The reaction CO2(g) + C(s) ⇌ 2 CO(g) has Kp = 5.78 at 1200 K. a. Calculate the total pressure at equilibrium when 4.45 g of CO2 is introduced into a 10.0-L container and heated to 1200 K in the presence of 2.00 g of graphite. b. Repeat the calculation of part a in the presence of 0.50 g of graphite.

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Convert the mass of CO2 to moles using its molar mass: \( \text{moles of CO}_2 = \frac{4.45 \text{ g}}{44.01 \text{ g/mol}} \).

Set up an ICE (Initial, Change, Equilibrium) table to determine the changes in moles of each species at equilibrium. Initially, you have the moles of CO2 calculated and 0 moles of CO. Assume x moles of CO2 react to form 2x moles of CO.

Express the equilibrium partial pressures in terms of x and the initial moles. Use the ideal gas law \( P = \frac{nRT}{V} \) to find the partial pressures of CO2 and CO at equilibrium.

Write the expression for the equilibrium constant \( K_p = \frac{(P_{CO})^2}{P_{CO_2}} \) and substitute the expressions for the partial pressures in terms of x.

Solve the equation for x to find the equilibrium moles of each gas, then calculate the total pressure by summing the partial pressures of CO2 and CO.

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 reaction CO2(g) + C(s) ⇌ 2 CO(g), Kp = 5.78 indicates that at equilibrium, the pressure of CO is favored over CO2. Understanding Kp is essential for calculating the equilibrium state of the system.

Ideal Gas Law

The Ideal Gas Law, represented as PV = nRT, relates the pressure (P), volume (V), number of moles (n), the ideal gas constant (R), and temperature (T) of a gas. This law is crucial for determining the total pressure in the container after introducing CO2 and graphite, as it allows for the calculation of the number of moles of gas present and how they contribute to the overall pressure at equilibrium.

Stoichiometry of the Reaction

Stoichiometry involves the quantitative relationships between reactants and products in a chemical reaction. In this case, understanding the stoichiometry of the reaction CO2(g) + C(s) ⇌ 2 CO(g) is vital for determining how the introduction of CO2 and graphite affects the equilibrium concentrations of CO and CO2, which in turn influences the total pressure in the system.

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