IB Chemistry HLTopic 5 — How Far? The Position of EquilibriumPaper 1 & 2HL only | Core skill~8 min read
The Reaction Quotient, Q
Le Chatelier tells you which way a system moves when you disturb it. The reaction quotient does something better: it tells you which way any mixture will move, even one you have just thrown together, using nothing but a calculation. Same expression as K, different moment in time.
📘 What you need to know
Q uses exactly the same expression as K — products over reactants, same powers.
The difference is when: K uses equilibrium concentrations, Q uses the concentrations at any moment you choose.
Q < K: too little product, so the reaction goes forwards (to the right).
Q = K: the mixture is already at equilibrium. No net change.
Q > K: too much product, so the reaction goes backwards (to the left).
Q changes as the reaction runs. K is fixed at a given temperature.
Q always moves towards K, and stops when it gets there.
Q is a snapshot, K is the destination
Picture K as the address the reaction is heading to. Q is where the reaction is right now. If Q is smaller than K, you have not gone far enough yet, so the reaction carries on forwards. If Q has somehow overshot K, the reaction reverses to come back.
For aA + bB ⇌ cC + dD
Q = [C]c[D]d[A]a[B]b
— identical to K, but with the concentrations you have now
🤔 Why does the comparison tell you the direction?
Q < K means the top of the fraction is too small relative to the bottom. The only way to make the top bigger and the bottom smaller is to convert reactants into products — the forward reaction. So the reaction must go forwards, and as it does, Q climbs until it equals K. If Q > K, everything runs the other way. You are not memorising a rule here; you are just reading a fraction.
Notice that the direction of the arrow is the direction of the reaction. You never have to reason about which side is “favoured” — you just look at which side of K your Q landed on.
🧩 Using Q to find the direction
Write the K expression from the balanced equation.
Put the given concentrations in, exactly as they are. Do not adjust anything.
Work out Q. Keep the full calculator value.
Compare Q with K and say which is bigger.
State the direction: Q smaller means forwards, Q bigger means backwards, equal means already at equilibrium.
A neat consequence: mix reactants with no product at all and the top of the fraction is zero, so Q = 0. Zero is smaller than every possible K, which is why a fresh mixture of reactants always starts by going forwards.
Q and K look identical on paper, so label your working. Write “Q =” when you are using the numbers you were handed, and “K =” only when you know the mixture is at equilibrium. Examiners can tell whether you understood the difference from that one letter.
Worked examples
WORKED EXAMPLE
Three mixtures, three verdicts
For PCl5(g) ⇌ PCl3(g) + Cl2(g), K = 1.80 at a certain temperature. All concentrations are in mol dm–3.
Mixture A: [PCl5] = 0.500, [PCl3] = 0.300, [Cl2] = 0.300
Mixture B: [PCl5] = 0.0500, [PCl3] = 0.300, [Cl2] = 0.300
Mixture C: [PCl5] = 0.0200, [PCl3] = 0.400, [Cl2] = 0.400
Deduce whether each is at equilibrium, and if not, which way it will go.
The expression, used for all threeQ = [PCl3][Cl2][PCl5]Mixture AQ = 0.300 × 0.3000.500 = 0.09000.500 = 0.180Q < K, so the reaction goes forwards (more PCl3 and Cl2)Mixture BQ = 0.300 × 0.3000.0500 = 1.80Q = K, so mixture B is already at equilibriumMixture CQ = 0.400 × 0.4000.0200 = 0.1600.0200 = 8.00Q > K, so the reaction goes backwards (more PCl5)same expression three times – only the numbers change
WORKED EXAMPLE
Testing a student’s claim
For H2(g) + I2(g) ⇌ 2HI(g), K = 56.3 at 700 K. A student prepares a mixture in which [H2] = 0.0500, [I2] = 0.0500 and [HI] = 0.300 mol dm–3, and claims it is at equilibrium. Show that the student is wrong and state what will happen.
Step 1: Calculate Q, not K — we do not yet know it is at equilibriumQ = [HI]2[H2][I2] = 0.30020.0500 × 0.0500= 0.09000.00250 = 36.0Step 2: CompareQ = 36.0 and K = 56.3, so Q is smaller than K. The mixture cannot be at equilibrium.The forward reaction runs: [HI] rises, [H2] and [I2] fall, until Q reaches 56.3“show that” means the numbers have to appear – a worded answer alone will not score
WORKED EXAMPLE
Linking Q back to Le Chatelier
A mixture of N2O4 and NO2 sits at equilibrium. Extra NO2 is injected at constant temperature and volume. Use Q to explain what happens.
N2O4(g) ⇌ 2NO2(g)
Step 1: Before the injectionQ = K, because the mixture was at equilibrium.Step 2: The instant NO2 is addedQ = [NO2]2[N2O4] top has increased, bottom unchangedSo Q is now bigger than K.Step 3: What that meansQ > K, so the reaction goes backwards until Q falls back to Kexactly what Le Chatelier predicts – Q just shows you the arithmetic behind it
🧠 Which way when Q is small?
Small Q means a small top, and the top is the products. Not enough product yet, so make some more — go forwards. Say it to yourself as “small Q, needs more product”. It stops you flipping the rule under pressure in an exam.
💡 Exam tip
Write the letter Q in your working, not K. It shows the examiner you know the mixture may not be at equilibrium yet.
Never adjust the numbers you are given. Q is deliberately calculated from a non-equilibrium mixture.
State the comparison in words: “Q is less than K, therefore…” That sentence usually carries the mark.
Then say what physically happens: which concentration rises and which falls, not just “shifts right”.
Q and K are compared, never subtracted. There is no meaning to Q – K.
If a question gives you concentrations and a value of K and asks for a direction, it is a Q question even if the word “quotient” never appears.
⚠ Common mix-up
Calling it K when it is Q. If the mixture is not at equilibrium, the number you calculate is Q by definition.
Getting the direction backwards. Q < K goes forwards. Check it against the fraction rather than trusting memory.
Thinking Q is constant. Q changes every second while the reaction runs. Only K is fixed.
Comparing Q to 1 instead of to K. The size of Q on its own tells you nothing. It is the comparison that matters.
Forgetting the powers. Q uses the same powers as K, from the same balanced equation.
Using Q values from different temperatures. K changes with temperature, so a comparison across two temperatures is meaningless.
Up next: Equilibrium Law Problem Solving (HL) — ICE tables, when the volume cancels, and the shortcut you are allowed to use when K is tiny.
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