By Contributor | Updated Aug 30 2022

The equilibrium constant K_c quantifies the ratio of product concentrations to reactant concentrations for a reaction conducted in solution or gas phase, where all species are expressed as molar concentrations. For the generic reaction A + B ⇌ AB, it is defined as

K_c = [AB] ⁄ ([A][B])

Below, we walk through two practical examples: the oxidation of carbon monoxide by nitric oxide, and the thermal decomposition of baking soda (sodium bicarbonate).

1. Oxidation of CO by NO

Consider the homogeneous equilibrium:

CO + 2 NO ⇌ CO₂ + N₂O

Given the following molar concentrations:

• [CO] = 2.0 mol L⁻¹
• [NO] = 0.5 mol L⁻¹
• [CO₂] = 1.2 mol L⁻¹
• [N₂O] = 3.0 mol L⁻¹

Compute the denominator first:

[CO] × [NO]² = 2.0 × (0.5)² = 1.0 mol³ L⁻³

Next, compute the numerator:

[CO₂] × [N₂O] = 1.2 × 3.0 = 3.6 mol² L⁻²

Finally, divide numerator by denominator:

K_c = (3.6 mol² L⁻²) ⁄ (1.0 mol³ L⁻³) = 3.6 mol⁻¹ L⁻¹

2. Thermal Decomposition of Baking Soda

This heterogeneous equilibrium involves solid sodium bicarbonate and gaseous products:

2 NaHCO₃ ⇌ Na₂CO₃ + CO₂ + H₂O

Only gaseous species appear in the K_c expression, because solids are omitted. With the following concentrations:

• [CO₂] = 1.8 mol L⁻¹
• [H₂O] = 1.5 mol L⁻¹

Calculate:

K_c = [CO₂] × [H₂O] = 1.8 × 1.5 = 2.7 mol² L⁻²

These step‑by‑step calculations illustrate how to determine K_c for both homogeneous and heterogeneous reactions.