AP Chemistry · Lesson 1

Rate laws and the collision model

Know Know it

The rate of a reaction is the change in concentration per unit time, usually in M/s. A rate law links the rate to concentrations: rate = k[A]^m[B]^n. The exponents m and n are the orders, and their sum is the overall order. Orders are found by experiment. They are often not the coefficients of the balanced equation.

The rate constant k is fixed at one temperature. Its units make the rate come out in M/s, so they depend on the overall order.

The collision model explains rates. Particles react only when they collide with energy at least equal to the activation energy and with a suitable orientation. Higher concentration means more collisions per second. Higher temperature means faster particles and, more importantly, a much larger fraction of collisions with enough energy.

Units of k for each overall order (concentration in M, time in s)
Overall orderRate law exampleUnits of k
0rate = kM s⁻¹
1rate = k[A]s⁻¹
2rate = k[A]² or k[A][B]M⁻¹ s⁻¹
3rate = k[A]²[B]M⁻² s⁻¹

Worked example Easy

For a fictional reaction 2P(g) + 2Q(g) → R(g) + 2S(g), experiments give rate = k[P][Q]². If [P] is tripled while [Q] stays the same, how does the rate change?

  1. It increases by a factor of 9
  2. It triplesAnswer
  3. It increases by a factor of 27
  4. It stays the same

How to solve it

  1. Read the order of P from the rate law, not the equation: it is 1.
  2. Rate ratio = (concentration ratio)^order = 3¹ = 3.
  3. The rate triples.

Why each choice is right or wrong

  • A. Incorrect. A factor of 9 would mean P is second order, as its coefficient of 2 suggests; the rate law shows P is first order.
  • B. Correct. P is first order in the rate law, so tripling [P] multiplies the rate by 3¹ = 3.
  • C. Incorrect. A factor of 27 would need P to be third order; only the exponent on [P] matters here, and it is 1.
  • D. Incorrect. The rate would stay the same only if P were zero order, but [P] appears in the rate law with an exponent of 1.

Trap Orders are not coefficients

Do not write a rate law by copying coefficients from the balanced overall equation. Only experimental data, or the rate-determining step of a mechanism, give the orders.

Explain Explain it

Task verbs: determine, justify

To find an order from a table, pick two trials in which only that one concentration changes. Then (rate 2 ÷ rate 1) = (conc 2 ÷ conc 1)^order. If doubling a concentration doubles the rate, the order is 1; if it makes the rate 4 times larger, the order is 2; if the rate does not change, the order is 0.

Once you have every order, put one trial's numbers into the rate law and solve for k. Write k with units, found from the overall order.

Worked example Medium

A student measures the initial rate of the reaction A + B → products at constant temperature.

Initial-rate data for A + B → products

Trial[A] (M)[B] (M)Initial rate (M/s)
10.100.201.6 × 10⁻³
20.200.203.2 × 10⁻³
30.100.406.4 × 10⁻³

What is the rate constant, k, with its units?

  1. 0.080 M⁻¹ s⁻¹
  2. 0.80 M⁻² s⁻¹
  3. 0.40 M⁻² s⁻¹Answer
  4. 0.40 M⁻¹ s⁻¹

How to solve it

  1. Trials 1 and 2: [A] doubles, rate doubles, so A is first order.
  2. Trials 1 and 3: [B] doubles, rate is 4 times larger, so B is second order. Rate = k[A][B]².
  3. k = 1.6 × 10⁻³ M/s ÷ (0.10 M × 0.040 M²) = 0.40 M⁻² s⁻¹.

Why each choice is right or wrong

  • A. Incorrect. 0.080 M⁻¹ s⁻¹ treats B as first order; trials 1 and 3 show the rate rising 4 times when [B] doubles, so B is second order.
  • B. Incorrect. 0.80 M⁻² s⁻¹ swaps the orders (A second, B first); trials 1 and 2 show the rate only doubling when [A] doubles.
  • C. Correct. Rate = k[A][B]²: from trial 1, k = 1.6 × 10⁻³ ÷ (0.10 × 0.20²) = 0.40, and a third-order rate law gives k in M⁻² s⁻¹.
  • D. Incorrect. The number 0.40 is right, but M⁻¹ s⁻¹ are the units for a second-order reaction; this rate law is third order overall.

Determine Your turn

In two trials of a reaction between X and Y, [X] is held at 0.050 M. When [Y] is raised from 0.10 M to 0.30 M, the initial rate rises from 1.5 × 10⁻³ M/s to 1.35 × 10⁻² M/s. Determine the order of the reaction with respect to Y, and support it with these data.

Write it, then compare. Nothing you type here is saved or graded.

Compare with a model answer

A full answer does this

  • Gives second order with respect to Y
  • Supports the order by showing the rate rises by a factor of 9 when [Y] triples, and 9 = 3²

Model answer

The reaction is second order with respect to Y. While [X] stays the same, [Y] increases by a factor of 0.30 ÷ 0.10 = 3, and the rate increases by a factor of (1.35 × 10⁻²) ÷ (1.5 × 10⁻³) = 9. Since 3² = 9, the order in Y is 2.

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