At Equilibrium 0.180 Mol of O2 Is Present. Calculate Kc.

When a chemical reaction reaches equilibrium, the equilibrium constant Kc provides crucial information about the reaction's favorability and the concentrations of reactants and products. This guide explains how to calculate Kc when 0.180 mol of O2 is present at equilibrium.

How to Calculate Kc

The equilibrium constant Kc is calculated using the concentrations of reactants and products at equilibrium. The formula accounts for the stoichiometry of the balanced chemical equation.

Kc = [Products] / [Reactants]

Where:

[Products] = Concentrations of products raised to their stoichiometric coefficients
[Reactants] = Concentrations of reactants raised to their stoichiometric coefficients

To calculate Kc, you'll need:

The balanced chemical equation
The equilibrium concentrations of all species
The stoichiometric coefficients from the balanced equation

Formula for Kc

The general formula for Kc is derived from the stoichiometry of the reaction. For a general reaction:

aA + bB ⇌ cC + dD

The equilibrium constant expression is:

Kc = ([C]ᶜ × [D]ᵈ) / ([A]ᵃ × [B]ᵇ)

Where:

a, b, c, d = stoichiometric coefficients
[A], [B], [C], [D] = equilibrium concentrations of species

Note: Concentrations must be in the same units (typically M or mol/L). The formula assumes the reaction is in a closed system at constant temperature.

Example Calculation

Let's calculate Kc for the reaction:

2NO(g) + O₂(g) ⇌ 2NO₂(g)

At equilibrium, the concentrations are:

[NO] = 0.200 M
[O₂] = 0.180 M
[NO₂] = 0.300 M

The equilibrium constant expression is:

Kc = [NO₂]² / ([NO]² × [O₂])

Plugging in the values:

Kc = (0.300)² / ((0.200)² × (0.180))

Kc = 0.0900 / (0.0400 × 0.180)

Kc = 0.0900 / 0.0072

Kc = 12.5

The equilibrium constant Kc for this reaction is 12.5.

Interpretation of Results

The value of Kc indicates the reaction's favorability:

Kc > 1: Products favored at equilibrium
Kc = 1: Equal concentrations of reactants and products
Kc < 1: Reactants favored at equilibrium

In our example, Kc = 12.5 indicates the reaction strongly favors the formation of NO₂.

Practical Consideration: The actual value of Kc depends on the specific reaction and conditions. Always verify the balanced chemical equation and equilibrium concentrations before calculating Kc.

Frequently Asked Questions

What units should be used for concentrations when calculating Kc?

Concentrations should be in moles per liter (mol/L or M). Ensure all concentrations are in the same units before plugging them into the Kc formula.

How does temperature affect Kc?

Kc is temperature-dependent. The value of Kc changes with temperature, following the van't Hoff equation. For accurate calculations, use the Kc value corresponding to the specific temperature of the reaction.

Can Kc be calculated from partial pressures?

No, Kc is calculated from concentrations, not partial pressures. For gas-phase reactions, use the equilibrium constant Kp (which uses partial pressures) instead of Kc.

What if the reaction involves solids or liquids?

Solids and liquids are not included in the Kc expression because their concentrations are constant. Only gaseous and aqueous species are included in the equilibrium expression.