Chemical Kinetics: Reaction Rates and Mechanisms (CHM 230 - Chapter 17 Study Notes)

Course and Chapter Overview

Instructor and Course Information

• Instructor: Dr. Dan Higgins

• Textbook: Chemistry, Atoms First, OpenStax, 2nd ed.

• Course Structure: Includes lectures, online homework, quizzes, exams, and laboratory work.

• Support Resources: Free tutoring and help rooms are available.

Chapter 17: Kinetics

I. Reaction Rates

• Chemical kinetics is the study of the rate of chemical reactions and the mechanisms by which they occur.

• The rate of a chemical reaction measures how much reactant is consumed or how much product is produced per unit time.

• The rate is always positive and has units of $\mathrm{M\,s^{-1}}$ (molarity per second).

B. Average Rates

• For a reaction $A \rightarrow B$, $[A]$ decreases and $[B]$ increases over time.

• The average rate can be expressed as:

  • $\text{av. rate} = -\frac{\Delta [A]}{\Delta t}$

  • $\text{av. rate} = +\frac{\Delta [B]}{\Delta t}$

• Example: For $\mathrm{Br_2(aq) + HCOOH(aq) \rightarrow 2Br^-(aq) + 2H^+(aq) + CO_2(g)}$, the average rate is calculated using changes in $[Br_2]$ over a time interval.

C. Instantaneous Rates

• The instantaneous rate is the rate at a specific instant, given by the (negative) slope of the tangent to the concentration vs. time curve.

• $\text{inst. rate} = -\frac{\Delta [Br_2]}{\Delta t}$ (as $\Delta t$ approaches zero)

D. Initial Rate

• The initial rate is the instantaneous rate at $t = 0$.

E. Rate Expressions

• Stoichiometry requires that the rate of disappearance of reactants equals the rate of appearance of products, adjusted for stoichiometric coefficients.

• For a general reaction $aA + bB \rightarrow cC + dD$:

  • $\text{rate} = -\frac{1}{a}\frac{\Delta [A]}{\Delta t} = -\frac{1}{b}\frac{\Delta [B]}{\Delta t} = \frac{1}{c}\frac{\Delta [C]}{\Delta t} = \frac{1}{d}\frac{\Delta [D]}{\Delta t}$

II. Dependence of Reaction Rate on Reactant Concentration

A. The Rate Law

• The rate law relates the reaction rate to the concentrations of reactants.

• For $aA + bB \rightarrow cC + dD$:

  • $\text{Rate} = k [A]^x [B]^y$

  • $k$ is the rate constant.

  • $x$ and $y$ are the orders with respect to $A$ and $B$ (determined experimentally, not from stoichiometry).

  • The overall order is $x + y$.

• Examples:

  • $2N_2O_5(s) \rightarrow 4NO_2(g) + O_2(g)$, $\text{rate} = k[N_2O_5]$ (first order overall)

  • $2NH_3(g) \rightarrow N_2(g) + 3H_2(g)$, $\text{rate} = k$ (zero order overall)

B. Experimental Determination of the Rate Law

• Use initial rates from experiments with varying reactant concentrations to determine the order with respect to each reactant.

• Example Table:

Experiment	[NO]	[H2]	Initial Rate (M/s)
1	5.0 × 10-3	2.0 × 10-3	1.25 × 10-5
2	1.0 × 10-2	2.0 × 10-3	5.0 × 10-5
3	1.0 × 10-2	4.0 × 10-3	1.0 × 10-4

• By comparing rates, deduce the order with respect to each reactant and solve for $k$.

C. Units of the Rate Constant

• The units of $k$ depend on the overall order of the reaction:

Order	Rate Law	Units of $k$
Zero	$\text{rate} = k$	$\mathrm{M\,s^{-1}}$
First	$\text{rate} = k[A]$	$\mathrm{s^{-1}}$
Second	$\text{rate} = k[A]^2$	$\mathrm{M^{-1}\,s^{-1}}$

III. Dependence of Reactant Concentration on Time

A. First-Order Reactions

• Rate law: $\text{rate} = k[A]$

• Integrated rate law: $\ln\left(\frac{[A]_t}{[A]_0}\right) = -kt$

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

• Half-life: $t_{1/2} = \frac{0.693}{k}$ (independent of initial concentration)

B. Second-Order Reactions

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

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

• A plot of $1/[A]_t$ vs. time yields a straight line with slope $k$.

• Half-life: $t_{1/2} = \frac{1}{k[A]_0}$ (depends on initial concentration)

C. Zero-Order Reactions

• Rate law: $\text{rate} = k$

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

• A plot of $[A]_t$ vs. time yields a straight line with slope $-k$.

• Half-life: $t_{1/2} = \frac{[A]_0}{2k}$ (depends on initial concentration)

IV. Collision Theory of Chemical Reactions

• Chemical reactions occur due to collisions between reactant molecules.

• Effective collisions require:

  1. Sufficient energy (activation energy, $E_a$)

  2. Proper orientation

• The reaction rate is proportional to the number of effective collisions per second.

V. Dependence of Reaction Rate on Temperature

A. The Arrhenius Equation

• The rate constant $k$ increases with temperature.

• Arrhenius equation: $k = Ae^{-E_a/(RT)}$

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

• A plot of $\ln k$ vs. $1/T$ yields a straight line with slope $-E_a/R$.

VI. Reaction Mechanisms

• A reaction mechanism is a sequence of elementary steps that describe the pathway from reactants to products.

• Intermediates are species formed in one step and consumed in another; they do not appear in the overall equation.

• The rate-determining step is the slowest step and determines the overall rate law.

• Molecularity refers to the number of molecules involved in an elementary step:

  • Unimolecular: one molecule ($\text{rate} = k[A]$)

  • Bimolecular: two molecules ($\text{rate} = k[A][B]$ or $k[A]^2$)

  • Termolecular: three molecules (rare)

VII. Catalysis

• A catalyst increases the rate of a reaction by providing an alternative pathway with lower activation energy.

• Catalysts are not consumed in the reaction.

• Homogeneous catalysis: Catalyst and reactants are in the same phase.

• Heterogeneous catalysis: Catalyst and reactants are in different phases.

VIII. Summary of Factors Affecting Reaction Rates

• Concentration: Higher concentration increases collision frequency and rate.

• Temperature: Higher temperature increases kinetic energy and rate.

• Catalysts: Lower activation energy, increasing rate.