Phosphorus pentachloride decomposes to phosphorus trichloride and chlorine at high temperatures according to the equation: PCl5(g) ⇌ PCl3(g) + Cl2(g). At 250 °C, 0.250 M PCl5 is added to the flask. If Kc = 1.80, what are the equilibrium concentrations of each gas? (LO 15.11) (a) [PCl5] = 0.028 M, [PCl3] = 0.222 M, and [Cl2] = 0.222 M (b) [PCl5] = 0.125 M, [PCl3] = 0.474 M, and [Cl2] = 0.474 M (c) [PCl5] = 1.80 M, [PCl3] = 1.80 M, and [Cl2] = 1.80 M (d) [PCl5] = 2.27 M, [PCl3] = 2.02 M, and [Cl2] = 2.02 M
Verified step by step guidance
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Step 1: Write the balanced chemical equation for the decomposition of phosphorus pentachloride: \( \text{PCl}_5(g) \rightleftharpoons \text{PCl}_3(g) + \text{Cl}_2(g) \).
Step 2: Set up an ICE (Initial, Change, Equilibrium) table to track the concentrations of each species. Initially, [PCl5] = 0.250 M, and [PCl3] = [Cl2] = 0 M.
Step 3: Define the change in concentration for the reaction. Let \( x \) be the amount of PCl5 that decomposes. Then, the changes are: \([-x]\) for PCl5, \([+x]\) for PCl3, and \([+x]\) for Cl2.
Step 4: Express the equilibrium concentrations in terms of \( x \): [PCl5] = 0.250 - x, [PCl3] = x, and [Cl2] = x.
Step 5: Use the equilibrium constant expression \( K_c = \frac{[\text{PCl}_3][\text{Cl}_2]}{[\text{PCl}_5]} \) and substitute the equilibrium concentrations to solve for \( x \). Set \( K_c = 1.80 \) and solve the equation to find the value of \( x \).
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 case, the decomposition of phosphorus pentachloride (PCl5) into phosphorus trichloride (PCl3) and chlorine (Cl2) reaches a state where the concentrations no longer change over time, despite the ongoing reactions.
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. For the reaction PCl5 ⇌ PCl3 + Cl2, Kc = [PCl3][Cl2]/[PCl5]. A Kc value greater than 1 indicates that products are favored at equilibrium, while a value less than 1 suggests that reactants are favored.
An ICE table is a tool used to organize the initial concentrations, the changes in concentrations as the reaction proceeds, and the equilibrium concentrations of reactants and products. By setting up an ICE table for the given reaction, one can systematically determine how the initial concentration of PCl5 affects the equilibrium concentrations of PCl3 and Cl2, allowing for the calculation of the final concentrations based on the equilibrium constant.
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