The Reaction Quotient Q
The same expression as K — but measured mid-reaction. It's the compass that tells you which way a reaction is about to move.
⏱️ About 14 min
You mix some reactants and some products together in a flask — not at equilibrium, just a random starting mix. Which way will the reaction go: forward to make more product, or backward to make more reactant? You don't have to guess. One number, the reaction quotient Q, answers it every time.
💡
The big idea: The reaction quotient Q uses the exact same formula as the equilibrium constant K, but you plug in the concentrations at ANY moment — not just at equilibrium. Comparing Q to K tells you which direction the reaction must shift to reach balance.
Same expression, any moment
You already know the equilibrium constant K: products over reactants, each raised to its coefficient, using the concentrations at equilibrium. The reaction quotient Q is the very same fraction — but you're allowed to plug in the concentrations at any instant, equilibrium or not.
That's the whole trick. K is a fixed target (it only changes with temperature). Q is a live snapshot of where the mixture is right now. Line the two up and you instantly know whether the reaction still has forward to go, reverse to go, or has arrived.
\[ Q = \frac{[\text{C}]^c\,[\text{D}]^d}{[\text{A}]^a\,[\text{B}]^b} \qquad \text{for } a\text{A} + b\text{B} \rightleftharpoons c\text{C} + d\text{D} \]
Identical to the K expression — products over reactants, coefficients as exponents — but evaluated at the current, not-necessarily-equilibrium concentrations.
🔑 K is the destination; Q is your GPS location
K tells you where the reaction ends up at a given temperature. Q tells you where the mixture is right now. Comparing them is like comparing your current position to your destination — it tells you which way to drive.
The three cases
To reach equilibrium a mixture always moves so that Q slides toward K. There are only three possibilities:
- Q < K — too few products relative to the target. The reaction shifts forward (left → right) to make more product, raising Q up to K.
- Q > K — too many products. The reaction shifts reverse (right → left) to rebuild reactants, lowering Q down to K.
- Q = K — the mixture is already at equilibrium. No net shift; forward and reverse rates are equal.
✨ One line to remember
The reaction always shifts to close the gap between Q and K. If Q is too small, make more products (forward). If Q is too big, make more reactants (reverse). Q chases K until they meet.
📝 Worked example: For A ⇌ B, K = 2.0 at this temperature. Right now [A] = 0.50 mol/L and [B] = 0.50 mol/L. Is the mixture at equilibrium? If not, which way does it shift?
- Write Q with the current values: Q = [B] / [A] = 0.50 / 0.50 = 1.0.
- Compare to K: Q = 1.0 and K = 2.0, so Q < K.
- Q < K means there is not enough product yet, so the reaction shifts forward (makes more B) until Q rises to 2.0.
✓ Not at equilibrium; Q (1.0) < K (2.0), so it shifts forward (toward B).
📝 Worked example: For N₂(g) + 3H₂(g) ⇌ 2NH₃(g), K = 0.50 at this temperature. A mixture has [N₂] = 1.0, [H₂] = 1.0, [NH₃] = 1.0 mol/L. Which way does it shift?
- Q = [NH₃]² / ([N₂] · [H₂]³) = (1.0)² / ((1.0) · (1.0)³) = 1.0 / 1.0 = 1.0.
- Compare: Q = 1.0 is greater than K = 0.50, so Q > K.
- Q > K means there is too much product, so the reaction shifts reverse (breaks NH₃ back into N₂ and H₂) until Q falls to 0.50.
✓ Q (1.0) > K (0.50), so it shifts reverse — toward the reactants.
✏️ Practice: For A ⇌ B, a mixture currently has [A] = 0.40 mol/L and [B] = 0.20 mol/L. Calculate the reaction quotient Q. (Q = [B] / [A].)
Solution
- Q = [B] / [A] for A ⇌ B (both coefficients are 1).
- = 0.20 / 0.40.
- = 0.50. If K were, say, 3.0, then Q < K and the reaction would shift forward to make more B.
✏️ Practice: For 2SO₂(g) + O₂(g) ⇌ 2SO₃(g), a mixture has [SO₃] = 0.40, [SO₂] = 0.20 and [O₂] = 0.50 mol/L. Calculate Q. (Q = [SO₃]² / ([SO₂]² · [O₂]).)
Solution
- Apply the coefficients as exponents: Q = [SO₃]² / ([SO₂]² · [O₂]).
- Numerator: (0.40)² = 0.16. Denominator: (0.20)² × 0.50 = 0.04 × 0.50 = 0.020.
- Q = 0.16 / 0.020 = 8.0. Compare this to K to see which way it shifts.
Check your understanding
1. How does the reaction quotient Q differ from the equilibrium constant K?
Q and K share the exact same expression. The difference is that Q is evaluated at any moment, while K uses the equilibrium concentrations.
2. A reaction has Q < K at this instant. Which way will it shift?
Q < K means too few products relative to the target, so the reaction shifts forward to make more product, raising Q until it equals K.
3. What is the precise condition for a mixture to be at equilibrium?
Equilibrium is exactly the state where Q = K. It does not require Q or K to equal 1, nor equal concentrations of products and reactants.
✅ Key takeaways
- Q (the reaction quotient) uses the same expression as K, but with the current concentrations.
- Q < K → the reaction shifts forward (makes more product) to raise Q toward K.
- Q > K → the reaction shifts reverse (makes more reactant) to lower Q toward K.
- Q = K is exactly the condition for equilibrium — no net shift.
- Comparing Q to K predicts direction without any guesswork.
➡️ Q tells you which way a mixture moves toward equilibrium. But what if a system is already at equilibrium and you disturb it — add a reactant, squeeze the volume, change the temperature? Le Châtelier's principle predicts the response, and it maps cleanly onto the Q-versus-K thinking you just learned.
Want to test yourself on this?
Try the Chemistry practice test →