Chapter 14: Chemical Kinetics II – Reaction Rates, Rate Laws, and Mechanisms

Reaction Rates and Stoichiometry

Defining Reaction Rate

Chemical kinetics studies the speed at which chemical reactions occur and the factors affecting them. The reaction rate can be measured using either the disappearance of reactants or the appearance of products.

• Rate Expression: For the reaction C2H5Cl(aq) + H2O(l) → C2H5OH(aq) + HCl(aq), the rate can be written as: $\text{Rate} = -\frac{\Delta [\text{C}_2\text{H}_5\text{Cl}]}{\Delta t} = \frac{\Delta [\text{C}_2\text{H}_5\text{OH}]}{\Delta t}$

• Negative sign for reactant disappearance, positive for product appearance.

Stoichiometric Coefficients and Rate

When the reaction is not 1:1 stoichiometry, use coefficients as fractions to relate rates:

• For 2 O3(g) → 3 O2(g): $\text{Rate} = -\frac{1}{2}\frac{\Delta [\text{O}_3]}{\Delta t} = \frac{1}{3}\frac{\Delta [\text{O}_2]}{\Delta t}$

Rate Laws and Rate Constants

General Rate Law

Rate laws are mathematical relationships determined experimentally. For a reaction A → B:

• $\text{Rate} = k[\text{A}]^x[\text{B}]^y$

• k: specific rate constant

• x, y: reaction orders with respect to each reactant

Reaction Order

• Order is determined experimentally, not from stoichiometry.

• Example: For Rate = k[NH4+][NO2-], the reaction is first order in each reactant and second order overall.

Units of Rate Constant (k)

• Zero order: M s-1 or M/s

• First order: s-1 or 1/s

• Second order: M-1 s-1 or 1/(M s)

Method of Initial Rates

Determining Rate Law Experimentally

• Choose experiments where one reactant is constant and the other varies.

• Set up a ratio of rates versus reactant concentration.

• General formula: $\text{conc ratio}^{\text{exponent}} = \text{rate ratio}$

Example Table: Rate Data for Ammonium and Nitrite Ions

Experiment Number	Initial [NH4+]	Initial [NO2-]	Observed Initial Rate (M/s)
1	0.0100	0.200	5.4 × 10-4
2	0.0200	0.200	1.08 × 10-3
3	0.0300	0.200	1.61 × 10-3
4	0.0100	0.0400	1.1 × 10-4
5	0.0100	0.0800	2.2 × 10-4
6	0.0100	0.120	3.2 × 10-4
7	0.0100	0.160	4.3 × 10-4

Integrated Rate Laws

Definitions

• Rate Law: Relates rate, rate constant (k), and concentration.

• Integrated Rate Law: Relates time and concentration.

First-Order Reactions

Rate Law and Integrated Form

• General rate law: $\text{Rate} = k[A]$

• Integrated rate law: $\ln[A] = -kt + \ln[A]_0$

• Plot of $\ln[A]$ vs. time is linear with slope $-k$.

Half-Life of First-Order Reaction

• Definition: Time for half of reactant to be consumed.

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

Second-Order Reactions

Rate Law and Integrated Form

• General rate law: $\text{Rate} = k[A]^2$

• Integrated rate law: $\frac{1}{[A]} = \frac{1}{[A]_0} + kt$

• Plot of $1/[A]$ vs. time is linear with slope $k$.

Half-Life of Second-Order Reaction

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

• Half-life depends on initial concentration.

Zero Order Reactions

Rate Law and Integrated Form

• General rate law: $\text{Rate} = k$

• Integrated rate law: $[A] = -kt + [A]_0$

• Plot of $[A]$ vs. time is linear with slope $-k$.

Temperature and Rate: Activation Energy and the Arrhenius Equation

Effect of Temperature

• Rate constant $k$ increases with temperature.

• Rate approximately doubles for every 10°C rise.

Arrhenius Equation

• $k = Ae^{-E_a/RT}$

• Linearized: $\ln k = -\frac{E_a}{R}\frac{1}{T} + \ln A$

• Plotting $\ln k$ vs. $1/T$ gives $E_a$ as the slope.

Collision Model and Orientation Factor

Collision Theory

• Molecules must collide to react.

• Only collisions with proper orientation and sufficient energy lead to reaction.

Activation Energy

• Minimum energy required for reaction is activation energy ($E_a$).

• Transition state (activated complex) is the highest energy state along the reaction pathway.

Reaction Mechanisms

Elementary Steps and Molecularity

• Mechanism: sequence of steps by which a reaction occurs.

• Elementary reaction: single step, classified by molecularity (unimolecular, bimolecular, termolecular).

Molecularity	Elementary Reaction	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 mechanism limits the overall reaction rate.

Plausible Mechanism Requirements

• Rate law must derive from the rate-determining step.

• All steps must balance and intermediates must be used up.

• Stoichiometry must match the overall reaction.

Intermediates

• Intermediates are produced in one step and consumed in another; they are not reactants or products.

Catalysis

Types of Catalysts

• Homogeneous Catalysts: Same phase as reactants.

• Heterogeneous Catalysts: Different phase than reactants.

• Enzymes: Biological catalysts.

Additional info: These notes are based on lecture slides from Louisiana State University, Prof. Matthew Chambers, and cover all major aspects of chemical kinetics relevant to a General Chemistry college course.