Chapter 15: Chemical Kinetics – Study Notes

Chemical Kinetics

Introduction to Chemical Kinetics

Chemical kinetics is the branch of chemistry that studies the speed (rate) of chemical reactions and the factors that affect these rates. Understanding kinetics is crucial for controlling reactions in industrial, biological, and environmental processes.

• Reaction Rate: The speed at which reactants are converted to products, typically measured as the change in concentration over time.

• Importance: Controlling reaction rates is essential in chemical manufacturing, biological systems, and environmental processes.

• Example: Ectothermic animals, such as lizards, experience slower metabolic reactions at lower temperatures, leading to lethargy.

Defining and Measuring Reaction Rates

Reaction Rate Concepts

The rate of a chemical reaction is defined as the change in concentration of a reactant or product per unit time. For reactants, the rate is negative (since they are consumed), and for products, it is positive (since they are formed).

• General Rate Expression: $\text{Rate} = -\frac{\Delta [\text{Reactant}]}{\Delta t} = \frac{\Delta [\text{Product}]}{\Delta t}$

• Units: Typically expressed in M/s (molarity per second).

• Average Rate: Change in concentration over a finite time interval.

• Instantaneous Rate: The rate at a specific moment, found by the slope of the tangent to the concentration vs. time curve.

Reaction Rate and Stoichiometry

For reactions with different stoichiometric coefficients, the rate of change for each species is related by the coefficients in the balanced equation.

• Example: For $\mathrm{H_2(g) + I_2(g) \rightarrow 2HI(g)}$, the rate of disappearance of H2 and I2 is half the rate of appearance of HI.

Methods for Measuring Reaction Rates

Reaction rates can be measured by monitoring the concentration of reactants or products over time using various techniques:

• Polarimetry: Measures changes in optical rotation.

• Spectrophotometry: Measures changes in light absorption.

• Pressure Measurement: Monitors changes in total or partial pressure for gaseous reactions.

• Aliquot Sampling: Samples are withdrawn and analyzed by titration, gravimetric analysis, or gas chromatography.

Factors Affecting Reaction Rate

Concentration and the Rate Law

The rate of a reaction often depends on the concentration of one or more reactants. The relationship is expressed by the rate law:

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

• k: Rate constant (depends on temperature and reaction).

• m, n: Reaction orders with respect to A and B (determined experimentally).

• Overall Order: Sum of the exponents (m + n).

Reaction Order and Its Effects

• Zero Order: Rate is independent of reactant concentration. Doubling [A] does not affect the rate.

• First Order: Rate is directly proportional to [A]. Doubling [A] doubles the rate.

• Second Order: Rate is proportional to [A]2. Doubling [A] quadruples the rate.

Determining Reaction Order

Reaction order is determined experimentally, often using the method of initial rates. By varying the concentration of one reactant at a time and measuring the initial rate, the order with respect to each reactant can be deduced.

Integrated Rate Laws

Relating Concentration and Time

Integrated rate laws provide equations that relate the concentration of reactants to time for different reaction orders.

• Zero Order: $[A]_t = [A]_0 - kt$

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

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

Graphical methods can be used to determine reaction order by plotting [A], ln[A], or 1/[A] versus time and identifying which yields a straight line.

Order	Integrated Rate Law	Graph for Straight Line	Slope
Zero	$[A]_t = [A]_0 - kt$	[A] vs. t	-k
First	$\ln [A]_t = \ln [A]_0 - kt$	ln[A] vs. t	-k
Second	$\frac{1}{[A]_t} = \frac{1}{[A]_0} + kt$	1/[A] vs. t	k

Half-Life of a Reaction

The half-life (t1/2) is the time required for the concentration of a reactant to decrease to half its initial value. The expression for half-life depends on the reaction order:

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

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

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

Temperature and Reaction Rate

The Arrhenius Equation

The rate constant (k) increases with temperature, described by the Arrhenius equation:

• $k = A e^{-E_a/(RT)}$

• A: Frequency factor (number of approaches to activation energy per unit time)

• Ea: Activation energy (minimum energy required for reaction)

• R: Gas constant (8.314 J/mol·K)

• T: Temperature in Kelvin

Increasing temperature increases the fraction of molecules with enough energy to overcome the activation barrier, thus increasing the reaction rate.

Arrhenius Plots

The Arrhenius equation can be linearized for graphical analysis:

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

• A plot of ln k versus 1/T yields a straight line with slope -Ea/R.

Collision Theory and Reaction Mechanisms

Collision Theory

For a reaction to occur, reactant molecules must collide with sufficient energy and proper orientation. Only a fraction of collisions are effective in producing products.

• Activation Energy: Minimum energy required for a successful collision.

• Orientation Factor (p): Probability that molecules are correctly oriented during collision.

Reaction Mechanisms

The reaction mechanism is the sequence of elementary steps by which an overall chemical reaction occurs. Each step has its own rate law and molecularity (number of particles involved).

• Unimolecular: One particle involved.

• Bimolecular: Two particles involved.

• Termolecular: Three particles involved (rare).

• Intermediates: Species produced in one step and consumed in another; do not appear in the overall equation.

• Rate-Determining Step (RDS): The slowest step, which controls the overall reaction rate.

Catalysis

Catalysts and Their Function

Catalysts increase reaction rates by providing alternative pathways with lower activation energies. They are not consumed in the overall reaction.

• Homogeneous Catalysts: Same phase as reactants.

• Heterogeneous Catalysts: Different phase than reactants.

• Enzymes: Biological catalysts, usually proteins, that speed up reactions by binding substrates at active sites.

Summary Table: Kinetics Relationships

Concept	Description
Rate Law	Relates rate to reactant concentrations
Integrated Rate Law	Relates concentration to time
Half-Life	Time for concentration to halve
Arrhenius Equation	Relates rate constant to temperature and activation energy
Mechanism	Sequence of elementary steps
Catalyst	Lowers activation energy, increases rate