Rate equations, orders and rate constants

Key definitions (spec 11.1)

• Rate of reaction: the change in concentration of a reactant or product per unit time, in mol dm^-3 s^-1.
• Rate equation: rate = k[A]^m[B]ⁿ, where m and n are the orders with respect to A and B.
• Order with respect to a reactant: the power to which its concentration is raised in the rate equation.
• Overall order: the sum of the individual orders, m + n.
• Rate constant, k: the constant of proportionality in the rate equation. It changes only with temperature (and with a catalyst).

What each order means

• Zero order: changing the concentration has no effect on the rate.
• First order: doubling the concentration doubles the rate.
• Second order: doubling the concentration multiplies the rate by 2² = 4.

Orders are usually 0, 1 or 2 and are found by experiment. They cannot be read from the balanced equation, because the equation shows the overall change, not the steps.

Units of k

Rearrange the rate equation and cancel units.

Calculating k

Substitute one set of rate and concentration data into the rate equation and solve for k. Keep the units by cancelling: for rate = k[A][B], k = rate / ([A][B]) = (mol dm^-3 s^-1) / (mol dm^-3)² = dm³ mol^-1 s^-1.

Worked example

For rate = k[NO]²[O2], the rate is 7.20 x 10^-3 mol dm^-3 s^-1 when [NO] = 0.0200 mol dm^-3 and [O2] = 0.0300 mol dm^-3. Find k with units.

1. k = rate / ([NO]²[O2]) = 7.20 x 10^-3 / (0.0200² x 0.0300)
2. = 7.20 x 10^-3 / 1.20 x 10^-5 = 600
3. Overall order 3, so units dm⁶ mol^-2 s^-1

Answer: k = 600 dm⁶ mol^-2 s^-1

Check yourself

1. For rate = k[A]²[B], what is the overall order of reaction?
   Show answer

   3. Overall order = 2 + 1 = 3.

2. What are the units of k for a reaction that is second order overall?
   • dm³ mol^-1 s^-1
   • s^-1
   • mol dm^-3 s^-1
   • dm⁶ mol^-2 s^-1
   Show answer

   dm³ mol^-1 s^-1. k = rate / [A]² = (mol dm^-3 s^-1) / (mol² dm^-6) = dm³ mol^-1 s^-1.

3. For rate = k[A][B]², k = 0.0450 dm⁶ mol^-2 s^-1. Calculate the rate when [A] = 0.200 mol dm^-3 and [B] = 0.100 mol dm^-3.
   Show answer

   9.0 x 10^-5 mol dm^-3 s^-1. rate = 0.0450 x 0.200 x 0.100² = 9.0 x 10^-5 mol dm^-3 s^-1.

4. A reaction is second order with respect to X. By what factor does the rate increase when [X] is tripled and everything else is kept the same?
   Show answer

   9. Rate is proportional to [X]², so the factor is 3² = 9.

5. A reaction is zero order with respect to Y. What does this mean?
   • Y does not take part in the reaction
   • The rate is zero when [Y] is doubled
   • Y is a catalyst
   • Changing [Y] has no effect on the rate
   Show answer

   Changing [Y] has no effect on the rate. [Y]⁰ = 1, so the rate does not depend on [Y]. Y still reacts, but not in the slow step.

6. For rate = k[A][B], the rate is 3.6 x 10^-4 mol dm^-3 s^-1 when [A] = 0.020 mol dm^-3 and [B] = 0.030 mol dm^-3. Calculate k.
   Show answer

   0.60 dm³ mol^-1 s^-1. k = 3.6 x 10^-4 / (0.020 x 0.030) = 0.60 dm³ mol^-1 s^-1.

7. Which change alters the value of the rate constant k for a reaction?
   • Doubling the concentration of a reactant
   • Increasing the volume of solution
   • Removing some product
   • Raising the temperature
   Show answer

   Raising the temperature. k depends on temperature (and on using a catalyst), not on concentrations.

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Sources

• Pearson Edexcel IAL Chemistry (2018) specification
• Pearson Edexcel IAL Chemistry (2018) scheme of work

Last updated 7 November 2026. Spotted a mistake? Tell us.