For the decomposition reaction PCl₅(g) ⇌ PCl₃(g) + Cl₂(g), K_p = 381 at 600 K and K_c = 46.9 at 700 K. (b) If 1.25 g of PCl₅ is introduced into an evacuated 0.500-L flask at 700 K and the decomposition reaction is allowed to reach equilibrium, what percent of the PCl₅ will decompose and what will be the total pressure in the flask?

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Convert the mass of PCl_5 to moles using its molar mass.

Calculate the initial concentration of PCl_5 by dividing the moles by the volume of the flask.

Set up an ICE (Initial, Change, Equilibrium) table to express the changes in concentration for PCl_5, PCl_3, and Cl_2 as the reaction reaches equilibrium.

Use the equilibrium constant K_c to write the expression for the equilibrium concentrations in terms of the change variable (x).

Solve the equilibrium expression for x to find the equilibrium concentrations, then calculate the percent decomposition of PCl_5 and the total pressure using the ideal gas law.

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Key Concepts

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

Equilibrium Constant (K)

The equilibrium constant (K) quantifies the ratio of the concentrations of products to reactants at equilibrium for a given reaction at a specific temperature. For gaseous reactions, Kp is used, which is based on partial pressures, while Kc is based on molar concentrations. Understanding how to use these constants is crucial for predicting the extent of a reaction and calculating equilibrium concentrations.

Decomposition Reactions

Decomposition reactions involve the breakdown of a compound into simpler products. In the case of PCl5, it decomposes into PCl3 and Cl2. Recognizing the stoichiometry of the reaction is essential for determining how much of the reactant will convert to products and for calculating changes in concentration or pressure as the system reaches equilibrium.

Ideal Gas Law

The Ideal Gas Law (PV=nRT) relates the pressure, volume, temperature, and number of moles of a gas. It is fundamental for calculating the total pressure in a flask after a reaction has occurred. By understanding how to apply this law, one can determine the total pressure resulting from the decomposition of PCl5 and the formation of PCl3 and Cl2 in the given volume.

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Textbook Question

For the decomposition reaction PCl₅(g) ⇌ PCl₃(g) + Cl₂(g), K_p = 381 at 600 K and K_c = 46.9 at 700 K. (a) Is the reaction endothermic or exothermic? Explain. Does your answer agree with what you would predict based on bond energies?

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