Chapter 14: Chemical Kinetics – Study Notes

Chemical Kinetics

Introduction to Chemical Kinetics

Chemical kinetics is the branch of chemistry that studies the rate at which chemical processes occur. It also provides insight into the reaction mechanism, which describes the step-by-step sequence of elementary reactions by which overall chemical change occurs.

• Rate of reaction: The speed at which reactants are converted to products.

• Reaction mechanism: The detailed process at the molecular level by which reactants become products.

• Example: The reaction of hydrogen and oxygen to form water is highly exothermic and can be explosive, illustrating the importance of kinetics in understanding reaction rates and safety.

Thermodynamics vs. Kinetics

Thermodynamics tells us whether a reaction is energetically favorable (ΔH < 0 for exothermic reactions), while kinetics tells us how fast the reaction will proceed.

• Thermodynamics: Concerns the energy changes and equilibrium position.

• Kinetics: Concerns the pathway and speed of the reaction.

• Example: Rolling a ball down a hill: thermodynamics determines the height difference, kinetics determines how quickly the ball rolls down.

Supersaturated Solutions

Non-Equilibrium States

A supersaturated solution contains more dissolved solute than is present in a saturated solution at the same temperature. This is a non-equilibrium state and can rapidly revert to equilibrium by crystallization.

• Adding a seed crystal to a supersaturated solution causes rapid crystallization until saturation is reached.

• Example: Sodium acetate solutions can be supersaturated and will crystallize upon seeding.

Factors Affecting Reaction Rates

Collision Theory

For a reaction to occur, reactant molecules must collide with sufficient energy and proper orientation.

• Physical state: Homogeneous mixtures react faster; powdered solids react faster than large pieces due to increased surface area.

• Example: Dust explosions occur because fine particles have a large surface area, increasing reaction rate.

Concentration of Reactants

Increasing the concentration of reactants increases the frequency of collisions, thus increasing the reaction rate.

• Example: Burning steel wool in pure oxygen (100% O2) is much faster than in air (20% O2).

Temperature

Higher temperatures increase the kinetic energy of molecules, leading to more frequent and energetic collisions.

• Reaction rates generally increase with temperature.

• Graph: Distribution of molecular speeds shifts to higher values at higher temperatures.

Presence of a Catalyst

Catalysts increase reaction rates by providing an alternative reaction pathway with a lower activation energy. They are not consumed in the reaction.

• Example: Enzymes are biological catalysts.

Measuring Reaction Rates

Definition and Calculation

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

• For a reaction A → B:

$\text{Rate} = -\frac{\Delta [A]}{\Delta t} = \frac{\Delta [B]}{\Delta t}$

• Negative sign for reactants (decreasing concentration), positive for products (increasing concentration).

• Example: If [A] decreases from 1.00 mol to 0.54 mol in 20 s, average rate = (0.54 - 1.00) / 20 = -0.023 mol s-1.

Instantaneous and Initial Rates

The instantaneous rate is the rate at a specific moment, found as the slope of the tangent to the concentration vs. time curve. The initial rate is the instantaneous rate at the start of the reaction.

Stoichiometry and Rate Relationships

For reactions with different stoichiometric coefficients, rates are related by those coefficients.

• For $2HI(g) \rightarrow H_2(g) + I_2(g)$:

$\text{Rate} = -\frac{1}{2} \frac{\Delta [HI]}{\Delta t} = \frac{\Delta [H_2]}{\Delta t} = \frac{\Delta [I_2]}{\Delta t}$

• General form for $aA + bB \rightarrow cC + dD$:

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

Concentration and Rate Laws

Rate Law and Rate Constant

The rate law expresses the rate as a function of reactant concentrations and a proportionality constant called the rate constant (k).

• General form: $\text{Rate} = k[A]^m[B]^n$

• m and n are the orders of the reaction with respect to A and B, determined experimentally.

• The overall order is m + n.

• Example: For $NH_4^+ (aq) + NO_2^- (aq) \rightarrow N_2(g) + 2H_2O(l)$, rate law is $\text{Rate} = k[NH_4^+][NO_2^-]$ (first order in each, second order overall).

Experimental Determination of Rate Laws

Initial rates are measured for different starting concentrations to determine the order with respect to each reactant.

Experiment	Initial [NH4+]	Initial [NO2-]	Observed Initial Rate (M/s)
1	0.010	0.200	5.4 × 10-7
2	0.020	0.200	1.08 × 10-6
5	0.200	0.040	2.16 × 10-6
6	0.200	0.080	4.33 × 10-6

• Doubling [NH4+] doubles the rate; doubling [NO2-] doubles the rate, indicating first order in each.

Order and Stoichiometry

Reaction order is not necessarily related to stoichiometric coefficients; it must be determined experimentally.

• Example: $2N_2O_5(g) \rightarrow 4NO_2(g) + O_2(g)$, rate law: $\text{Rate} = k[N_2O_5]$ (first order in $N_2O_5$).

Integrated Rate Laws

First-Order Reactions

For a first-order reaction, the integrated rate law is:

$\ln \frac{[A]_t}{[A]_0} = -kt$

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

• Example: Decomposition of dimethyl ether, $(CH_3)_2O$, at 510°C with $k = 6.8 \times 10^{-4} s^{-1}$.

Second-Order Reactions

For a second-order reaction (in A), the integrated rate law is:

$\frac{1}{[A]_t} = kt + \frac{1}{[A]_0}$

• Plotting $\frac{1}{[A]}$ vs. $t$ yields a straight line with slope $k$.

Half-Life of Reactions

First-Order Half-Life

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

For first-order reactions:

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

• Half-life is independent of initial concentration.

Second-Order Half-Life

For second-order reactions:

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

• Half-life depends on the initial concentration.

Summary Table: Key Equations in Chemical Kinetics

Process	Integrated Rate Law	Half-Life Expression
First-order	$\ln [A]_t = -kt + \ln [A]_0$	$t_{1/2} = \frac{0.693}{k}$
Second-order	$\frac{1}{[A]_t} = kt + \frac{1}{[A]_0}$	$t_{1/2} = \frac{1}{k[A]_0}$

Additional info: These notes cover the fundamental concepts of chemical kinetics, including factors affecting rates, rate laws, integrated rate laws, and half-life calculations, as presented in a typical General Chemistry course.