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At Equilibrium 0.190 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 oxygen (O2) 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 reactants and products at that point.

When you know the moles of a product at equilibrium, you can calculate Kc if you have information about the reaction stoichiometry and the volume of the system. This guide explains how to perform that calculation.

The Kc Formula

Equilibrium Constant Formula

For a general reaction: aA + bB ⇌ cC + dD

The equilibrium constant Kc is expressed as:

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

Where:

  • [A], [B], [C], [D] are the equilibrium concentrations of reactants and products
  • a, b, c, d are the stoichiometric coefficients

To calculate Kc when you know the moles of a product, you'll need to convert moles to concentrations using the volume of the system.

Step-by-Step Calculation

  1. Identify the balanced chemical equation for your reaction
  2. Determine the stoichiometric coefficients for all species
  3. Convert moles of each species to concentrations using the volume of the system
  4. Substitute the concentrations into the Kc formula
  5. Calculate the numerical value of Kc

Important Notes

  • All concentrations must be in the same units (typically M or mol/L)
  • The reaction must be properly balanced
  • Pure solids and liquids are not included in the Kc expression

Worked Example

Consider the reaction: 2NO(g) + O2(g) ⇌ 2NO2(g)

At equilibrium, 0.190 mol of O2 is present in a 2.00 L solution. Calculate Kc.

  1. First, convert moles of O2 to concentration: [O2] = 0.190 mol / 2.00 L = 0.0950 M
  2. From the balanced equation, 1 mol of O2 reacts with 2 mol of NO to produce 2 mol of NO2
  3. Assuming x mol of NO2 is produced, the equilibrium concentrations are:
    • [NO] = 2x M (since 2 mol NO react with 1 mol O2)
    • [O2] = 0.0950 M (given)
    • [NO2] = 2x M
  4. The Kc expression is: Kc = [NO2]² / ([NO]²[O2])
  5. Substitute the concentrations: Kc = (2x)² / ((2x)² × 0.0950)
  6. Simplify: Kc = 4x² / (4x² × 0.0950) = 1 / 0.0950 ≈ 10.53

The equilibrium constant Kc for this reaction is approximately 10.53.

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 ≈ 10.53 indicates that products (NO2) are strongly favored at equilibrium.

Frequently Asked Questions

What units should I use for Kc?

Kc is a dimensionless quantity because it's a ratio of concentrations. The units cancel out in the calculation.

Can I use moles directly in the Kc formula?

No, you must convert moles to concentrations (mol/L) by dividing by the volume of the system.

What if my reaction has solids or liquids?

Pure solids and liquids are not included in the Kc expression because their concentrations are constant.

How accurate is this calculation?

The accuracy depends on the precision of your mole measurements and volume measurements.