Chemical Kinetics: Reaction Rates and Rate Laws

• Chemical kinetics, also known as reaction kinetics, studies the rates of chemical processes.
• It investigates how experimental conditions affect reaction speed.
• It provides information about the reaction's mechanism and transition states and allows the construction of mathematical models.

Factors Affecting Reaction Rates

• Reactant concentration: Reaction rate often increases with the concentration of reactants.
• Temperature: Increasing temperature usually increases reaction rate by providing more energy.
• Catalysts: Catalysts speed up reactions by lowering activation energy or changing the reaction mechanism; they are not consumed.
• Pressure: The rate of gaseous reactions increases with pressure.
• Light: Photochemical reactions proceed faster in the presence of light.
• Surface area: Increasing the surface area increases the reaction rate for surface reactions.

Rate Laws

Differential Rate Law

• Expresses reaction rate in terms of changes in reactant concentration over time.
• The rate = $-\frac{d[A]}{dt} = k[A]^n$ , where:
  • rate = reaction rate
  • [A] = concentration of reactant A
  • t = time
  • k = rate constant
  • n = order of reaction with respect to A.

Integrated Rate Law

• Expresses reactant concentration as a function of time.
• Its form depends on the order of the reaction.

Zero-Order Reactions

• $rate = k$
• $[A]_t = [A]_0 - kt$
• $t_{1/2} = \frac{[A]_0}{2k}$

First-Order Reactions

• $rate = k[A]$
• $ln[A]_t = ln[A]_0 - kt$
• $t_{1/2} = \frac{0.693}{k}$

Second-Order Reactions

• $rate = k[A]^2$
• $\frac{1}{[A]_t} = \frac{1}{[A]_0} + kt$
• $t_{1/2} = \frac{1}{k[A]_0}$
• $[A]_t$ is the concentration of A at time t.
• $[A]_0$ is the initial concentration of A.
• $t_{1/2}$ is the half-life of the reaction.

Reaction Mechanisms

• Reaction mechanism is the step-by-step sequence of elementary reactions by which overall chemical change occurs.

Elementary Reactions

• Elementary reactions occur in a single step.
• Their rate law can be written directly from their stoichiometry.

Rate-Determining Step

• The rate-determining step is the slowest step in a reaction mechanism.
• This step limits the overall rate of the reaction.

Activation Energy

• The activation energy ($E_a$) is the minimum energy required for a chemical reaction to occur.
• It's the energy needed to overcome the barrier between reactants and products.

Arrhenius Equation

• The Arrhenius equation relates the rate constant to activation energy, temperature, and a pre-exponential factor (A).
• $k = Ae^{-\frac{E_a}{RT}}$ , where:
  • k is the rate constant.
  • A is the pre-exponential factor.
  • $E_a$ is the activation energy.
  • R is the ideal gas constant (8.314 J/(mol·K)).
  • T is the absolute temperature in Kelvin.

Determining Activation Energy

• The natural logarithm of the Arrhenius equation allows for determination of activation energy from experimental data: $ln(k) = ln(A) - \frac{E_a}{RT}$
• By plotting ln(k) versus 1/T, a straight line is obtained with a slope of $-E_a/R$, from which $E_a $ can be calculated.