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At Equilibrium 0.150 Mol of O2 Is Present Calculate Kc

Reviewed by Calculator Editorial Team

When a chemical reaction reaches equilibrium, the equilibrium constant (Kc) describes the ratio of product concentrations to reactant concentrations. This calculator helps determine Kc when you know the moles of a product at equilibrium.

Introduction

The equilibrium constant (Kc) is a fundamental concept in chemical equilibrium. It quantifies how far a reaction proceeds to reach equilibrium, based on the concentrations of products and reactants.

When you know the moles of a product at equilibrium, you can calculate Kc using the stoichiometry of the reaction. This is particularly useful when you don't have direct concentration measurements but know the volume of the system.

The Kc Formula

The general form of the equilibrium constant expression depends on the balanced chemical equation. For a reaction:

aA + bB ⇌ cC + dD

The equilibrium constant Kc is expressed as:

Kc = [C]c[D]d / [A]a[B]b

Where [X] represents the molar concentration of species X.

When you know the moles of a product at equilibrium, you can calculate concentrations using the volume of the system (V):

[X] = moles of X / V

Step-by-Step Calculation

  1. Write the balanced chemical equation for your reaction.
  2. Determine the stoichiometric coefficients for each species.
  3. Measure or know the moles of each species at equilibrium.
  4. Calculate the concentration of each species using [X] = moles/V.
  5. Substitute these concentrations into the Kc expression.
  6. Calculate the numerical value of Kc.

Worked Example

Consider the reaction:

2NO(g) + O2(g) ⇌ 2NO2(g)

At equilibrium, 0.150 mol of NO2 is present in a 5.00 L container. Calculate Kc.

  1. From the balanced equation, the stoichiometry shows 2 mol NO2 forms from 1 mol O2.
  2. Therefore, moles of O2 = 0.150 mol NO2 / 2 = 0.075 mol O2.
  3. Assuming all NO reacted, initial moles of NO = 2 × moles of O2 = 0.150 mol NO.
  4. At equilibrium, moles of NO = initial moles - moles reacted = 0.150 - 0.150 = 0 mol.
  5. Calculate concentrations:
    • [NO2] = 0.150 mol / 5.00 L = 0.0300 M
    • [O2] = 0.075 mol / 5.00 L = 0.0150 M
    • [NO] = 0 mol / 5.00 L = 0 M
  6. Substitute into Kc expression:

    Kc = [NO2]2 / ([NO]2[O2]) = (0.0300)2 / (0 × 0.0150)

  7. The calculation shows Kc is undefined (division by zero), indicating the reaction strongly favors products.

Interpreting Kc

The value of Kc tells you about the position of equilibrium:

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

In our example, Kc is undefined, which means the reaction proceeds almost completely to products.

FAQ

What if I don't know the initial moles of reactants?
You can assume all reactants have been consumed to calculate the maximum possible product formation, or use stoichiometry to relate known quantities.
Can Kc be negative?
No, Kc is always positive because concentrations are squared in the expression, making negative values meaningless.
What units does Kc have?
Kc is unitless because it's a ratio of concentrations, which cancel out the units.
How does temperature affect Kc?
Kc changes with temperature according to the van't Hoff equation, which relates Kc to the change in Gibbs free energy.