14.4
Calculating the Equilibrium Constant
The equilibrium constant for a reaction is calculated from the equilibrium concentrations (or pressures) of its reactants and products. If these conce…
The equilibrium constant, Kc, can be determined by substituting the corresponding values into the equilibrium constant expression if the concentrations of all the reactants and products at equilibrium are known.
A gaseous mixture of sulfur dioxide and oxygen at 530 °C is allowed to react according to the reaction shown. At equilibrium, the mixture contains 0.10 molar of sulfur dioxide, 0.15 molar of oxygen, and 10.88 molar of sulfur trioxide.
By substituting the values into the equilibrium expression, the Kc equals 7.9 × 104.
The Kc can also be calculated as long as the initial concentration of all of the components and the equilibrium concentration of at least one compound is known.
The unknown equilibrium concentrations can then be calculated using the reaction stoichiometry. An ICE table is used to organize the information for the initial, change, and equilibrium concentrations of the reaction.
When a reaction mixture containing 0.11 molar nitrogen and 0.36 molar hydrogen is allowed to reach equilibrium at 500 °C, it produces 0.020 molar ammonia at equilibrium. To calculate the Kc, the equilibrium concentrations of the nitrogen and hydrogen need to be determined.
The stoichiometry of the reaction shows that 1 mole of nitrogen gas and 3 moles of hydrogen gas are required to produce 2 moles of ammonia gas.
The change, x, when multiplied by the coefficients of the reactants and products, denotes the concentration of the reactants consumed and the concentration of the product produced to reach equilibrium.
Since 2x equals 0.020, x equals 0.010. The equilibrium concentration of nitrogen and hydrogen can then be determined by subtracting the respective concentration change from their initial concentration which equals 0.10 and 0.33 molar, respectively.
Substituting equilibrium concentrations in the Kc expression, the Kc equals 0.11.
The Kp for reactions involving gases can be calculated using an ICE table and the equilibrium expression written with partial pressures.
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Q1: How do you calculate the equilibrium constant if all equilibrium concentrations are known?
Substitute the equilibrium concentrations of all reactants and products directly into the equilibrium constant expression, Kc. For example, a gaseous mixture at equilibrium containing 0.10 M sulfur dioxide, 0.15 M oxygen, and 10.88 M sulfur trioxide yields Kc = 7.9 × 10⁴ when substituted into the expression. This direct method requires knowing all equilibrium concentrations.
Q2: What is an ICE table and why is it used in equilibrium calculations?
An ICE table organizes Initial, Change, and Equilibrium concentrations for a reaction. It systematically tracks how concentrations change as a reaction reaches equilibrium, allowing you to calculate unknown equilibrium concentrations from initial concentrations and stoichiometry. This structured approach is essential when only initial concentrations and one equilibrium value are provided.
Q3: How do you use stoichiometry to find unknown equilibrium concentrations?
Use the reaction coefficients to relate concentration changes across all species. If 2x moles of ammonia form at equilibrium, then x moles of nitrogen are consumed and 3x moles of hydrogen are consumed based on the stoichiometry. Subtract these changes from initial concentrations to find equilibrium values, which can then be substituted into the Kc expression.
Q4: What information do you need to calculate Kc when equilibrium concentrations are unknown?
You need the initial concentrations of all reactants and products, plus the equilibrium concentration of at least one compound. Using reaction stoichiometry and an ICE table, you can derive the remaining equilibrium concentrations. For instance, knowing initial nitrogen and hydrogen concentrations and equilibrium ammonia concentration allows calculation of all equilibrium values needed for Kc.
Q5: How does the change variable x relate to reaction stoichiometry in an ICE table?
The variable x represents the extent of reaction. When multiplied by each species' stoichiometric coefficient, it gives the concentration change for that species. For the ammonia synthesis reaction, if 2x = 0.020 M ammonia produced, then x = 0.010 M, meaning 0.010 M nitrogen consumed and 0.030 M hydrogen consumed based on their coefficients.
Q6: Can you calculate Kp using the same ICE table method as Kc?
Yes, Kp for gaseous reactions can be calculated using an ICE table and the equilibrium expression written with partial pressures instead of concentrations. The same systematic approach of organizing initial, change, and equilibrium values applies, but you substitute partial pressure values into the Kp expression rather than molar concentrations.
Q7: What does the equilibrium constant value tell you about a reaction?
The magnitude of Kc indicates the extent of reaction at equilibrium. A large Kc, such as 7.9 × 10⁴, indicates the reaction strongly favors products at equilibrium. A small Kc, such as 0.11, indicates the reaction favors reactants. The value is temperature-dependent and characteristic of each reaction, allowing prediction of equilibrium composition.