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Introduction to rate law

You cannot read a rate law off the balanced equation, no matter how tempting. The orders come from watching what the rate actually does when you change a concentration in the lab.

§1

The rate law and its orders.

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A rate law writes the rate as rate = k[A]m[B]n. The exponents m and n are the orders with respect to each reactant, and k is the rate constant. The overall order is the sum of the exponents.

The orders are determined experimentally, by measuring how the rate responds when one concentration is changed. They are not read from the balanced equation's coefficients (except, later, for a single elementary step).

The order tells how the rate responds to a concentration. For a reactant that is first order, doubling its concentration doubles the rate; second order, doubling it quadruples the rate; zero order, changing it does nothing.

UNIT 5 TOPIC 5.2 • INTRODUCTION TO RATE LAW RATE LAW FINDER THE RATE LAW rate = k[A]m[B]n ★ Orders m and n are found EXPERIMENTALLY (from initial-rate data) — not from the balanced coefficients. Trial [A] (M) [B] (M) rate (M·s⁻¹) 1 0.10 0.10 2.0×10⁻³ 2 0.20 0.10 8.0×10⁻³ 3 0.20 0.20 1.6×10⁻² READING THE ORDERS OFF THE DATA Trial 1→2: [A] ×2, [B] fixed → rate ×4 2m = 4 → m = 2 Trial 2→3: [B] ×2, [A] fixed → rate ×2 2n = 2 → n = 1 rate = k[A]²[B] Overall order = m + n = 2 + 1 = 3 WHAT k IS k is the rate constant of the reaction. Its units depend on the overall order. Its value changes with temperature. ORDER SUMMARY [A] doubles → rate ×4 ⇒ m = 2 (2nd order in A) [B] doubles → rate ×2 ⇒ n = 1 (1st order in B) rate carries units M·s⁻¹ (set by overall order) CED ANCHOR Reaction orders (m, n) must be determined EXPERIMENTALLY from initial-rate data — they cannot be read off the coefficients of the balanced equation. AP Chemistry · Unit 5 · Kinetics
Fig. 5.2.1 A rate law, rate = k[A]^m[B]^n, is found from experiment. Compare trials to see how the rate responds when a concentration changes: that response gives each reactant's order. Orders come from data, never from the balanced coefficients.
§2

Finding orders from data.

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Change one concentration at a time and watch the rate.

  1. Compare two trials. Find trials where only one concentration changes; hold the others fixed.
  2. See how the rate responds. If doubling a concentration doubles the rate, it is first order; quadruples, second order; unchanged, zero order.
  3. Assign each order. Repeat for each reactant to get all the exponents.
  4. Solve for k. Substitute a trial's rate and concentrations into the rate law and solve for the rate constant.
§3

The pieces you'll meet.

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A short glossary for rate laws.

rate law
Rate law
rate = k[A]^m[B]^n, from experiment.
order
Order
The exponent on a concentration; how the rate depends on it.
k
Rate constant
The proportionality constant in the rate law.
overall
Overall order
The sum of the individual orders.
response
Rate response
First order: doubling doubles; second: doubling quadruples; zero: no change.
not coeff
Not coefficients
Orders come from data, not from balanced coefficients.
§4

Worked example: find the orders from trials.

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Data. When [A] doubles (B fixed), the rate doubles. When [B] doubles (A fixed), the rate quadruples.

Order in A. Doubling [A] doubles the rate → first order in A (exponent 1).

Order in B. Doubling [B] quadruples the rate → second order in B (exponent 2).

Rate law. rate = k[A][B]², overall order 3. Notice these exponents came from the data, not from any coefficients in the balanced equation.

§5

Mistakes that cost real points.

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Pitfall · 01

"The orders in the rate law are just the coefficients from the balanced equation."

Orders are determined experimentally and generally do not match the coefficients (except for a single elementary step). A reaction 2A + B → products can be first order in A, or zero order in B — only data can tell.

Fix. Find orders from experiment (how the rate responds to concentration), not by copying coefficients from the overall equation.

Pitfall · 02

"Doubling the concentration always doubles the rate."

That is true only for a reactant that is first order. For a second-order reactant, doubling quadruples the rate; for zero order, doubling does nothing. The response depends on the order.

Fix. Use the order: first order → ×2, second order → ×4, zero order → ×1, when a concentration doubles.

Pitfall · 03

"The rate constant k changes when you change the concentration."

k is a constant at a given temperature; it does not change when concentrations change (only the rate does). Changing concentration changes the rate through the rate law, while k stays fixed.

Fix. Hold k constant at fixed temperature; only concentrations (and thus the rate) change during a run.

§6

Skill Check.

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