Chapter 14: Chemical Kinetics – Study Notes

Chemical Kinetics

Introduction to Chemical Kinetics

Chemical kinetics is the study of the speed, or rate, at which chemical reactions occur. Understanding reaction rates helps chemists control and optimize chemical processes. The detailed sequence of steps by which reactants are converted into products is called the reaction mechanism.

• Reaction rate: The change in concentration of a reactant or product per unit time.

• Chemical kinetics: The field that studies reaction rates and mechanisms.

• Mechanism: The step-by-step pathway from reactants to products.

Factors That Affect Reaction Rates

Physical State of Reactants

The physical state of reactants influences how readily they collide and react. Homogeneous reactions (all reactants in the same phase, such as all gases or all liquids) tend to be faster than heterogeneous reactions (reactants in different phases, such as a solid and a liquid).

• In heterogeneous reactions, increasing the surface area of a solid reactant (e.g., using a powder instead of a chunk) increases the reaction rate.

Reactant Concentrations

Increasing the concentration of reactants generally increases the reaction rate because more molecules are present, leading to more frequent collisions.

Temperature

Raising the temperature usually increases the reaction rate. Higher temperatures mean molecules move faster, collide more often, and with greater energy.

Presence of a Catalyst

Catalysts increase reaction rates without being consumed in the overall reaction. They provide alternative pathways (mechanisms) with lower activation energies and are essential in many biological and industrial processes.

Measuring Reaction Rates

Definition of Rate

The rate of a reaction is defined as the change in concentration of a reactant or product over a specific time interval:

• Average rate: Change over a finite time period.

• Instantaneous rate: Rate at a specific moment (slope of the tangent to the concentration vs. time curve).

• Initial rate: Instantaneous rate at time zero, often the focus in kinetics studies.

Relative Rates and Stoichiometry

Reaction rates can be measured using either reactant consumption or product formation. The rates are related by the stoichiometry of the balanced equation. For example, in the reaction:

$aA + bB \rightarrow cC + dD$

The rate can be expressed as:

$\text{Rate} = -\frac{1}{a} \frac{d[A]}{dt} = -\frac{1}{b} \frac{d[B]}{dt} = \frac{1}{c} \frac{d[C]}{dt} = \frac{1}{d} \frac{d[D]}{dt}$

Determining the Rate Law

Experimental Determination

To determine how each reactant affects the rate, experiments are performed where the concentration of one reactant is varied while others are held constant. The resulting changes in rate reveal the order with respect to each reactant.

Rate Law and Reaction Order

The rate law expresses the relationship between the reaction rate and the concentrations of reactants:

$\text{Rate} = k[A]^m[B]^n$

• k: Rate constant (depends on temperature).

• m, n: Reaction orders with respect to A and B (determined experimentally).

• Overall order: Sum of the exponents (e.g., if m = 1 and n = 1, overall order = 2).

Note: Reaction order is not necessarily related to the stoichiometric coefficients in the balanced equation.

Types of Rate Laws

First-Order Reactions

For a first-order reaction, the rate depends linearly on the concentration of one reactant:

$\text{Rate} = k[A]$

The integrated rate law is:

$\ln[A]_t = -kt + \ln[A]_0$

A plot of $\ln[A]$ versus time yields a straight line with slope $-k$.

Half-Life of a First-Order Reaction

The half-life ($t_{1/2}$) is the time required for half of the reactant to be consumed:

$t_{1/2} = \frac{0.693}{k}$

Second-Order Reactions

For a second-order reaction (with respect to one reactant):

$\text{Rate} = k[A]^2$

The integrated rate law is:

$\frac{1}{[A]_t} = kt + \frac{1}{[A]_0}$

A plot of $1/[A]$ versus time is linear for a second-order reaction.

The half-life for a second-order reaction is:

$t_{1/2} = \frac{1}{k[A]_0}$

Note: The half-life depends on the initial concentration for second-order reactions.

Zero-Order Reactions

For zero-order reactions, the rate is independent of reactant concentration:

$\text{Rate} = k$

The concentration decreases linearly with time.

The Collision Model and Activation Energy

Collision Theory

According to the collision model, molecules must collide to react. The rate depends on:

• Frequency of collisions

• Orientation of molecules during collisions

• Energy of collisions (must be above a minimum threshold called activation energy)

Activation Energy and Transition State

The activation energy (E_a) is the minimum energy required for a reaction to occur. Reactants must reach a high-energy, unstable arrangement called the transition state (or activated complex) before forming products.

Temperature Dependence of Rate Constant

The rate constant increases with temperature, as described by the Arrhenius equation:

$k = A e^{-E_a/(RT)}$

Taking the natural logarithm gives:

$\ln k = -\frac{E_a}{R} \cdot \frac{1}{T} + \ln A$

This equation allows determination of activation energy from a plot of $\ln k$ versus $1/T$.

Reaction Mechanisms

Elementary Steps and Molecularity

A reaction mechanism consists of a sequence of elementary steps. The molecularity of a step is the number of molecules involved:

• Unimolecular: One molecule decomposes or rearranges.

• Bimolecular: Two molecules collide.

• Termolecular: Three molecules collide (rare).

Molecularity	Example	Rate Law
Unimolecular	A → products	Rate = k[A]
Bimolecular	A + B → products	Rate = k[A][B]
Termolecular	A + B + C → products	Rate = k[A][B][C]

Rate-Determining Step

The slowest step in a reaction mechanism limits the overall rate and determines the observed rate law.

Intermediates

Intermediates are species produced in one step and consumed in another. They do not appear in the overall balanced equation and are not the same as transition states.

Catalysis

Role of Catalysts

Catalysts increase reaction rates by providing alternative mechanisms with lower activation energies. They are not consumed in the reaction.

Types of Catalysts

• Homogeneous catalysts: Catalyst and reactants are in the same phase (e.g., all dissolved in solution).

• Heterogeneous catalysts: Catalyst is in a different phase (e.g., solid catalyst with gaseous reactants).

• Enzymes: Biological catalysts with specific active sites for substrates (reactants).

Enzyme Catalysis and the Lock-and-Key Model

Enzymes are highly specific catalysts. The substrate fits into the enzyme's active site like a key fits into a lock, facilitating the reaction.