This AP Chemistry lesson on chemical equilibrium notes gives the key ideas first, then worked examples and diagrams. After that, practise with the worksheet on chemical equilibrium and check yourself with the quiz.
Quick answer: At chemical equilibrium the forward and reverse reaction rates are equal, so concentrations stay constant. The equilibrium constant K = products over reactants (each raised to its coefficient) depends only on temperature. Comparing Q with K predicts the direction of change, ICE tables find equilibrium concentrations, and Le Chatelier’s principle predicts the shift after a disturbance.
Level: AP Chemistry · Curriculum: AP Chem Unit 7
Chemical equilibrium notes: the key ideas
What is chemical equilibrium?
Many reactions are reversible: products re-form reactants. In a closed vessel the forward and reverse rates become equal, and the concentrations stay constant even though both reactions continue. This is dynamic equilibrium; nothing looks as if it were happening, but molecules are still reacting.
The equilibrium constant for aA + bB ⇌ cC + dD is Kc = [C]c[D]d/([A]a[B]b), using equilibrium concentrations in mol/L. Pure solids and pure liquids are left out because their concentration is constant. For gases, Kp uses partial pressures.
The value of K depends only on temperature. A large K (above about 10³) means products dominate; a small K (below about 10⁻³) means reactants dominate. If you reverse a reaction, K becomes 1/K; if you multiply the equation by n, K becomes Kn; if you add two reactions, you multiply their K values. The two constants are linked by Kp = Kc(RT)Δn, where Δn is moles of gas on the right minus moles on the left.
How do you use the reaction quotient Q?
The reaction quotient Q has the same form as K but uses the concentrations at any moment. Comparing Q with K tells you which way the mixture will move.
Bilal in Lahore has H₂(g) + CO₂(g) ⇌ H₂O(g) + CO(g) with Kc = 0.50 at a certain temperature. A mixture contains [H₂] = 0.40 M, [CO₂] = 0.40 M, [H₂O] = 0.30 M and [CO] = 0.30 M.
Q = (0.30 × 0.30)/(0.40 × 0.40) = 0.0900/0.160 = 0.56.
Since Q > K, there are too many products: the reaction shifts in reverse (to the left).
How do you solve an ICE table?
An ICE table lists Initial, Change and Equilibrium concentrations. Let the change be x, scaled by the coefficients, then substitute the equilibrium row into K. If the equation is a perfect square, take square roots; otherwise use the quadratic formula, or an approximation when K is very small and x is under 5 % of the initial value.
For H₂(g) + I₂(g) ⇌ 2 HI(g), Kc = 64. Start with 0.40 M H₂ and 0.40 M I₂ and no HI.
Change: H₂ −x, I₂ −x, HI +2x. Then (2x)²/(0.40 − x)² = 64, so 2x/(0.40 − x) = 8, which gives 2x = 3.2 − 8x and x = 0.32.
[H₂] = [I₂] = 0.08 M and [HI] = 0.64 M. Check: 0.64²/0.08² = 64 ✓.
N₂O₄(g) ⇌ 2 NO₂(g) has Kc = 0.20. Start with 0.50 M N₂O₄ only.
(2x)²/(0.50 − x) = 0.20, so 4x² + 0.20x − 0.10 = 0. The quadratic formula gives x = [−0.20 + √(0.04 + 1.60)]/8 = 0.135.
[NO₂] = 2x = 0.27 M and [N₂O₄] = 0.50 − 0.135 = 0.365 M. Check: 0.270²/0.365 = 0.20 ✓.
What does Le Chatelier’s principle predict?
When a system at equilibrium is disturbed, it shifts to partly oppose the change. Only a change in temperature alters K; other disturbances change Q and the system moves until Q = K again.
| Disturbance | Shift | Does K change? |
|---|---|---|
| Add reactant or remove product | To the right | No |
| Add product or remove reactant | To the left | No |
| Compress (smaller volume) | Towards fewer moles of gas | No |
| Raise temperature | In the endothermic direction | Yes |
| Add catalyst or inert gas (constant volume) | No shift | No |
The equilibrium mixture of Example 3 is [N₂O₄] = 0.365 M and [NO₂] = 0.270 M. The volume is halved at constant temperature. Concentrations double at once: 0.730 M and 0.540 M.
Q = 0.540²/0.730 = 0.40 > K = 0.20, so the system shifts left, towards the side with fewer moles of gas. The new equilibrium is [N₂O₄] = 0.80 M and [NO₂] = 0.40 M, which satisfies 0.40²/0.80 = 0.20 ✓.
A catalyst does not shift an equilibrium or change K: it speeds up both directions equally. Also, adding an inert gas at constant volume does not change the partial pressures, so nothing shifts. And remember that K only changes with temperature, even when the position of the equilibrium moves.
When a problem says “predict the shift”, compute Q whenever you have numbers. Q below K means the forward reaction runs; Q above K means the reverse reaction runs. It works for every disturbance, not only for concentrations.
- K = [products]^coefficients / [reactants]^coefficients; solids and pure liquids are omitted.
- Q < K: forward reaction; Q > K: reverse reaction; Q = K: equilibrium.
- Kp = Kc(RT)^Δn, with Δn = moles of gas products − moles of gas reactants.
- Reversing a reaction gives 1/K; multiplying by n gives K^n; adding reactions multiplies K.
- Only temperature changes K; catalysts and inert gases do not shift the equilibrium.
Equilibrium constants and shifts: frequently asked questions
Does equilibrium mean the concentrations are equal?
No. At equilibrium the rates are equal and the concentrations are constant, but they are usually different. The size of K tells you which side is favoured.
Why are solids not included in K?
The concentration of a pure solid or liquid is fixed by its density, so it does not change during the reaction. It is absorbed into the value of K.
What is the difference between Q and K?
Q uses the concentrations at any moment, while K uses only equilibrium concentrations. Comparing them shows which direction the reaction will move.
How does temperature change K?
Increasing the temperature favours the endothermic direction. K rises for an endothermic reaction and falls for an exothermic one.
When can you use the small-x approximation?
When K is very small compared with the initial concentration, so x is under about 5 % of it. Always check the assumption after you have solved.
