At 70 K, CCl4 decomposes to carbon and chlorine. The Kp for the decomposition is 0.76. Find the starting pressure of CCl4 at this temperature that will produce a total pressure of 1.0 atm at equilibrium.

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Write the balanced chemical equation for the decomposition of CCl4. CCl4(g) ightarrow C(s) + 2 Cl2(g).

Define the initial pressure of CCl4 as P0 and the change in pressure due to decomposition as x. At equilibrium, the pressure of CCl4 will be P0 - x and the pressure of Cl2 will be 2x.

Set up the expression for Kp using the equilibrium partial pressures. Kp = (P_{Cl2})^2 / P_{CCl4} = (2x)^2 / (P0 - x).

Substitute the given Kp value and solve for x in terms of P0. 0.76 = (2x)^2 / (P0 - x).

Use the total pressure at equilibrium (1.0 atm) to find a relationship between P0 and x. Total pressure = P_{CCl4} + P_{Cl2} = (P0 - x) + 2x = P0 + x = 1.0 atm.

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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 the products to the reactants at equilibrium for a given reaction at a specific temperature. For the decomposition of CCl4, Kp = 0.76 indicates the relationship between the pressures of carbon and chlorine produced and the remaining CCl4 at equilibrium.

Decomposition Reaction

A decomposition reaction is a type of chemical reaction where a single compound breaks down into two or more simpler products. In this case, CCl4 decomposes into carbon and chlorine gas, which affects the total pressure in the system as the reaction progresses towards equilibrium.

Total Pressure and Partial Pressure

Total pressure in a gas mixture is the sum of the partial pressures of all individual gases present. At equilibrium, the total pressure of 1.0 atm is the result of the partial pressures of CCl4, carbon, and chlorine. Understanding how to relate these pressures using Kp is essential for calculating the initial pressure of CCl4 needed to achieve the desired total pressure.

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