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Chemistry 2 Unit 2: Chemical kinetics

Kinetics studies how fast reactions happen and why, through rate laws, activation energy and reaction mechanisms.

Covers: Reaction rates, rate laws and orders, integrated rate laws and half-life, collision theory and activation energy, the Arrhenius equation, reaction mechanisms, catalysts

Study guide

The rate of a reaction is the change in concentration per unit time. Rates depend on concentration, temperature, surface area and catalysts. A rate law, rate = k[A]^m[B]^n, relates rate to reactant concentrations; the exponents (orders) must be found experimentally, not from the balanced equation. The overall order is the sum of the exponents. The method of initial rates compares experiments: if doubling [A] doubles the rate, the reaction is first order in A; if it quadruples the rate, it's second order; if the rate doesn't change, it's zero order. The rate constant k depends on temperature, and its units depend on the overall order.

Integrated rate laws relate concentration to time. For zero order, [A] vs. time is linear; for first order, ln[A] vs. time is linear (ln[A] = −kt + ln[A]₀); for second order, 1/[A] vs. time is linear. The half-life is the time for half of a reactant to be used up. For first-order reactions, t½ = 0.693 ÷ k and doesn't depend on concentration, which is why radioactive decay is first order.

Collision theory says molecules must collide with enough energy (the activation energy, Ea) and the correct orientation to react. Raising the temperature increases the fraction of molecules with energy above Ea, greatly increasing the rate. The Arrhenius equation, k = Ae^(−Ea/RT), describes this. A reaction mechanism is a series of elementary steps; for an elementary step, the rate law comes directly from its molecularity. The slowest step is the rate-determining step and sets the overall rate law. Intermediates are formed in one step and used up in a later one. A catalyst speeds up a reaction by providing a new pathway with a lower activation energy; it is not consumed and doesn't change ΔH or the equilibrium position. Enzymes are biological catalysts.

Taking the natural log of the Arrhenius equation gives ln k = −(Ea/R)(1/T) + ln A. A plot of ln k versus 1/T is a straight line with slope −Ea/R. With two temperatures, ln(k₂/k₁) = (Ea/R)(1/T₁ − 1/T₂). In a mechanism, a catalyst is consumed in an early step and regenerated in a later one, so it appears as a reactant first. An intermediate is produced first and consumed later. Neither appears in the overall balanced equation.

Rates of disappearance and appearance are linked by the balanced equation's coefficients. In 2NO₂ → 2NO + O₂, NO₂ disappears twice as fast as O₂ appears. The rate of reaction is Δ[species]/Δt divided by that species' coefficient, with a minus sign for reactants. Changing the rate, for example by grinding a solid or adding a catalyst, changes how fast products form but not how much forms. The final amount of product is set by the limiting reactant.

A reaction energy profile shows reactants, the transition state at the top of each energy hill, and products. The height from reactants to the peak is Ea, and the difference between reactants and products is ΔH. In a multistep mechanism, each step has its own peak, intermediates sit in the valleys, and the step with the highest peak is usually rate-determining.

Key ideas

• Reaction orders come from experiments, not balanced equations.
• Integrated rate laws give straight-line plots for each order.
• First-order half-life doesn't depend on concentration.
• Higher temperature increases the fraction of molecules above Ea.
• Catalysts lower activation energy without being consumed.

Formulas and rules

Common mistakes

• Using coefficients from the overall equation as reaction orders.
• Thinking a catalyst shifts equilibrium; it only speeds up reaching it.

Words to know

Reaction rate

Change in concentration per unit time.

Rate law

An equation relating rate to reactant concentrations.

Rate constant (k)

The proportionality constant in a rate law.

Reaction order

The exponent of a concentration in the rate law.

Method of initial rates

Comparing initial rates to find reaction orders.

Integrated rate law

An equation relating concentration to time.

Half-life

Time for half of a reactant to be consumed.

Collision theory

Reactions need collisions with enough energy and correct orientation.

Activation energy

The minimum energy needed for a reaction to occur.

Arrhenius equation

Relates the rate constant to temperature and activation energy.

Reaction mechanism

The series of elementary steps in a reaction.

Elementary step

A single molecular event in a mechanism.

Molecularity

The number of particles colliding in an elementary step.

Rate-determining step

The slowest step in a mechanism.

Intermediate

A species formed in one step and used up in another.

Catalyst

A substance that speeds up a reaction without being consumed.

Enzyme

A biological catalyst.

Sample practice questions

13 more questions like these, from level 1 to 5, are in the practice set.