Calculating Equilibrium Concentrations

Calculating Equilibrium Concentrations

When you know the initial concentrations of reactants and products but have no direct measurement of what the system looks like at equilibrium, you need a systematic method to find the equilibrium concentrations. The textbook lays out a clear five-step procedure for this, and we will work through each step carefully.

The core idea is simple: you let a variable $x$ represent how much of one substance reacts (or is produced) as the system moves to equilibrium. Then, using the stoichiometric coefficients from the balanced equation, you express every other substance's change in terms of $x$. Finally, you plug these expressions into the equilibrium constant expression and solve for $x$.

The Five-Step Procedure

Step 1: Write the balanced equation for the reaction.

This is non-negotiable. Without the correct stoichiometry, every subsequent step will be wrong.

Step 2: Construct an ICE table (Initial, Change, Equilibrium).

Under the balanced equation, draw a table with three rows for each substance:

• Initial concentration (the known starting amounts, in mol/L).
• Change in concentration as the system goes to equilibrium. Define $x$ as the concentration (mol/L) of one substance that reacts. Then use the stoichiometric ratios to write the change for every other substance in terms of $x$. Remember: reactants decrease (so the change is $-x$ times their coefficient), and products increase (so the change is $+x$ times their coefficient).
• Equilibrium concentration = Initial + Change.

Step 3: Substitute the equilibrium concentrations into the equilibrium expression and solve for $x$.

This often leads to a quadratic equation. When solving, you must choose the root that makes chemical sense — concentrations cannot be negative, and $x$ cannot exceed the initial amount of a reactant.

Step 4: Calculate the equilibrium concentrations from the value of $x$.

Plug $x$ back into the expressions from the ICE table.

Step 5: Check your results by substituting them back into the equilibrium expression.

You should recover the given $K_c$ value (within rounding).

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Where to See the Method in Action …