Chapter 14: Chemical Kinetics and Reaction Rates

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Thermochemistry and Chemical Kinetics

Introduction to Reaction Rates

Chemical kinetics is the study of the speed or rate at which chemical reactions occur and the factors that affect these rates. Understanding reaction rates is crucial for controlling industrial processes, biological systems, and environmental phenomena.

Reaction Rate: The change in concentration of a reactant or product per unit time, typically expressed in M/s (molarity per second).
Average Rate: Calculated over a time interval using the formula for reactants or for products.
Instantaneous Rate: The rate at a specific moment, found as the slope of the tangent to the concentration vs. time curve.
Factors Affecting Rate: Concentration, temperature, surface area, presence of a catalyst, and the nature of reactants.

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Example: The conversion of diamond to graphite is extremely slow, while the decomposition of sodium azide in airbags is very fast.

Measuring and Calculating Reaction Rates

Reaction rates are determined by monitoring the change in concentration of reactants or products over time. Data can be presented in tables or graphs.

Concentration vs. Time Graphs: Show how reactant and product concentrations change during a reaction.
Average Rate Calculation: Use concentration data at two time points to find the average rate.
Stoichiometry and Rate: For a reaction , the rate can be related to each species by .

Concentration vs. time graph for N2O5 decomposition Table of concentration data for N2O5, NO2, and O2

Rate Laws and Reaction Order

The rate law expresses the relationship between the rate of a reaction and the concentration of its reactants. The form of the rate law must be determined experimentally.

General Rate Law:
Order of Reaction: The exponents m and n indicate the order with respect to each reactant; the sum is the overall order.
Units of Rate Constant (k): Depend on the overall order of the reaction.

Rate Law	Overall Reaction Order	Units for k
Rate = k	Zeroth order	M/s or M s-1
Rate = k[A]	First order	1/s or s-1
Rate = k[A][B]	Second order	1/(M·s) or M-1 s-1
Rate = k[A][B]2	Third order	1/(M2·s) or M-2 s-1

Table of rate law, order, and units for k

Experimental Determination of Rate Laws

Rate laws are determined by measuring initial rates with varying reactant concentrations (method of initial rates).

Initial Rate: The rate measured immediately after reactants are mixed.
Procedure: Compare rates from experiments with different initial concentrations to deduce the order with respect to each reactant.
Example: If doubling [A] doubles the rate, the reaction is first order in A.

Initial rates graph

Integrated Rate Laws

Integrated rate laws relate the concentration of reactants to time and are used to determine how much reactant remains after a given time or how long it takes to reach a certain concentration.

Zero-Order:
First-Order: or
Second-Order:
Half-Life (t1/2): The time required for the concentration of a reactant to decrease by half.

Zero-order reaction surface diagram Cyclopropane to propene reaction First-order half-life graph Second-order half-life graph Test plots for zero, first, and second order

Temperature and Reaction Rates

Temperature has a profound effect on reaction rates, as described by collision theory and the Arrhenius equation.

Collision Theory: Molecules must collide with sufficient energy and proper orientation to react.
Activation Energy (Ea): The minimum energy required for a reaction to occur.
Arrhenius Equation: , where k is the rate constant, A is the frequency factor, Ea is activation energy, R is the gas constant, and T is temperature in Kelvin.
Effect of Temperature: Increasing temperature increases the fraction of molecules with enough energy to overcome Ea, thus increasing the rate.

Potential energy diagram for a reaction Distribution of collision energies at different temperatures

Reaction Mechanisms

A reaction mechanism is a sequence of elementary steps that describes the pathway from reactants to products. Each step can be unimolecular, bimolecular, or termolecular.

Elementary Step: A single molecular event, such as a collision or decomposition.
Molecularity: The number of reactant particles involved in an elementary step (unimolecular, bimolecular, termolecular).
Intermediates: Species produced in one step and consumed in another; do not appear in the overall reaction.
Rate-Determining Step: The slowest step in the mechanism, which controls the overall rate.
Valid Mechanism: Must sum to the overall reaction and have a rate law consistent with experimental data.

Elementary step molecular diagrams Unimolecular reaction diagram Bimolecular reaction diagram Termolecular reaction diagram Funnel analogy for rate-limiting step Energy diagram for two-step mechanism

Catalysis

Catalysts increase the rate of a chemical reaction by providing an alternative pathway with a lower activation energy. They are not consumed in the reaction and can be identified in a mechanism as substances that appear in the initial step and are regenerated in a later step.

Effect on Energy Diagram: Catalysts lower the activation energy, making it easier for reactants to be converted to products.
Homogeneous Catalysis: Catalyst is in the same phase as the reactants.
Heterogeneous Catalysis: Catalyst is in a different phase, often a solid surface.

Elephant toothpaste demonstration Catalyzed vs. uncatalyzed energy diagram Catalyzed pathway energy diagram

Summary Table: Integrated Rate Laws

Order	Integrated Rate Law	Plot for Straight Line	Half-life Expression
Zero		vs.
First		vs.
Second		vs.

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