Equilibrium Constant Calculation Simplifying Assumption Explained

 

This is part of the HSC Chemistry course under the topic Calculating Equilibrium Constant. 

HSC Chemistry Syllabus

  • Perform calculations to find the value of Keq and concentrations of substances within an equilibrium system, and use these values to make predictions on the direction in which a reaction may proceed. 

    Simplifying Assumption in Equilibrium Constant Calculations

    This video explains the reasoning and validity behind the commonly made assumption 'x is negligible' when performing equilibrium constant calculations.

     

    What Is the Simplifying Assumption?

    In many equilibrium problems, you’ll start with a known initial concentration of a reactant and assume that the change in its concentration is relatively small compared to its original value. This lets you simplify the expression for equilibrium concentrations and avoid complex algebra.

    The assumption is:

    If the change in concentration, x, is small compared to the initial amount, you can approximate:

      Initial concentration − x ≈ Initial concentration

    This makes solving for x in the equilibrium expression much easier.

    When Is It Valid?

    You can safely use the simplifying assumption when the following conditions are met:

    1. The equilibrium constant (K) is very small

    • If K < 10⁻⁴, the system strongly favours the reactants.

    • This means the reaction hardly proceeds — so the change in concentration of the reactants is minimal.

    2. The initial concentration is relatively large

    • A high starting concentration makes the subtraction of a small x even more negligible.

    • The assumption works best when x is less than 5% of the initial concentration.

    3. You check your assumption

    • After solving for x, substitute it back in and calculate what percentage of the initial value it is.

    • If x < 5% of initial concentration, the assumption was valid.

    When Is it Invalid?

    When none of the above criteria are met, then it is generally invalid to assume the change in concentration i.e. x, is negligible compared to the initial concentration. In these cases, it is more accurate to calculate the equilibrium concentrations by applying more rigorous algebra such as quadratic equations.