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Given The Following Equilibria Calculate The Concentration of Each

Reviewed by Calculator Editorial Team

This guide explains how to calculate the concentrations of species in chemical equilibria when given the equilibrium constant. We'll cover the fundamental principles, step-by-step calculation methods, and practical examples to help you master this essential chemistry concept.

Introduction

Chemical equilibria describe the dynamic balance between reactants and products in a chemical reaction. The equilibrium constant (Keq) quantifies this balance, allowing us to predict the concentrations of species at equilibrium.

When given an equilibrium expression and initial concentrations, we can calculate the final concentrations of all species using the law of mass action and the concept of equilibrium shifts.

Chemical Equilibrium Basics

The equilibrium constant Keq is defined as:

Keq = [Products]/[Reactants]

Where [ ] represents the molar concentrations of species

For a general reaction:

aA + bB ⇌ cC + dD

The equilibrium expression becomes:

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

Key points to remember:

  • Solid and liquid reactants/products are not included in the equilibrium expression
  • The equilibrium constant is temperature-dependent
  • Keq values greater than 1 indicate products favor the reaction
  • Keq values less than 1 indicate reactants favor the reaction

Calculation Method

To calculate equilibrium concentrations, follow these steps:

  1. Write the balanced chemical equation
  2. Write the equilibrium expression
  3. Determine the initial concentrations of all species
  4. Assume a value for x (the change in concentration)
  5. Express all concentrations in terms of x
  6. Substitute into the equilibrium expression and solve for x
  7. Calculate the equilibrium concentrations

For reactions with more than one phase change, use ICE tables to organize your calculations.

Worked Example

Let's calculate the equilibrium concentrations for the reaction:

N2(g) + 3H2(g) ⇌ 2NH3(g)

Keq = 1.6 × 10-2 at 500°C

Initial concentrations: [N2] = 0.5 M, [H2] = 1.5 M, [NH3] = 0 M

Step-by-step solution:

  1. Write the equilibrium expression: Keq = [NH3]2/([N2][H2]3)
  2. Assume x = change in concentration of N2 and H2, and 2x = change in NH3
  3. Express concentrations in terms of x:
    • [N2] = 0.5 - x
    • [H2] = 1.5 - 3x
    • [NH3] = 0 + 2x
  4. Substitute into equilibrium expression:

    1.6 × 10-2 = (2x)2/[(0.5 - x)(1.5 - 3x)3]

  5. Solve the quadratic equation to find x ≈ 0.025 M
  6. Calculate equilibrium concentrations:
    • [N2] = 0.5 - 0.025 = 0.475 M
    • [H2] = 1.5 - 0.075 = 1.425 M
    • [NH3] = 0 + 0.05 = 0.05 M

Common Errors to Avoid

When calculating equilibrium concentrations, watch out for these mistakes:

  • Forgetting to include the stoichiometric coefficients in the equilibrium expression
  • Incorrectly assuming the change in concentration for all species is the same
  • Not accounting for the proper sign (positive or negative) when setting up the ICE table
  • Using the wrong units (always use molar concentrations)
  • Solving the quadratic equation incorrectly

Double-check your calculations and verify that the equilibrium concentrations make sense in the context of the reaction.

Frequently Asked Questions

What if the equilibrium constant is very large or very small?

A very large Keq indicates the reaction strongly favors products, while a very small Keq indicates the reaction strongly favors reactants. In both cases, the equilibrium concentrations will be very different from the initial concentrations.

How do I handle reactions with more than one phase change?

Use an ICE table to organize your calculations. For each phase change, write the change in concentration in terms of x, and solve the resulting equation to find x.

What if the reaction is reversible and the equilibrium constant changes?

If the equilibrium constant changes, the equilibrium position will shift to accommodate the new value. You'll need to recalculate the equilibrium concentrations using the new Keq.