Chapter 15: Chemical Kinetics – Study Notes

Chemical Kinetics

Introduction to Chemical Kinetics

Chemical kinetics is the branch of chemistry that studies the rates at which chemical reactions occur and the factors that affect these rates. Understanding kinetics is essential for controlling reactions in industrial, laboratory, and biological settings.

• Chemical kinetics focuses on how quickly reactants are converted into products.

• It is distinct from thermodynamics, which tells us if a reaction is possible, but not how fast it will occur.

• Applications include pharmaceuticals, food science, environmental chemistry, and engineering.

Key Concepts in Kinetics

• Reaction rate: The change in concentration of a reactant or product per unit time.

• Rate law: An equation that relates the reaction rate to the concentrations of reactants.

• Order of reaction: The power to which the concentration of a reactant is raised in the rate law.

• Rate constant (k): A proportionality constant specific to a given reaction at a given temperature.

Rates of Chemical Reactions

Defining Reaction Rate

The rate of a chemical reaction measures how quickly reactants are consumed or products are formed over time.

• Expressed as: Rate = Δ[Concentration]/ΔTime

• For a general reaction: aA + bB → cC + dD

The rate can be written as:

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

• The negative sign for reactants indicates their concentration decreases over time.

• Stoichiometric coefficients are used to relate the rates of change for each species.

Example: Calculating Reaction Rate

• Given: [A]0 = 0.50 M, [A]30s = 0.40 M

• Rate for A: $\text{Rate}_A = \frac{[A]_{30s} - [A]_0}{30\,\text{s}} = \frac{0.40 - 0.50}{30} = -0.0033\,\text{M/s}$

• The negative value indicates a decrease in [A].

Comparing Spontaneous and Fast Reactions

• Spontaneous does not mean fast. Some reactions are thermodynamically favorable but occur slowly (e.g., rusting of iron).

• Other reactions are both spontaneous and fast (e.g., combustion of gasoline).

Factors Affecting Reaction Rates

Concentration of Reactants

Increasing the concentration of reactants generally increases the rate of reaction due to a higher probability of collisions between reactant molecules.

• Higher concentration → more frequent collisions → higher reaction rate.

Temperature

Raising the temperature increases the kinetic energy of molecules, leading to more frequent and energetic collisions.

• Higher temperature → faster molecular motion → increased reaction rate.

• Rule of thumb: Reaction rate roughly doubles for every 10°C increase in temperature (varies by reaction).

Surface Area

For reactions involving solids, increasing the surface area (e.g., by grinding into a powder) exposes more particles to react, increasing the rate.

• Example: Powdered coffee creamer is flammable due to its high surface area.

Presence of a Catalyst

A catalyst increases the reaction rate by providing an alternative pathway with a lower activation energy, without being consumed in the reaction.

• Catalysts do not affect the equilibrium position, only the rate at which equilibrium is reached.

Rate Laws and Reaction Order

Rate Law Expressions

The rate law for a reaction expresses the rate as a function of the concentrations of reactants, each raised to a power (the order with respect to that reactant):

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

• k = rate constant (depends on temperature and reaction)

• m, n = reaction orders (determined experimentally, not from stoichiometry)

Determining Rate Laws Experimentally

• Conduct experiments varying the concentration of one reactant at a time.

• Observe how the rate changes to determine the order with respect to each reactant.

• Substitute data into the rate law to solve for the rate constant, k.

Units of the Rate Constant (k)

Overall Order	Units of k
0	M·s-1
1	s-1
2	M-1·s-1
3	M-2·s-1

Integrated Rate Laws and Half-Life

Integrated Rate Laws

Integrated rate laws relate the concentration of reactants to time, allowing calculation of concentrations after a given period.

• Zero order: $[A]_t = [A]_0 - kt$

• First order: $\ln([A]_t) = \ln([A]_0) - kt$

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

• $[A]_0$ = initial concentration, $[A]_t$ = concentration at time t, k = rate constant, t = time

Half-Life (t1/2)

The half-life is the time required for half of a reactant to be consumed. It depends on the order of the reaction.

Order	Half-life Expression
Zero	$t_{1/2} = \frac{[A]_0}{2k}$
First	$t_{1/2} = \frac{0.693}{k}$
Second	$t_{1/2} = \frac{1}{k[A]_0}$

Temperature Dependence: The Arrhenius Equation

Arrhenius Equation

The Arrhenius equation describes how the rate constant (k) changes with temperature (T):

• $k = Ae^{-E_a/(RT)}$

• Where A = frequency factor, $E_a$ = activation energy, R = gas constant, T = temperature (K)

For comparing rate constants at two temperatures:

• $\ln\left(\frac{k_2}{k_1}\right) = -\frac{E_a}{R}\left(\frac{1}{T_2} - \frac{1}{T_1}\right)$

Example: Calculating k at a New Temperature

• Given: $k_1 = 2.64 \times 10^2\,\text{s}^{-1}$ at $T_1 = 25^\circ$C ($298$K),$E_a = 74.0$kJ/mol,$T_2 = 50^\circ$C ($323$ K)

• Use the Arrhenius equation to solve for $k_2$.

Summary Table: Rate Laws and Half-Lives

Order	Integrated Rate Law	Half-life
Zero	$[A]_t = [A]_0 - kt$	$t_{1/2} = \frac{[A]_0}{2k}$
First	$\ln([A]_t) = \ln([A]_0) - kt$	$t_{1/2} = \frac{0.693}{k}$
Second	$\frac{1}{[A]_t} = \frac{1}{[A]_0} + kt$	$t_{1/2} = \frac{1}{k[A]_0}$

Applications and Real-World Examples

• Combustion reactions (e.g., burning fuels) are fast and exothermic.

• Food spoilage and preservation involve controlling reaction rates.

• Industrial catalysts (e.g., in the Haber process for ammonia synthesis) increase production efficiency.

• Explosive reactions (e.g., coffee creamer dust explosions) demonstrate the effect of surface area and concentration on reaction rates.

Additional info: Some context and examples were inferred to provide a complete, self-contained study guide suitable for exam preparation.