Reaction kinetics: Class 11 Chemistry

Key points

Chemical kinetics studies how fast reactions go and the factors that affect their speed. The rate of reaction is the change in concentration of a reactant or product per unit time. Its unit is mol dm⁻³ s⁻¹. Reactant concentration falls with time and product concentration rises, so the rate is written with a minus sign for reactants and a plus sign for products to keep it positive.

The average rate is found over a time interval, for example rate = −Δ[A]/Δt. The instantaneous rate is the rate at one moment and is found from the slope of the tangent to the concentration against time curve. Rates are fast at the start and slow down as reactants are used up. For a reaction such as 2N₂O₅ → 4NO₂ + O₂, the rates of the species are linked by their coefficients.

Rates are measured by following a property that changes with time: volume of gas evolved, change in mass, colour intensity with a colorimeter, pressure or conductivity, or by titrating small samples taken at intervals. The method must suit the reaction.

The rate law (rate equation) expresses the rate in terms of concentrations of reactants raised to powers found by experiment: rate = k[A]ᵐ[B]ⁿ. The powers m and n are not necessarily the coefficients in the balanced equation. The order of reaction is the sum of the powers (m + n). The order can be zero, a whole number or a fraction.

The rate constant k is the rate when all concentrations are 1 mol dm⁻³. It depends on temperature and catalyst but not on concentration. Its units depend on the order:

• Zero order: mol dm⁻³ s⁻¹
• First order: s⁻¹
• Second order: dm³ mol⁻¹ s⁻¹
• General: (mol dm⁻³)^(1 − n) s⁻¹ for order n

Molecularity is the number of molecules colliding in the elementary step of a reaction. It is always a small whole number (1, 2 or at most 3) and applies to a single step. Order is found by experiment and can be zero or fractional. Many reactions occur in several steps, called the reaction mechanism, and the slowest step, the rate determining step, controls the overall rate. For a one step reaction, order and molecularity can be the same.

A first order reaction has rate = k[A]. The half-life t½ is the time for the concentration of a reactant to fall to half of its initial value. For first order, t½ = 0.693/k, which does not depend on the initial concentration. For zero order, t½ = [A]₀/2k and for second order t½ = 1/(k[A]₀). Radioactive decay and the decomposition of H₂O₂ are first order. After n half-lives the amount left is (1/2)ⁿ of the original.

Collision theory says that a reaction occurs only when reacting particles collide with sufficient energy and with a correct orientation. Most collisions are not effective. The minimum energy needed is the activation energy Ea. Raising concentration raises the number of collisions per second, so the rate increases. In the transition state theory, colliding molecules form an unstable activated complex at the top of the energy barrier before the products form.

An energy profile diagram plots the potential energy against the progress of reaction. Reactants are at one level, the peak is the activated complex, and products are at another level. Ea is the height from reactants to the peak. The difference in energy between products and reactants is ΔH. A low activation energy means a fast reaction.

Temperature: a rise of 10 °C roughly doubles or triples the rate for many reactions. At higher temperature more molecules have energy equal to or above Ea, and collisions are more frequent. The Arrhenius equation k = A e^(−Ea/RT) shows that k increases with temperature and decreases with Ea. Here A is the frequency factor and R is the gas constant.

Other factors: a larger concentration or pressure for gases increases the rate; a finer powder has a larger surface area and reacts faster; light speeds up photochemical reactions such as H₂ with Cl₂. The nature of reactants also matters. Ionic reactions in solution are very fast, while reactions that break strong covalent bonds are slow.

A catalyst changes the rate without being used up. It provides a new path with a lower activation energy, so more molecules can react. It does not change ΔH or the position of equilibrium. Positive catalysts speed up reactions (MnO₂ with KClO₃, iron in the Haber process), while inhibitors slow them. Enzymes are biological catalysts, and a poison reduces a catalyst's activity.

Study tip: Derive units of k by putting units into the rate law each time instead of memorising them blindly. Learn to draw the energy profile diagram with and without a catalyst, labelling Ea and ΔH. For half-life questions, count half-lives first, then use the fraction (1/2)ⁿ.

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Common mistakes

• Writing the order from the coefficients in the balanced equation. The order must be found from experiment.
• Saying that the rate constant changes with concentration. It changes with temperature and catalyst only.
• Giving the wrong unit for k. The unit changes with order, so derive it from rate = k[A]ⁿ.
• Saying a catalyst gives the reaction more energy. It lowers the activation energy.
• Using t½ = 0.693/k for reactions that are not first order.

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