Phosphorus trichloride gas and chlorine gas react to form phosphorus pentachloride gas: PCl₃(𝑔) + Cl₂(𝑔) ⇌ PCl₅(𝑔). A 7.5-L gas vessel is charged with a mixture of PCl₃(𝑔) and Cl₂(𝑔), which is allowed to equilibrate at 450 K. At equilibrium the partial pressures of the three gases are 𝑃_PCl3= 0.124 atm, 𝑃_Cl2= 0.157 atm, and 𝑃_PCl5= 1.30 atm. (a) What is the value of 𝐾_𝑝 at this temperature?

검증된 단계별 안내

Step 1: Understand the problem. We are given the equilibrium partial pressures of PCl₃, Cl₂, and PCl₅. We are asked to find the equilibrium constant, K_p, for the reaction at this temperature.

Step 2: Write down the expression for K_p. For the reaction aA + bB ⇌ cC + dD, the equilibrium constant expression is K_p = (P_C^c * P_D^d) / (P_A^a * P_B^b), where P_X is the partial pressure of X.

Step 3: Substitute the given values into the K_p expression. For the reaction PCl₃(𝑔) + Cl₂(𝑔) ⇌ PCl₅(𝑔), the K_p expression is K_p = P_PCl5 / (P_PCl3 * P_Cl2).

Step 4: Substitute the given partial pressures into the K_p expression. P_PCl5 = 1.30 atm, P_PCl3 = 0.124 atm, and P_Cl2 = 0.157 atm.

Step 5: Calculate the value of K_p by dividing the partial pressure of PCl₅ by the product of the partial pressures of PCl₃ and Cl₂.

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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 products to the partial pressures of reactants at equilibrium for a given reaction at a specific temperature. For the reaction PCl3(g) + Cl2(g) ⇌ PCl5(g), Kp is calculated using the formula Kp = (P_PCl5) / (P_PCl3 * P_Cl2), 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. According to Dalton's Law of Partial Pressures, the total pressure of a gas mixture is the sum of the partial pressures of each individual gas. In this question, the partial pressures of PCl3, Cl2, and PCl5 are given, which are essential for calculating the equilibrium constant Kp.

Le Chatelier's Principle

Le Chatelier's Principle states that if a dynamic equilibrium is disturbed by changing the conditions, the system will adjust itself to counteract the change and restore a new equilibrium. This principle helps in understanding how changes in concentration, pressure, or temperature can affect the position of equilibrium in reactions like the one involving PCl3, Cl2, and PCl5.