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Chemical Kinetics

14 min read

Rate of reaction

Chemical kinetics studies how fast reactions go. The rate is the change in concentration of a reactant or product per unit time (mol dm⁻³ s⁻¹). It is found from the gradient of a concentration–time graph. The rate depends on concentration, temperature, surface area, catalysts and light.

Rate equations and order

k is the rate constant; m and n are the orders with respect to A and B and are found by experiment, not from the balanced equation. The overall order is m + n.
OrderIf the concentration doubles, the rate…Graph of rate against concentration
Zerodoes not changeHorizontal line
FirstdoublesStraight line through the origin
SecondquadruplesUpward curve
Worked exampleFind the order

In an experiment the initial rate is 2.0 × 10⁻³ mol dm⁻³ s⁻¹ when [A] = 0.10 mol/dm³ and 8.0 × 10⁻³ when [A] = 0.20 mol/dm³. What is the order with respect to A and the rate constant?

  1. Doubling [A] multiplies the rate by 4, so the reaction is second order in A.
  2. Rate = k[A]²; use the first experiment.

Answer: Second order, k = 0.20 dm³ mol⁻¹ s⁻¹.

The half-life is the same each time: here about 2.3 seconds.

For a first-order reaction the half-life (the time for the concentration to halve) is constant: t½ = 0.693 ÷ k.

Collision theory, activation energy and temperature

For a reaction to occur, particles must collide with at least the activation energy Eₐ and with the correct orientation. Increasing the temperature gives the particles more energy, so a much larger fraction of the collisions are successful. A rise of 10 °C often doubles the rate. A catalyst gives a different route with a lower activation energy and is not used up.

Maxwell–Boltzmann distributionA graph of the number of molecules against their energy. At the lower temperature the curve is tall and narrow. At the higher temperature it is lower and wider, so more molecules have energy above the activation energy shown by the vertical line, and the reaction is faster.energy of moleculesnumber of moleculesactivation energy EₐT₁ (lower)T₂ (higher)more molecules above Eₐ
The Arrhenius equation: R = 8.314 J mol⁻¹ K⁻¹ and T is in kelvin. A graph of ln k against 1/T is a straight line of gradient −Eₐ/R.
Try itHow temperature changes the rate

Choose the activation energy and a temperature. See how many times faster the reaction is than at 300 K.

Catalysis

TypeDescriptionExample
HomogeneousCatalyst in the same phase as the reactantsH⁺ in ester hydrolysis
HeterogeneousCatalyst in a different phase; reactants adsorb on the surfaceIron in the Haber process, V₂O₅ in the contact process
EnzymesBiological catalysts, very specific and sensitive to temperature and pHAmylase, catalase
Check yourself The rate of a reaction is first order in A. When [A] triples the rate…
Check yourself A catalyst increases the rate because it…
Check yourself The half-life of a first-order reaction is 20 s. How long for 75% to react?

Key terms

Rate constant
The constant k in the rate equation, dependent on temperature.
Order of reaction
The power to which a concentration is raised in the rate equation.
Activation energy
The minimum energy that colliding particles need for a reaction.
Half-life
The time for the concentration of a reactant to fall by half.

Summary

  • Rate = k[A]ᵐ[B]ⁿ; orders are found by experiment.
  • First-order half-life t½ = 0.693 ÷ k.
  • Collision theory: only collisions with energy ≥ Eₐ and the right orientation react.
  • Arrhenius: k = A e^(−Eₐ/RT); catalysts lower Eₐ.
Chemical Equilibrium Electrochemistry