🎓 Prepared by students from Boğaziçi University

What is a Rate Law?

A rate law is a mathematical expression that relates the reaction rate to the concentrations of reactants. It has the form: rate = k[A]^m[B]^n, where the exponents m and n are determined experimentally, not from stoichiometry.

Short answer

Rate law expresses how reaction rate depends on reactant concentration. The rate constant k is specific to temperature. The reaction order m (for [A]) and n (for [B]) are found by fitting experimental data — they do NOT equal stoichiometric coefficients.

First-order vs second-order rate dependence

x: [Reactant] concentration (M) · y: Reaction rate (M/s)First-order: rate = k[A]Second-order: rate = k[A]²

Try it: interactive calculator

Reaction rate

1M/s

= 1 * (1 ** 1) * (1 ** 1)

Rate constant1 L^(m+n-1)/mol^(m+n-1)/s[A] concentration1 MOrder in [A]1 [B] concentration1 MOrder in [B]1

Step-by-step worked examples

For the reaction 2A + B → products, the rate law is found to be: rate = k[A][B]². Find the rate if k = 0.5 M⁻²s⁻¹, [A] = 0.2 M, [B] = 0.1 M.

rate = k[A][B]²
rate = (0.5)(0.2)(0.1)²
rate = (0.5)(0.2)(0.01)
rate = 0.001 M/s = 1.0 × 10⁻³ M/s

Reactant concentration is doubled. If reaction is first-order in [A], what happens to rate?

First-order: rate = k[A]¹ = k[A]
If [A] doubles: new rate = k(2[A]) = 2k[A]
Rate also doubles (×2)

For a second-order reaction in [A], if [A] is tripled, how does rate change?

Second-order: rate = k[A]²
If [A] triples: new rate = k(3[A])² = 9k[A]²
Rate increases nine-fold (×9)

Flashcards

Quick quiz

Q1.For rate = k[A]²[B], the order in [A] is:

Correct answer: C. The exponent of [A] is 2, so the order in [A] is 2 (second-order).

Q2.If a reaction is first-order in A and the rate law is rate = k[A], doubling [A] results in:

Correct answer: C. First-order: rate ∝ [A]. Double [A] → double rate.

Q3.For rate = k[X]³, if [X] is doubled, rate increases by factor of:

Correct answer: C. rate = k[X]³. If [X] → 2[X]: rate = k(2[X])³ = 8k[X]³. Factor is 8.

Q4.Rate constant k has units that depend on:

Correct answer: B. Units of k = (concentration)^(1−overall order) × (time)^(−1). Order determines k's units.

📄Download this topic as a printable worksheet (PDF)Summary + 10 questions + answer key — print it, share it in class.↓

Study better with Bounlu apps

Notek

The full card deck, worked steps and AI-tutor support for “What is a Rate Law?” are in Notek — study by hand before your exam.

Get it free

PromyNever miss an exam or homework deadline with Promy: AI turns the dates in your inbox into reminders automatically.

Common mistakes

✗

Assuming rate law exponents equal stoichiometric coefficients. — Correct: Exponents are found experimentally — they rarely equal coefficients.

✗

Writing rate law for a reaction without experimental data. — Correct: Rate law MUST be determined experimentally; never predict it from equation.

✗

Forgetting that k changes with temperature. — Correct: k is temperature-dependent; rate law is valid only at a given temperature.

✗

Confusing 'order in [A]' with total order. — Correct: Order in [A] = exponent m; total order = m + n.

FAQ

What is the general form of a rate law?

rate = k[A]^m[B]^n, where k is the rate constant, m and n are exponents determined experimentally.

How do you determine a rate law?

Experimentally — measure initial rates at different concentrations and find the exponents that fit the data.

What is the difference between zero-order, first-order, and second-order?

Zero-order: rate = k (independent of [A]). First-order: rate ∝ [A]. Second-order: rate ∝ [A]².

Can a rate law exponent be a fraction?

Yes — fractional exponents are possible for complex or chain reactions.