Rate and rate law

MDCAT Chemistry · Chemistry · Reaction kinetics. The idea in plain words, the rules to remember, the mistake to avoid and a worked example, written and checked by Mega Lecture.

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The idea

The rate of reaction is the change in concentration of a reactant or product per unit time. It is greatest at the start and falls as the reactants are used up. The rate at one instant is the gradient of the tangent to the concentration–time curve.

The rate law shows how the rate depends on concentration. The powers in it are the orders. They are found only by experiment and cannot be read from the balanced equation.

Reactions between ions in solution are very fast because no bonds need to be broken first. Most reactions of covalent molecules are slow or moderate. A rate is followed by measuring any property that changes with concentration.

Rules to remember

Common mistake

Students take the orders from the coefficients in the balanced equation. Orders come only from experimental data: compare two experiments in which just one concentration changes.

Worked example

For A + B → products, doubling [A] alone doubles the rate, and doubling [B] alone makes the rate 4 times as great. When [A] = 0.10 and [B] = 0.20 mol dm−3 the rate is 2.0 × 10−3 mol dm−3 s−1. What is the value of k?

  1. Rate × 2 when [A] × 2: first order in A. Rate × 4 = 22 when [B] × 2: second order in B.
  2. Rate law: rate = k[A][B]2, third order overall.
  3. k = rate ÷ ([A][B]2) = (2.0 × 10−3) ÷ (0.10 × 0.202) = (2.0 × 10−3) ÷ (4.0 × 10−3) = 0.50.

Answer: k = 0.50 dm6 mol−2 s−1

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