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Ch.15 - Chemical Equilibrium
All textbooksBrown 15th EditionCh.15 - Chemical EquilibriumProblem 34a
Chapter 15, Problem 34a

Phosphorus trichloride gas and chlorine gas react to form phosphorus pentachloride gas: PCl3(𝑔) + Cl2(𝑔) β‡Œ 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 𝑃PCl3 = 0.124 atm, 𝑃Cl2 = 0.157 atm, and 𝑃PCl5 = 1.30 atm. (a) What is the value of 𝐾𝑝 at this temperature?

Verified step by step guidance
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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, Kp, for the reaction at this temperature.
Step 2: Write down the expression for Kp. For the reaction aA + bB β‡Œ cC + dD, the equilibrium constant expression is Kp = (PCc * PDd) / (PAa * PBb), where PX is the partial pressure of X.
Step 3: Substitute the given values into the Kp expression. For the reaction PCl3(𝑔) + Cl2(𝑔) β‡Œ PCl5(𝑔), the Kp expression is Kp = PPCl5 / (PPCl3 * PCl2).
Step 4: Substitute the given partial pressures into the Kp expression. PPCl5 = 1.30 atm, PPCl3 = 0.124 atm, and PCl2 = 0.157 atm.
Step 5: Calculate the value of Kp by dividing the partial pressure of PCl5 by the product of the partial pressures of PCl3 and Cl2.

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Key Concepts

Here are the essential concepts you must grasp in order to answer the question correctly.

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) β‡Œ 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.
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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.
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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.
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Related Practice
Textbook Question

The equilibrium 2 NO(𝑔) + Cl2(𝑔) β‡Œ 2 NOCl(𝑔) is established at 500.0 K. An equilibrium mixture of the three gases has partial pressures of 0.095 atm, 0.171 atm, and 0.28 atm for NO, Cl2, and NOCl, respectively. (a) Calculate 𝐾𝑝 for this reaction at 500.0 K.

Textbook Question

The equilibrium 2 NO(𝑔) + Cl2(𝑔) β‡Œ 2 NOCl(𝑔) is established at 500.0 K. An equilibrium mixture of the three gases has partial pressures of 0.095 atm, 0.171 atm, and 0.28 atm for NO, Cl2, and NOCl, respectively. (b) If the vessel has a volume of 5.00 L, calculate Kc at this temperature.

Textbook Question

A mixture of 0.2000 mol of CO2, 0.1000 mol of H2, and 0.1600 mol of H2O is placed in a 2.000-L vessel. The following equilibrium is established at 500 K: CO2(g) + H2(g) β‡Œ CO(g) + H2O(g) (d) Calculate Kc for the reaction.

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