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Ch.15 - Chemical Equilibrium
All textbooksBrown 14th EditionCh.15 - Chemical EquilibriumProblem 34
Chapter 15, Problem 34

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. (b) Does the equilibrium favor reactants or products? (c) Calculate Kc for this reaction at 450 K.

Verified step by step guidance
1
To determine whether the equilibrium favors reactants or products, compare the partial pressures of the reactants (PCl3 and Cl2) and the product (PCl5). Since P(PCl5) = 1.30 atm is significantly higher than P(PCl3) = 0.124 atm and P(Cl2) = 0.157 atm, the equilibrium favors the products.
To calculate the equilibrium constant Kc, first understand that Kc is related to the equilibrium constant Kp through the equation: Kc=Kp/(RT)Δn, where Δn is the change in moles of gas.
Calculate Kp using the expression: Kp=(P(PCl5))/(P(PCl3)×P(Cl2)). Substitute the given partial pressures into this equation.
Determine Δn, the change in moles of gas, by subtracting the sum of moles of reactants from the sum of moles of products. For the reaction PCl3(g) + Cl2(g) ↔ PCl5(g), Δn = 1 - (1 + 1) = -1.
Finally, use the relationship between Kp and Kc: Kc=Kp×(RT)Δn, where R is the ideal gas constant (0.0821 L atm/mol K) and T is the temperature in Kelvin (450 K). Substitute the values to find Kc.

Key Concepts

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

Chemical Equilibrium

Chemical equilibrium occurs when the rates of the forward and reverse reactions are equal, resulting in constant concentrations of reactants and products. In this state, the system is dynamic, meaning that reactions continue to occur, but there is no net change in the concentrations. Understanding equilibrium is crucial for analyzing how changes in conditions (like concentration or temperature) affect the position of the equilibrium.
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Partial Pressure

Partial pressure is the pressure exerted by a single component of a gas mixture. It is a key concept in gas law calculations and is used to determine the behavior of gases in reactions. In the context of equilibrium, the partial pressures of the reactants and products can be used to assess the extent of the reaction and to calculate the equilibrium constant (Kc).
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Equilibrium Constant (Kc)

The equilibrium constant (Kc) is a numerical value that expresses the ratio of the concentrations of products to reactants at equilibrium, each raised to the power of their coefficients in the balanced equation. It provides insight into the favorability of a reaction; a large Kc indicates that products are favored, while a small Kc suggests that reactants are favored. Calculating Kc involves using the equilibrium concentrations or partial pressures of the gases involved in the reaction.
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Related Practice
Textbook Question

The equilibrium 2 NO(𝑔) + Cl2(𝑔) ⇌ 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) ⇌ 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

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 𝑃PCl3 = 0.124 atm, 𝑃Cl2 = 0.157 atm, and 𝑃PCl5 = 1.30 atm. (a) What is the value of 𝐾𝑝 at this temperature?