AHL: Reaction quotient

IB Chemistry HL· 30 min read

1. Definition and Expression of the Reaction Quotient★★☆☆☆⏱ 15 min

📘 Definition

Reaction Quotient

$Q$ , or $Q_{c}$ for concentration, $Q_{p}$ for partial pressure

A dimensionless quantity that describes the ratio of product to reactant concentrations (or partial pressures) at any given point in a reversible reaction, regardless of whether equilibrium has been reached.

Example:

For the general reaction $a A + b B ⇌ c C + d D$ , $Q_{c} = \frac{[ C ] ^{c} [ D ] ^{d}}{[ A ] ^{a} [ B ] ^{b}}$ where $[X]$ = concentration of $X$ at time $t$ .

The reaction quotient has the exact same form as the equilibrium constant $K_{c}$ . The only fundamental difference is that $K_{c}$ is only calculated from concentrations at equilibrium, while $Q$ can be calculated at any time during the reaction.

📐 Worked Example

Write the reaction quotient expression $Q_{c}$ for the reversible reaction: $2 S O_{2 (g)} + O_{2 (g)} ⇌ 2 S O_{3 (g)}$

1
Recall the general form of $Q_{c}$ :
2
$Q_c = \frac{[C]^c[D]^d}{[A]^a[B]^b}$
3
Where exponents equal the stoichiometric coefficients of each species, and products go in the numerator, reactants in the denominator.
4
Substitute the species and coefficients from the given reaction:
5
$Q_c = \frac{[SO_3]^2}{[SO_2]^2[O_2]}$

Exam tip:

Always match exponents to the balanced equation's stoichiometric coefficients, never use 1 for all exponents by default.

2. Predicting Reaction Direction from $Q$ vs $K$★★★☆☆⏱ 20 min

The primary application of the reaction quotient is to predict which direction a reaction will proceed to reach equilibrium. By comparing the calculated $Q$ to the known equilibrium constant $K$ at the same temperature, we get three clear outcomes:

If $Q < K$ : The product concentration term is too small. The reaction proceeds forward to make more products, increasing $Q$ until $Q = K$ .
If $Q > K$ : The product concentration term is too large. The reaction proceeds reverse to make more reactants, decreasing $Q$ until $Q = K$ .
If $Q = K$ : The reaction is already at equilibrium, with no net change in concentrations.

📐 Worked Example

For the reaction $N_{2} (g) + 3 H_{2} (g) ⇌ 2 N H_{3} (g)$ , $K_{c} = 0.064$ at 450°C. A reaction mixture has $[N_{2}] = 1.00$ M, $[H_{2}] = 0.50$ M, $[N H_{3}] = 0.25$ M. Calculate $Q_{c}$ and predict the direction of reaction.

1
Write the correct $Q_{c}$ expression from the balanced equation:
2
$Q_c = \frac{[NH_3]^2}{[N_2][H_2]^3}$
3
Substitute the given concentration values into the expression:
4
$Q_c = \frac{(0.25)^2}{(1.00)(0.50)^3} = \frac{0.0625}{0.125} = 0.5$
5
Compare $Q_{c}$ to $K_{c}$ : $0.5 > 0.064$ , so $Q_{c} > K_{c}$ . When $Q > K$ , the reaction proceeds in the reverse direction to produce more reactants.

Exam tip:

Double-check arithmetic for exponents, as a small calculation error can reverse your prediction.

3. $Q$ and Disturbances to Equilibrium★★★☆☆HL only⏱ 15 min

When a system at equilibrium is disturbed by a change in concentration, pressure, or volume (at constant temperature), the value of $Q$ changes immediately, while $K$ remains unchanged. Comparing the new $Q$ to the original $K$ confirms the direction of shift predicted by Le Chatelier's principle.

📐 Worked Example

The reaction $H_{2} (g) + I_{2} (g) ⇌ 2 H I (g)$ is at equilibrium, so $Q = K_{c}$ . Additional $H_{2}$ is added to the vessel at constant temperature. Use $Q$ to predict the direction of shift.

1
At original equilibrium:
2
$Q_{original} = \frac{[HI]^2}{[H_2]_{original}[I_2]} = K_c$
3
After adding $H_{2}$ , $[H_{2}]$ immediately increases, so the denominator of $Q$ becomes larger:
4
$Q_{new} = \frac{[HI]^2}{[H_2]_{new}[I_2]}$
5
A larger denominator means $Q_{n e w} < K_{c}$ . Temperature is constant so $K_{c}$ does not change. Since $Q < K$ , the reaction shifts forward to produce more $H I$ , which matches Le Chatelier's prediction.

4. Common Pitfalls

Wrong move:

Claiming reaction proceeds forward when $Q > K$ , reverse when $Q < K$ .

Why:

Confusing which term is too large: $Q > K$ means product concentration is too high, not too low.

Correct move:

$Q < K$ → forward direction; $Q > K$ → reverse direction.

Wrong move:

Using experimental rate law exponents instead of stoichiometric coefficients for $Q$ .

Why:

Mixing up the form of rate laws and equilibrium expressions.

Correct move:

$Q$ exponents always match the stoichiometric coefficients from the balanced equation.

Wrong move:

Changing the value of $K$ after a concentration change, and comparing new $K$ to old $Q$ .

Why:

Confusing the factors that change $Q$ vs $K$ .

Correct move:

Only temperature changes $K$ . All other disturbances change $Q$ , not $K$ .

Wrong move:

Putting reactants in the numerator and products in the denominator of the $Q$ expression.

Why:

Reversing the order from memory, especially in exam pressure.

Correct move:

Always products over reactants, raised to their stoichiometric coefficients.

5. Quick Reference Cheatsheet

Condition	Reaction Direction	Key Note
$Q < K$	Forward (→)	More products needed, $Q$ increases to $K$
$Q > K$	Reverse (←)	More reactants needed, $Q$ decreases to $K$
$Q = K$	At equilibrium	No net change in concentrations
Same expression as $K$	All cases	$Q$ = any time, $K$ = only equilibrium
Only $T$ changes $K$	All disturbances	Concentration/pressure change $Q$ only

When this came up on past exams

AI-estimated based on syllabus patterns — cross-check with official past papers for accuracy. Use only as revision-focus signals.

2025 · 2
Calculate Q and predict direction
2023 · 1
Compare Q and K after concentration change
2021 · 2
Confirm equilibrium shift with Q

Going deeper

syllabusIB Chemistry HL 2025 SyllabusOfficial AHL equilibrium topic reference

What's Next

Mastering the reaction quotient is a critical foundation for all advanced equilibrium topics in IB Chemistry HL. The ability to predict reaction direction from $Q$ is used across acid-base equilibria, solubility equilibria, and Gibbs free energy calculations for non-spontaneous reactions. It also provides a quantitative confirmation of Le Chatelier's qualitative predictions for equilibrium shifts, which is often tested in extended response questions. Your next steps build directly on this concept to solve more complex equilibrium problems.