How to Calculate Kc from Kp
Chemical reactions reach a state of equilibrium when the rates of the forward and reverse reactions are equal. The equilibrium constant is a measure of the extent to which a chemical reaction proceeds to completion. It is represented by the letter Kc for concentration or Kp for pressure. The equilibrium constant is defined as the ratio of the product of the concentrations or pressures of the products raised to their stoichiometric coefficients to the product of the concentrations or pressures of the reactants raised to their stoichiometric coefficients.
Understand the Relationship between Kc and Kp
The relationship between Kc and Kp can be derived from the ideal gas law. At constant temperature and volume, the pressure of a gas is directly proportional to its concentration. Therefore, the equilibrium constant can be expressed in terms of concentration or pressure.
Write the Balanced Chemical Equation
The first step in calculating Kc from Kp is to write the balanced chemical equation for the reaction. Make sure the coefficients are in their lowest whole number ratio.
Determine the Stoichiometric Coefficients
The stoichiometric coefficients in the balanced chemical equation represent the mole ratios of the reactants and products. These coefficients are used to determine the equilibrium concentrations or pressures of the substances involved in the reaction.
Write the Equilibrium Expression
The equilibrium expression is the mathematical representation of the equilibrium constant. It is written by substituting the equilibrium concentrations or pressures of the reactants and products into the equilibrium constant expression.
Determine the Equilibrium Concentrations or Pressures
The equilibrium concentrations or pressures can be determined from the initial concentrations or pressures and the extent of the reaction. The extent of the reaction is given by the reaction quotient Qc or Qp, which is the expression obtained by substituting the initial concentrations or pressures into the equilibrium constant expression.
Calculate Kc or Kp
Once the equilibrium concentrations or pressures are known, they can be substituted into the equilibrium constant expression to calculate Kc or Kp. It is important to note that Kc and Kp have different units and are related by the ideal gas law.
Example Calculation
Consider the following equilibrium reaction: N2(g) + 3H2(g) ⇌ 2NH3(g). The equilibrium constant is Kp = 9.0 x 10^-3 atm^2. Suppose the partial pressures of N2, H2, and NH3 at equilibrium are 0.40 atm, 1.20 atm, and 0.30 atm, respectively. Calculate Kc for the reaction.
Solution
Step 1: Write the balanced chemical equation: N2(g) + 3H2(g) ⇌ 2NH3(g)
Step 2: Determine the stoichiometric coefficients: 1, 3, 2
Step 3: Write the equilibrium expression: Kp = (P(NH3))^2 / (P(N2) x P(H2))^3
Step 4: Determine the equilibrium concentrations: [N2] = 0.40 atm, [H2] = 1.20 atm, [NH3] = 0.30 atm
Step 5: Calculate Kc using the ideal gas law: Kc = Kp(RT)^(Δn), where R is the gas constant (0.0821 L atm/mol K), T is the temperature in Kelvin (assume 298 K), Δn is the difference in moles of gas products and reactants (2 - 1 - 3 = -2)
Kc = Kp(RT)^(-2) = 9.0 x 10^-3 (0.0821 x 298)^(-2) = 1.7 x 10^-5
Check Your Answer
To check your answer, substitute the equilibrium concentrations into the equilibrium constant expression and verify that the result is equal to the calculated Kc.
Practice Problems
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Consider the following equilibrium reaction: 2NO(g) + O2(g) ⇌ 2NO2(g). The equilibrium constant is Kc = 4.3 x 10^-3 M^-1. Suppose the initial concentrations of NO, O2, and NO2 are 0.10 M, 0.20 M, and 0.30 M, respectively. Calculate the equilibrium concentrations of all species and the equilibrium constant.
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Consider the following equilibrium reaction: 2SO2(g) + O2(g) ⇌ 2SO3(g). The equilibrium constant is Kp = 4.6 x 10^2 atm^-1. Suppose the partial pressures of SO2, O2, and SO3 at equilibrium are 0.20 atm, 0.10 atm, and 0.30 atm, respectively. Calculate the equilibrium partial pressures of all species and the equilibrium constant.
