = \( \frac{137 \times 285}{P_{SO2Cl2}} \).

Rearrange the equation to solve for the unknown partial pressure of SO2Cl2. This can be done by isolating P_{SO2Cl2} on one side of the equation: P_{SO2Cl2} = \( \frac{137 \times 285}{Kp} \).

Substitute the value of Kp into the equation. Given that Kp = 2.91 \(\times\) 10^3, the equation to find P_{SO2Cl2} becomes P_{SO2Cl2} = \( \frac{137 \times 285}{2.91 \times 10^3} \).

Calculate the value of P_{SO2Cl2} using the values provided and the rearranged equation to find the partial pressure of SO2Cl2 in the mixture 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 numerical value that expresses the ratio of the partial pressures of the products to the reactants at equilibrium for a given reaction at a specific temperature. For the reaction SO2Cl2(g) ⇌ SO2(g) + Cl2(g), Kp is calculated using the formula Kp = (P_SO2 * P_Cl2) / P_SO2Cl2, where P represents the partial pressures of the gases involved.

Partial Pressure

Partial pressure is the pressure exerted by a single component of a gas mixture. It can be determined using Dalton's Law, which states that the total pressure of a gas mixture is equal to the sum of the partial pressures of its individual components. In this case, the partial pressures of SO2 and Cl2 are given, and the partial pressure of SO2Cl2 can be derived from the equilibrium constant.

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 the context of this reaction, if the concentrations or pressures of the reactants or products are altered, the system will shift in a direction that minimizes the effect of that change, which is essential for understanding how equilibrium is established and maintained.

Consider the reaction: SO2Cl2(g) ⇌ SO2(g) + Cl2(g) Kp = 2.91⨉103 at 298 K In a reaction at equilibrium, the partial pressure of SO2 is 137 torr and that of Cl2 is 285 torr. What is the partial pressure of SO2Cl2in this mixture?