VIII. Chemical Kinetics

Key focus of this chapter: reaction rate

This chapter reviews reaction rates, rate laws, integrated rate laws and half-lives, catalysis, and reaction mechanisms.

A. Reaction rate

: the change in reactant or product concentration per unit time. Average rates use a finite interval, Δt; instantaneous rates use the slope of the concentration–time curve at a particular time.

Reaction rates often decrease as reactants are consumed, but the time dependence follows the rate law; a zero-order reaction has a constant rate while its zero-order conditions hold.
A negative sign converts the decrease in reactant concentration to a positive disappearance rate; product formation has a positive concentration change.
For a given reaction, species disappear or form at rates proportional to their stoichiometric coefficients; the reaction rate is normalized by those coefficients.

Question: Express the reaction rate in terms of the concentration change of each species.

CS₂(g) + 3O₂(g) → CO₂(g) + 2SO₂(g)

B. Factors that affect reaction rate

Concentration	• The effect of reactant concentration depends on the rate law. Increasing the concentration increases the rate for a positive order in that reactant; a zero-order rate is independent of its concentration.
Pressure	• Compressing a gaseous reaction mixture increases reactant concentrations. The effect on the reaction rate depends on the rate law; adding an inert gas at constant volume does not increase reactant concentrations.
Surface area	• For a heterogeneous reaction involving a solid, increasing its exposed surface area can increase the reaction rate by providing more sites for contact.
Catalysis	• A catalyst increases the reaction rate by providing an alternative pathway with a lower activation energy.
Temperature	• Increasing temperature usually increases the reaction rate because a larger fraction of collisions can overcome the activation energy. A doubling per 10 °C is an approximate rule for some reactions, not a universal law.
Types of reactant	• Reaction rates depend on the reactants, their physical states, and the reaction mechanism. Ionic reactions are not universally faster than reactions involving covalent compounds.

Fig 1. Factors that affect the reaction rate

C. Rate law

: an equation that relates reaction rate to reactant concentrations raised to experimentally determined powers (reaction orders), multiplied by the rate constant. Overall rate-law exponents generally cannot be inferred from the balanced overall equation; coefficients give exponents only for an elementary step.

1. Rate constant k

: the proportionality constant in a specified rate law. It depends on temperature and the reaction pathway.

** At fixed temperature, medium, and mechanism, changing reactant concentration does not change k. The units depend on the overall order N: M^1−N·s⁻¹ when rate is in M/s.

Unit of rate constant

The Arrhenius equation, k = A e^−E_a/(RT), relates k to temperature and activation energy.

Overall reaction order	Rate law	Rate constant, k	k unit

Question: Using the illustrative experimental data supplied for this reaction, determine the reaction orders (m and n) with respect to CH₄and O₂, the overall reaction order, and the rate constant k.

CH₄(g) + 2O₂(g) → CO₂(g) + 2H₂O(g) Rate = k[CH₄]^m[O₂]ⁿ

Trial
1 2 3	0.01 0.03 0.02 0.03 0.02 0.09	0.3 1.2 3.6

Solution:

2. Half-life, t_1/2

: the time required for the reactant concentration to decrease to half its initial value. A first-order process has a constant half-life; zero- and second-order half-lives depend on the initial concentration.

Example: A first-order reactant has a half-life of 2 minutes and an initial concentration of 36 M.

Question: During a first-order decay process, the amount of reactant remaining decreases from 64 g to 16 g in 24 hours. Calculate the half-life.

Solution:

3. Simple types of reaction order

Reaction orders	Rate law	Equation (concentration vs. time)	Graph	Half-life, t1/2
Zeroth order
First order
Second order

D. Catalysis

Catalysis is the acceleration of a reaction by a catalyst. A catalyst participates in a reaction pathway and is regenerated, so it is not consumed overall.

Activation energy, E_a, is the energy barrier for a reaction pathway. A catalyst provides an alternative pathway with a lower activation barrier.

At fixed temperature and otherwise comparable conditions, a lower activation barrier generally gives a larger rate constant. A catalyst speeds both forward and reverse reactions and does not change reaction ΔG, ΔH, ΔS, or the equilibrium constant for the same initial and final states.

A transition state lies at an energy maximum along an elementary reaction coordinate. It is not a stable intermediate.

Fig. 2 Exothermic reaction with catalysis

Fig. 3 Effects of temperature, reactant concentration, and a catalyst on rate and thermodynamics

E. Reaction mechanisms

A reaction mechanism is a sequence of elementary steps that sums to the overall reaction. An intermediate is formed and then consumed; a catalyst is consumed in an early step and regenerated later. Both cancel from the overall equation.

In the illustration, B is the catalyst and C is the intermediate. If the indicated first step is elementary and rate determining, its rate law is k[A][B]. Rate laws for more complex mechanisms may require additional analysis.