Chapter 14: Chemical Kinetics – Key Concepts and Study Guide

Chapter 14: Chemical Kinetics

14.1 Factors Affecting Reaction Rate

Chemical kinetics studies the speed at which chemical reactions occur and the factors that influence these rates.

• Nature of reactants: Different substances react at different rates due to their chemical properties.

• Concentration: Higher concentration of reactants generally increases the reaction rate.

• Temperature: Increasing temperature usually increases reaction rate by providing more energy to reactant molecules.

• Catalysts: Catalysts speed up reactions without being consumed.

• Surface area: For heterogeneous reactions, greater surface area increases rate.

14.2 Rate of Reaction: Units and Measurement

The rate of reaction is defined as the change in concentration of a reactant or product per unit time. It is commonly measured in mol/L·s.

• Average rate: Calculated over a time interval.

• Instantaneous rate: Rate at a specific moment, found using the slope of a concentration vs. time graph.

• Rate equation: Expresses rate as a function of reactant concentrations.

Example: For the reaction A → B, the rate can be written as $\text{Rate} = -\frac{d[A]}{dt} = \frac{d[B]}{dt}$.

14.3 Rate Laws: Forms and Determination

A rate law expresses the relationship between the rate of a reaction and the concentration of reactants.

• General form: $\text{Rate} = k[A]^m[B]^n$ where k is the rate constant, m and n are reaction orders.

• Order of reaction: The sum of exponents in the rate law; can be determined experimentally.

• Zero, first, and second order: Different integrated rate laws and behaviors.

Example: For a first-order reaction, $\text{Rate} = k[A]$.

14.4 Concentration vs. Time: Integrated Rate Laws

Integrated rate laws relate reactant concentration to time for different reaction orders.

• Zero order: $[A]_t = [A]_0 - kt$

• First order: $\ln [A]_t = \ln [A]_0 - kt$

• Second order: $\frac{1}{[A]_t} = \frac{1}{[A]_0} + kt$

• Half-life: Time required for concentration to decrease by half; depends on order.

Example: For a first-order reaction, half-life is $t_{1/2} = \frac{0.693}{k}$.

14.5 Collision Theory and Reaction Mechanisms

Collision theory explains that molecules must collide with sufficient energy and proper orientation to react. The activation energy is the minimum energy required for a reaction.

• Arrhenius equation: $k = A e^{-E_a/RT}$, where $E_a$ is activation energy, R is gas constant, T is temperature.

• Frequency factor (A): Represents the frequency of collisions with correct orientation.

• Graphical determination: Plotting $\ln k$ vs. $1/T$ yields a straight line; slope = $-E_a/R$.

Example: Determining $E_a$ from an Arrhenius plot.

14.6 Reaction Mechanisms and Rate Laws

A reaction mechanism is a sequence of elementary steps describing how a reaction occurs at the molecular level.

• Elementary reaction: A single step with its own rate law.

• Molecularity: Number of molecules involved in an elementary step (unimolecular, bimolecular, etc.).

• Rate-determining step: The slowest step controls the overall rate.

• Intermediates: Species formed and consumed during the mechanism; not present in overall equation.

• Catalysts: Increase rate by providing alternative pathway; appear in mechanism but not in overall equation.

Example: For a two-step mechanism, the rate law is determined by the slow step.

14.7 Catalysts and Activation Energy

Catalysts increase the rate of reaction by lowering the activation energy, allowing more molecules to react. The Boltzmann distribution explains how more molecules have sufficient energy to overcome the activation barrier when it is lowered.

• Homogeneous catalyst: Same phase as reactants.

• Heterogeneous catalyst: Different phase from reactants.

• Effect on rate: Catalysts do not affect equilibrium, only the rate.

Example: Enzymes act as biological catalysts.