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Difficulty: HardEquilibrium Constant Expression and Calculations
Consider the gas-phase reversible reaction involved in the steam reforming of methane:
CH4(g)+H2O(g)⇌CO(g)+3H2(g)\text{CH}_4(g) + \text{H}_2\text{O}(g) \rightleftharpoons \text{CO}(g) + 3\text{H}_2(g)
What are the units of the equilibrium constant KcK_c when concentrations are expressed in mol⋅dm−3\text{mol}\cdot\text{dm}^{-3}?

Answer: mol^2 dm^-6 / mol^2dm^-6 / mol2 dm-6 / mol2dm-6 / mol^2/dm^6 / mol2/dm6 / (mol dm^-3)^2 / (mol/dm^3)^2

Answer

The units of KcK_c for this reaction are mol2dm−6\text{mol}^2\text{dm}^{-6} (or (mol⋅dm−3)2(\text{mol}\cdot\text{dm}^{-3})^2).
The reaction produces 4 moles of gaseous products (1 mol CO\text{CO} + 3 mol H2\text{H}_2) from 2 moles of gaseous reactants (1 mol CH4\text{CH}_4 + 1 mol H2O\text{H}_2\text{O}). Substituting concentration units into Kc=[CO][H2]3[CH4][H2O]K_c = \frac{[\text{CO}][\text{H}_2]^3}{[\text{CH}_4][\text{H}_2\text{O}]} yields (mol⋅dm−3)4(mol⋅dm−3)2=(mol⋅dm−3)2=mol2dm−6\frac{(\text{mol}\cdot\text{dm}^{-3})^4}{(\text{mol}\cdot\text{dm}^{-3})^2} = (\text{mol}\cdot\text{dm}^{-3})^2 = \text{mol}^2\text{dm}^{-6}.

Step-by-Step Solution

1
Write the equilibrium constant expression for the reaction.
Kc=[CO][H2]3[CH4][H2O]K_c = \frac{[\text{CO}][\text{H}_2]^3}{[\text{CH}_4][\text{H}_2\text{O}]}
The equilibrium constant expression places product concentrations in the numerator and reactant concentrations in the denominator, each raised to the power of their stoichiometric coefficients.
2
Substitute the concentration unit (mol⋅dm−3\text{mol}\cdot\text{dm}^{-3}) for each species into the KcK_c expression.
\text{Units of } K_c = \frac{(\text{mol}\cdot\text{dm}^{-3}) \times (\text{mol}\cdot\text{dm}^{-3})^3}{(\text{mol}\cdot\text{dm}^{-3}) \times (\text{mol}\cdot\text{dm}^{-3})} = \frac{(\text{mol}\cdot\text{dm}^{-3})^4}{(\text{mol}\cdot\text{dm}^{-3})^2}
Replacing the concentration terms with the standard concentration units isolates the dimensional units of KcK_c.
3
Simplify the powers of the concentration units.
(\text{mol}\cdot\text{dm}^{-3})^{4 - 2} = (\text{mol}\cdot\text{dm}^{-3})^2 = \text{mol}^2\text{dm}^{-6}
Dividing exponential terms with the same base subtracts the powers, yielding the final net units.

Key Concept

Determining the units of equilibrium constants (KcK_c) from reaction stoichiometry.
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Topics

Equilibrium Constant Expression and Calculations