3.2.3(f)-(g) - Equilibrium constant Kc

Meaning of $K_c$

A reversible reaction reaches dynamic equilibrium when the forward and reverse reactions happen at the same rate. At that point, the concentrations of reactants and products stay constant, even though particles are still reacting both ways.

$K_c$ is a number calculated from those equilibrium concentrations. It is useful because it lets chemists compare equilibrium mixtures more precisely than saying "mostly products" or "mostly reactants".

For a general homogeneous equilibrium:

the $K_c$ expression is:

The products are on the top of the fraction. The reactants are on the bottom. The powers come from the balancing numbers in the chemical equation.

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The most important word is equilibrium. A starting concentration tells you what was mixed at the beginning. A $K_c$ calculation needs the concentrations once the mixture has reached equilibrium.

Calculating from Concentrations

Once you have the correct $K_c$ expression, the calculation is substitution. Put each equilibrium concentration into the expression and calculate carefully.

You do not need to work out the units of $K_c$ in this topic (units of equilibrium constants come later, in 5.1.2). Give the value of $K_c$ to an appropriate number of significant figures unless the question tells you otherwise.

Worked example: direct substitution

Hydrogen and iodine react to form hydrogen iodide:

At equilibrium, the concentrations are:

First write the expression:

Now substitute:

So $K_c = 48.0$ for this reaction at this temperature. The value is much larger than 1, so the equilibrium mixture contains a relatively large amount of product compared with reactants.

Common errors in this kind of calculation:

• using starting concentrations instead of equilibrium concentrations
• putting reactants on the top of the fraction
• forgetting to square a concentration when the coefficient is 2
• rounding too early in the calculation
• adding concentration terms instead of multiplying them

Powers from Coefficients

The powers in a $K_c$ expression are not chosen from the state symbols, the type of molecule or the reaction order. They come from the balanced chemical equation.

For example:

has this $K_c$ expression:

The coefficient 2 in front of $\mathrm{SO_3}$ becomes the power 2 on $[\mathrm{SO_3}]$. The coefficient 2 in front of $\mathrm{SO_2}$ becomes the power 2 on $[\mathrm{SO_2}]$. The coefficient 1 in front of $\mathrm{O_2}$ is usually not written as a power.

Worked example: using powers

For the same equilibrium, suppose the equilibrium concentrations are:

Substitute into the expression:

Notice the denominator: $(0.0200)^2(0.0100)$. If $[\mathrm{SO_2}]$ were not squared, the answer would be completely different.