Carbon monoxide and chlorine gas react to form phosgene: CO(g) + Cl₂(g) ⇌ COCl₂(g) K_p = 3.10 at 700 K If a reaction mixture initially contains 215 torr of CO and 245 torr of Cl₂, what is the mole fraction of COCl₂ when equilibrium is reached?

Verified step by step guidance

1. Identify the initial pressures of the reactants: CO = 215 torr and Cl2 = 245 torr.
2. Set up an ICE (Initial, Change, Equilibrium) table to track the changes in pressure for each species during the reaction.
3. Define the change in pressure for CO and Cl2 as -x, and for COCl2 as +x, since they react in a 1:1:1 ratio.
4. Write the expression for the equilibrium constant Kp in terms of partial pressures: Kp = (P_COCl2) / (P_CO * P_Cl2).
5. Substitute the equilibrium pressures from the ICE table into the Kp expression and solve for x, then calculate the mole fraction of COCl2 using its partial pressure at equilibrium.

Key Concepts

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 CO(g) + Cl2(g) ⇌ COCl2(g), Kp = 3.10 indicates that at equilibrium, the concentration of COCl2 is favored relative to the reactants. Understanding Kp is essential for calculating the equilibrium concentrations or partial pressures in a reaction.

Mole Fraction

Mole fraction is a way of expressing the concentration of a component in a mixture, defined as the number of moles of that component divided by the total number of moles of all components in the mixture. It is a dimensionless quantity that ranges from 0 to 1. In this context, calculating the mole fraction of COCl2 at equilibrium requires determining the total moles of gas present and the moles of COCl2 formed.

Reaction Stoichiometry

Reaction stoichiometry involves the quantitative relationships between reactants and products in a chemical reaction. For the given reaction, the stoichiometry indicates a 1:1:1 ratio among CO, Cl2, and COCl2. This relationship is crucial for determining how the initial amounts of reactants change as the reaction proceeds to equilibrium, allowing for the calculation of the final concentrations or partial pressures of each species.