Chemical Kinetics: Chapter 14 Study Notes

Chemical Kinetics

Introduction to Chemical Kinetics

Chemical kinetics is the study of the speed at which chemical reactions occur and the factors that influence these rates. Understanding kinetics is essential for controlling reactions in industrial, biological, and environmental contexts.

• Reaction rate: The speed at which reactants are converted to products.

• Chemical kinetics: The study of reaction rates.

• Mechanism: The step-by-step sequence of elementary reactions by which overall chemical change occurs.

Factors That Affect Reaction Rates (Section 14.1)

Several factors influence how quickly a chemical reaction proceeds:

1. Physical state of the reactants:

   • Reactants must collide to react; more frequent collisions lead to faster reactions.

   • Homogeneous reactions (all reactants in the same phase, e.g., all gases or liquids) are typically faster.

   • Heterogeneous reactions (involving solids) are slower; increasing surface area (e.g., using a powder) speeds up the reaction.

2. Reactant concentrations:

   • Higher concentrations increase the number of collisions, generally increasing the reaction rate.

3. Reaction temperature:

   • Increasing temperature raises the kinetic energy of molecules, resulting in more frequent and energetic collisions.

4. Presence of a catalyst:

   • Catalysts speed up reactions by providing alternative pathways with lower activation energy, without being consumed in the reaction.

   • They are crucial in biological systems (e.g., enzymes).

Reaction Rate (Section 14.2)

The rate of a reaction is defined as the change in concentration of a reactant or product per unit time.

• Formula: $\text{Rate} = \frac{\Delta [A]}{\Delta t}$ where $\Delta$ means "change in," [A] is molar concentration, and $t$ is time.

• Types of rate measured:

  • Average rate

  • Instantaneous rate

  • Initial rate

Calculating Average and Instantaneous Rates

Average rate is determined over a time interval, while instantaneous rate is the slope of the concentration vs. time curve at a specific moment.

• Example: For the reaction $\mathrm{C_4H_9Cl(aq) + H_2O(l) \rightarrow C_4H_9OH(aq) + HCl(aq)}$, the rate can be measured by the change in $[\mathrm{C_4H_9Cl}]$ over time: $\text{Rate} = -\frac{\Delta [\mathrm{C_4H_9Cl}]}{\Delta t}$

Relative Rates and Stoichiometry

Reaction rates depend on the stoichiometry of the balanced equation. The rate of disappearance of reactants and appearance of products may differ based on their coefficients.

• General formula: $aA + bB \rightarrow cC + dD$ $\text{Rate} = -\frac{1}{a} \frac{\Delta [A]}{\Delta t} = -\frac{1}{b} \frac{\Delta [B]}{\Delta t} = \frac{1}{c} \frac{\Delta [C]}{\Delta t} = \frac{1}{d} \frac{\Delta [D]}{\Delta t}$

Determining Concentration Effect on Rate (Section 14.3)

To determine how each reactant affects the rate, vary the concentration of one reactant at a time while keeping others constant.

• Example Table:

  Experiment Number	Initial NH4+ (M)	Initial NO2- (M)	Observed Initial Rate (M/s)
  1	0.0100	0.200	5.4 × 10-7
  2	0.0200	0.200	1.1 × 10-6
  3	0.0300	0.200	1.6 × 10-6
  4	0.0200	0.040	2.2 × 10-7
  5	0.0200	0.080	4.3 × 10-7
  6	0.0200	0.008	4.1 × 10-8

• Rate law: $\text{Rate} = k[\mathrm{NH_4^+}][\mathrm{NO_2^-}]$

Reaction Order and Rate Law

The exponents in the rate law indicate the order of the reaction with respect to each reactant. The overall order is the sum of individual orders.

• Example: $\text{Rate} = k[\mathrm{NH_4^+}]^1[\mathrm{NO_2^-}]^1$ Overall order = 1 + 1 = 2 (second order)

• Rate constant (k): A temperature-dependent proportionality constant.

Order ≠ Stoichiometry

Reaction order must be determined experimentally and does not necessarily match the stoichiometric coefficients in the balanced equation.

• Examples: $2\mathrm{N_2O_5}(g) \rightarrow 4\mathrm{NO_2}(g) + \mathrm{O_2}(g)$ $\text{Rate} = k[\mathrm{N_2O_5}]$ $\mathrm{H_2}(g) + \mathrm{I_2}(g) \rightarrow 2\mathrm{HI}(g)$ $\text{Rate} = k[\mathrm{H_2}][\mathrm{I_2}]$

Relative Value of k

• Large $k$ (e.g., $k \sim 10^9$ or higher): Fast reaction

• Small $k$ (e.g., $k \sim 10$ or lower): Slow reaction

First-Order Reactions (Section 14.4)

First-order reactions depend on the concentration of one reactant to the first power.

• Rate law: $\text{Rate} = k[A]$

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

• Graph: Plotting $\ln[A]$ vs. $t$ yields a straight line with slope $-k$.

• Example: Conversion of methyl isonitrile to acetonitrile.

Second-Order Reactions

Second-order reactions depend on the concentration of one reactant squared.

• Rate law: $\text{Rate} = k[A]^2$

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

• Graph: Plotting $1/[A]$ vs. $t$ yields a straight line with slope $k$.

Zero-Order Reactions

Zero-order reactions have rates independent of reactant concentration.

• Rate law: $\text{Rate} = k$

• Graph: Concentration vs. time is linear.

Half-Life

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

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

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

Additional info:

• Practice exercises and sample problems are included throughout the notes to reinforce concepts and calculations.