Equilibrium Constants

students, imagine a bottle of water with a fizzing tablet dropped in it. At first, lots of reaction happens quickly. Later, the bubbling slows down, but the reaction does not stop completely. Instead, forward and reverse reactions can happen at the same time. This is the big idea behind chemical equilibrium ⚖️.

In this lesson, you will learn how chemists describe equilibrium using equilibrium constants, how to write expressions for them, and how to use them to predict whether a reaction mixture has mostly products or mostly reactants. You will also see how equilibrium constants connect to the IB Chemistry SL theme of Reactivity 2 — How Much, How Fast, and How Far?, because equilibrium helps answer “how far” a reaction goes.

What is chemical equilibrium?

Chemical equilibrium is a dynamic state. That means the reaction is still happening, but the rate of the forward reaction equals the rate of the reverse reaction. Because the two rates are equal, the concentrations of reactants and products stay constant over time.

For a reversible reaction such as:

$$aA + bB \rightleftharpoons cC + dD$$

the system reaches equilibrium when neither side is being used up overall. The reactants and products are not necessarily equal in amount; they are just constant.

It is important to remember that equilibrium only happens in a closed system, where substances cannot escape. If a gas can leave the container, or if a product is removed, the equilibrium position can change.

A useful real-life example is the reaction between nitrogen, hydrogen, and ammonia in the Haber process:

$$\mathrm{N_2(g) + 3H_2(g) \rightleftharpoons 2NH_3(g)}$$

Factories use this equilibrium to make ammonia for fertilizers. The amount of ammonia made depends on the equilibrium conditions and the equilibrium constant.

The equilibrium constant $K$

The equilibrium constant is a number that tells us the balance between products and reactants at equilibrium. For a general reaction:

$$aA + bB \rightleftharpoons cC + dD$$

the equilibrium constant in terms of concentration is:

$$K_c = \frac{[C]^c[D]^d}{[A]^a[B]^b}$$

Here, square brackets mean concentration in $\mathrm{mol\,dm^{-3}}$. The exponents come from the balanced equation coefficients.

This expression only includes aqueous substances and gases. Pure solids and pure liquids are left out because their concentrations do not change in the same way during the reaction.

For gases, we sometimes use partial pressures instead:

$$K_p = \frac{(p_C)^c(p_D)^d}{(p_A)^a(p_B)^b}$$

The exact form depends on the data given in the question. students, the key skill is to write the expression correctly from the balanced equation.

Example: writing an expression for $K_c$

For the reaction:

$$\mathrm{H_2(g) + I_2(g) \rightleftharpoons 2HI(g)}$$

the equilibrium constant is:

$$K_c = \frac{[HI]^2}{[H_2][I_2]}$$

Notice that the coefficient $2$ becomes the exponent on $[HI]$.

What does the size of $K$ mean?

The value of $K$ tells you which side is favored at equilibrium.

If $K \gg 1$, products are favored. The equilibrium mixture contains mostly products.
If $K \ll 1$, reactants are favored. The equilibrium mixture contains mostly reactants.
If $K \approx 1$, neither side is strongly favored.

This does not mean the reaction is fast or slow. A reaction can have a large $K$ and still be slow, or a small $K$ and still be fast. Rate and equilibrium are related, but they are not the same idea.

A common misconception is that a large $K$ means a reaction goes to completion. That is not always true. It means the equilibrium position lies far toward products, but some reactant still remains at equilibrium.

Units and the meaning of $K$

In many IB questions, you may see $K_c$ written without units. Strictly speaking, the units depend on the reaction because the concentration terms may not cancel.

For example, in:

$$\mathrm{H_2(g) + I_2(g) \rightleftharpoons 2HI(g)}$$

$$K_c = \frac{[HI]^2}{[H_2][I_2]}$$

the units cancel, so $K_c$ is often treated as unitless in practice. However, in some reactions the expression may not cancel in a simple way. In IB Chemistry SL, the main focus is usually on correct construction and interpretation rather than advanced unit analysis.

Heterogeneous equilibria and why solids are omitted

In reactions involving solids and liquids, only gases and aqueous species are included in the equilibrium expression.

For example:

$$\mathrm{CaCO_3(s) \rightleftharpoons CaO(s) + CO_2(g)}$$

The equilibrium constant is:

$$K_c = [CO_2]$$

The solids $\mathrm{CaCO_3(s)}$ and $\mathrm{CaO(s)}$ are excluded because their effective concentrations remain constant.

This is useful in mineral chemistry and decomposition reactions. If the pressure of $\mathrm{CO_2}$ increases, the position of equilibrium shifts, but the solid concentrations are not written in the equilibrium expression.

Calculating an equilibrium constant from data

Sometimes you are given equilibrium concentrations and asked to calculate $K_c$.

For example, suppose:

$$\mathrm{H_2(g) + I_2(g) \rightleftharpoons 2HI(g)}$$

At equilibrium, the concentrations are:

$$[H_2] = 0.20\,\mathrm{mol\,dm^{-3}}$$

$$[I_2] = 0.20\,\mathrm{mol\,dm^{-3}}$$

$$[HI] = 1.60\,\mathrm{mol\,dm^{-3}}$$

Then:

$$K_c = \frac{(1.60)^2}{(0.20)(0.20)} = \frac{2.56}{0.04} = 64$$

So the equilibrium constant is $64$, which means products are favored at equilibrium.

When doing calculations, always check that the concentrations are equilibrium values, not initial values. This is a common exam trap.

Using an ICE table

When the problem gives initial amounts and change, but not equilibrium values, an ICE table helps.

ICE stands for:

Initial
Change
Equilibrium

Suppose we have:

$$\mathrm{N_2O_4(g) \rightleftharpoons 2NO_2(g)}$$

If the initial concentration of $\mathrm{N_2O_4}$ is $0.50\,\mathrm{mol\,dm^{-3}}$ and none of $\mathrm{NO_2}$ is present at first, we can let the change in $\mathrm{N_2O_4}$ be $-x$ and the change in $\mathrm{NO_2}$ be $+2x$.

So the equilibrium concentrations are:

$$[N_2O_4] = 0.50 - x$$

$$[NO_2] = 2x$$

Then substitute into the equilibrium expression:

$$K_c = \frac{[NO_2]^2}{[N_2O_4]} = \frac{(2x)^2}{0.50 - x}$$

If $K_c$ is given, you can solve for $x$ and then find equilibrium concentrations. This procedure is a major skill in IB Chemistry SL.

Equilibrium constants and the position of equilibrium

The equilibrium constant helps describe the extent of reaction. A reaction with a very large $K$ goes much further toward products than a reaction with a small $K$.

However, the value of $K$ is fixed only at a given temperature. If temperature changes, the equilibrium constant changes too. This is one of the few conditions that changes $K$ itself. Changing concentration, pressure, or volume shifts the equilibrium position, but does not change the value of $K$ at constant temperature.

This links directly to Le Châtelier’s principle. If you increase the concentration of a reactant, the system shifts to reduce that change. The reaction quotient changes temporarily, and the system adjusts until it returns to the same $K$ value at that temperature.

Reaction quotient $Q$ versus equilibrium constant $K$

The reaction quotient has the same form as the equilibrium constant, but it uses concentrations or pressures at any time, not necessarily at equilibrium.

For the reaction:

$$aA + bB \rightleftharpoons cC + dD$$

$$Q_c = \frac{[C]^c[D]^d}{[A]^a[B]^b}$$

Compare $Q$ with $K$:

If $Q < K$, the reaction proceeds forward to make more products.
If $Q > K$, the reaction proceeds backward to make more reactants.
If $Q = K$, the system is already at equilibrium.

This is a powerful way to predict the direction of change. students, it is like checking whether a classroom is too crowded on one side or the other and then seeing which way people move to balance it out 🙂.

Why equilibrium constants matter in chemistry

Equilibrium constants are used in industry, environmental science, and biology. In the Haber process, manufacturers use $K$ along with temperature and pressure to decide the best conditions for maximizing ammonia production. In acid-base chemistry, equilibrium constants help describe how strongly acids and bases dissociate. In environmental systems, they help explain gas exchange and dissolution reactions.

So equilibrium constants are not just numbers on a page. They are tools for predicting the amount of product formed and understanding how chemical systems behave in the real world.

Conclusion

Equilibrium constants are one of the main ways chemists describe reversible reactions. They show the balance between products and reactants at equilibrium, help predict the position of equilibrium, and connect directly to the idea of how far a reaction goes. Remember that $K$ depends on temperature, that solids and pure liquids are omitted from the expression, and that large or small values of $K$ tell you whether products or reactants are favored. Together with rates of reaction and reaction extent, equilibrium constants give a complete picture of reactivity in IB Chemistry SL.

Study Notes

Chemical equilibrium is dynamic: the forward and reverse reaction rates are equal.
At equilibrium, concentrations stay constant, but reactions still continue.
For $aA + bB \rightleftharpoons cC + dD$, the equilibrium expression is $K_c = \frac{[C]^c[D]^d}{[A]^a[B]^b}$.
Use concentrations for $K_c$ and partial pressures for $K_p$.
Pure solids and pure liquids are omitted from equilibrium expressions.
A large $K$ means products are favored; a small $K$ means reactants are favored.
$K$ changes only when temperature changes.
Concentration, pressure, and volume changes affect the position of equilibrium, not the value of $K$ at constant temperature.
The reaction quotient $Q$ predicts direction: $Q < K$ forward, $Q > K$ backward, $Q = K$ at equilibrium.
ICE tables are useful for calculating equilibrium concentrations from initial values.
Equilibrium constants help explain industrial processes like the Haber process and connect to the “how far” part of Reactivity 2.