AP Chem Score Calculators

Unit 7 Equilibrium

AP Chemistry Reaction Quotient

How to write Q, compare it with K to predict which way a reaction goes, and use it to explain every Le Chatelier shift, in four worked examples.

The equilibrium constant tells you where a reaction ends up. The reaction quotient tells you where it is now, and the comparison between the two tells you which way it has to move. This page assumes you can write an equilibrium expression, covered in AP Chemistry Kc and Kp.

What the Reaction Quotient Is

For aA + bB ⇌ cC + dD, the reaction quotient has exactly the same form as K:

Qc = [C]c[D]d / [A]a[B]b    or, with partial pressures, Qp = (PC)c(PD)d / (PA)a(PB)b

  • The difference is the data: K uses equilibrium values, while Q uses the values present right now.
  • K is fixed at a given temperature; Q changes as the reaction proceeds.
  • Pure solids and pure liquids are left out of Q, exactly as they are left out of K.

How Comparing Q and K Predicts the Direction

ComparisonWhat it meansWhat happens
Q < KToo little product compared with equilibriumNet forward reaction; Q rises to K
Q = KAt equilibriumNo net change; forward and reverse rates are equal
Q > KToo much product compared with equilibriumNet reverse reaction; Q falls to K
Fig. 1 · Two mixtures on either side of K
Q Always Moves Toward K: N₂O₄(g) ⇌ 2NO₂(g) Kc = 4.6 × 10⁻³ at 25°C; Q = [NO₂]² / [N₂O₄] (logarithmic scale) Q < K too little product: shifts forward Q > K too much product: shifts in reverse 10−5 10−4 10−3 10−2 10−1 Value of Q (each mark is 10 times the one before) K = 4.6 × 10−3 Mixture A Q = 5.0 × 10−4 Mixture B Q = 1.8 × 10−2 Mixture A makes more NO₂ until Q rises to K; mixture B makes more N₂O₄ until Q falls to K.

Whichever side it starts on, the mixture moves toward the same K, which is why a reversible reaction reaches the same equilibrium from pure reactants, pure products, or any mixture in between.

How Q Explains Le Chatelier’s Principle

A change in concentration, volume, or pressure moves Q away from K without changing K. The system then shifts to bring Q back to K. Thinking in terms of Q replaces memorized “shifts left, shifts right” rules with one test that always works, and it is the reasoning free-response answers are expected to show. Only a change in temperature changes K itself. The stress-by-stress rules are collected in AP Chemistry Le Chatelier’s principle.

Worked Example 1: Writing Q for Three Reactions

Write the reaction quotient for each reaction.

(a) 2SO2(g) + O2(g) ⇌ 2SO3(g): Qc = [SO3]2 / ([SO2]2[O2])
(b) CaCO3(s) ⇌ CaO(s) + CO2(g): Qp = PCO2; both solids are left out.
(c) NH3(aq) + H2O(l) ⇌ NH4+(aq) + OH−(aq): Q = [NH4+][OH−] / [NH3]; liquid water is left out.

Coefficients become exponents, and every species that is a pure solid or liquid drops out, in Q just as in K.

Worked Example 2: Predicting the Direction for N₂O₄ and NO₂

N2O4(g) ⇌ 2NO2(g) has Kc = 4.6 × 10−3 at 25°C. A flask contains [N2O4] = 0.050 M and [NO2] = 0.030 M. Which way does the reaction go?

Q: (0.030)2 ÷ 0.050 = 0.00090 ÷ 0.050 = 1.8 × 10−2.
Compare: Q (1.8 × 10−2) > K (4.6 × 10−3).
Direction: the reaction runs in reverse, turning brown NO2 into colorless N2O4, so the brown color fades until Q falls to K.

This is mixture B in Fig. 1. Mixture A, with [N2O4] = 0.20 M and [NO2] = 0.010 M, has Q = 5.0 × 10−4, below K, so it shifts forward instead.

Worked Example 3: Finding Q From Moles in a Flask

PCl5(g) ⇌ PCl3(g) + Cl2(g) has Kc = 0.042 at a certain temperature. A 2.0 L flask contains 0.40 mol PCl5, 0.10 mol PCl3, and 0.10 mol Cl2. Which way does the reaction go?

Concentrations: [PCl5] = 0.40 ÷ 2.0 = 0.20 M; [PCl3] = [Cl2] = 0.10 ÷ 2.0 = 0.050 M.
Q: (0.050)(0.050) ÷ 0.20 = 0.0125, about 0.013.
Compare: Q (0.013) < K (0.042), so the reaction shifts forward, decomposing more PCl5.

Convert moles to concentrations first. Plugging moles straight in gives 0.025, a different number, because this reaction has more moles of gas on one side. To go on and find the equilibrium concentrations, set up an ICE table in the direction Q tells you.

Worked Example 4: Using Q to Explain a Dilution Shift

Fe3+(aq) + SCN−(aq) ⇌ FeSCN2+(aq) is at equilibrium. The solution is diluted with water to twice its volume. Which way does the equilibrium shift?

Effect on concentrations: every concentration is cut in half the moment the water is added.
New Q: (½[FeSCN2+]) ÷ [(½[Fe3+])(½[SCN−])] = 2 × K.
Direction: Q > K, so the reaction shifts in reverse, toward the side with more dissolved particles, until Q falls back to K.

The red color fades by more than dilution alone would cause. The same algebra explains why compressing a gas mixture shifts it toward fewer moles of gas.

Five Reaction Quotient Practice Questions With Answers

  1. Write Qp for 2NO(g) + O2(g) ⇌ 2NO2(g).
    Show answerQp = (PNO2)2 / [(PNO)2(PO2)].
  2. For H2(g) + CO2(g) ⇌ H2O(g) + CO(g), K = 0.64. A mixture has [H2] = [CO2] = 0.20 M and [H2O] = [CO] = 0.10 M. Which way does it shift?
    Show answerQ = (0.10)(0.10) ÷ [(0.20)(0.20)] = 0.25. Q < K, so it shifts forward.
  3. What is true about a system when Q = K?
    Show answerIt is at equilibrium: the forward and reverse rates are equal, so there is no net change in any concentration.
  4. Ksp for Ag2CrO4 is 1.1 × 10−12. Solutions are mixed so that [Ag+] = 2.0 × 10−4 M and [CrO42−] = 1.0 × 10−4 M. Does a precipitate form?
    Show answerQ = (2.0 × 10−4)2(1.0 × 10−4) = 4.0 × 10−12. Q > Ksp, so solid Ag2CrO4 precipitates.
  5. N2O4(g) ⇌ 2NO2(g) is at equilibrium when the volume is suddenly halved. Use Q to predict the shift.
    Show answerEvery concentration doubles, so Q = (2[NO2])2 ÷ (2[N2O4]) = 2K. Q > K, so it shifts in reverse, toward fewer moles of gas.

Common Reaction Quotient Mistakes

  • Using moles instead of concentrations when the volume is not 1 L.
  • Including solids or liquids in Q.
  • Getting the direction backward. Q < K means too little product, so the reaction moves forward.
  • Saying a stress changes K. Only temperature changes K; everything else changes Q.
  • Forgetting the exponents from the coefficients.
  • Mixing concentrations and pressures in the same expression.

Q also appears in solubility questions, where Q > Ksp means a precipitate forms (see AP Chemistry Ksp and molar solubility), and in electrochemistry through the Nernst equation. To see how stronger equilibrium answers could move your overall estimate, try the AP Chem Score Calculator.

Frequently Asked Questions

What is the reaction quotient?

The reaction quotient, Q, has the same form as the equilibrium constant expression (products over reactants, each raised to its coefficient), but it uses the concentrations or pressures present at any moment, not only at equilibrium. Comparing Q with K tells you which way the reaction will go.

What is the difference between Q and K?

K uses equilibrium concentrations and is constant at a given temperature. Q uses whatever concentrations are present right now, so it changes as the reaction runs. When Q equals K, the system is at equilibrium.

What happens when Q is less than K?

There is too little product compared with equilibrium, so the forward reaction is faster than the reverse until Q rises to K. The reaction shifts toward products. When Q is greater than K, it shifts toward reactants instead.

Do solids and liquids appear in the reaction quotient?

No. Just as in K, pure solids and pure liquids are left out of Q because their concentrations do not change. Only gases (as concentrations or partial pressures) and aqueous species appear.

Does adding a reactant change K?

No. Adding or removing a substance, or changing the volume, changes Q, not K. Only a change in temperature changes the value of K.

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