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Chapter 14

Chapter 14: Chemical Kinetics

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Rates of reaction and the particulate nature of matter

  • Kinetics:
    • Rates of reaction (speed)
    • The sequential steps of a reaction
  • Affect the rates?
    • Concentration of the reactants
      • The more stuff that is present, the more collisions will occur and the rate of reaction will increase
    • Temperature of reaction
      • As the temperature increases, the rates also increase
    • Structure and orientation of particles
      • B-A + C → A-C + B
      • A-B + C -/->

Rates in a chemical reaction

  • Rate = $\frac{\text{Concentration Change}}{\text{Time Change}}$
  • 2 N2O5 → 4NO2 + O2
  • Rate of formation for NO2: $\frac{\Delta [NO_2]}{\Delta t} = 3.7\times 10^{-5} M s^{-1}$
  • Rate for formation for O2: $9.00\times 10 ^{-6} M s^{-1}$
  • Rates must be positive
  • General rate of reaction
    • Not formation or decomposition, but the rate of the entire reaction
    • Use stoichiometry to make sure that everything is equal to each other
    • Get one rate of reaction
      • Take each of the terms and divide it by the stoichiometry

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  • Instantaneous rate: rate of reaction at a single point in time
    • It is the slope tangent to the curve

The Rate Law

  • How the reaction proceeds over the entirety of the reaction
  • aA + bB → products
    • Rate Law: $\text{Rate} = k[A]^m[B]^n$
      • These exponents tell us how sensitive the reaction is to changes in concentration 
      • These exponents must be experimentally determined
        • This is because there are sequential steps for the reaction
      • The larger the exponent, the more sensitive it is to changes in concentration
  • 3 common reaction orders that we can think about
    • We mean exponents by orders (m/n = 0, 1, 2)
      • Technically they can go higher or negative, but that is beyond the scope of General Chemistry II
    • If n = 0, the change in concentration has no effect on the rate
    • If n = 1, the rate is directly proportional to the concentration
    • If n = 2, the rate is proportional to the square of the concentration
  • Overall reaction order: sum exponents
    • $\text{Rate} = k[A]^2[B]^1, \text{rate} = 3$

Determining the Order of a Reaction

  • Initial rates: start of reaction
    • Change concentration and see the effect on the rate

The Integrated Rate Laws

First Order Integrated Rate Law

  • $\text{Rate} = k[A]^1 = \frac{-\Delta [A]}{\Delta t}$
  • $ln[A]_t = -kt + ln[A]_0$
    • $y=mx+b$ format

Second Order Integrated Rate Law

  • $\text{Rate} = k[A]^2 = \frac{-\Delta [A]}{\Delta t}$
  • $\frac{1}{[A]_t} = +kt + \frac{1}{[A]_0}$

Zeroth Order Integrated Rate Law

  • $\text{Rate} = k[A]^0 = \frac{-\Delta [A]}{\Delta t}$
  • $[A]_t = -kt + [A]_0$

The Half-Life of the Reaction

  • The time needed for the concentration to be one half of its initial value
  • First order: $ln[A]_t = -kt + ln[A]_0$
    • $ln(\frac{[A]_t}{[A]_0}) = -kt$
    • $[A]_t = \frac{1}{2}[A]_0$
    • $ln(\frac{\frac{1}{2}[A]_t}{[A]_0}) = -kt$
    • $-ln(2) = -kt_{\frac{1}{2}}$
    • $t_{\frac{1}{2}} = \frac{ln(2)}{k}$
    • For the first order reaction, $t_{\frac{1}{2}}$ has no concentration dependence
  • Second order: $t_{\frac{1}{2}} = \frac{1}{k[A]_0}$
  • Zeroth Order: $t_{\frac{1}{2}} = \frac{[A]_0}{2k}$

The Effect of Temperature on Reaction Rates

  • The Arrhenius Equation
    • $k=Ae^{\frac{-Ea}{RT}}$
    • A is the frequency factor
    • -Ea is the activation energy
    • R is the gas law constant
    • T is the temperature in kelvin
  • Activation energy
    • The amount of energy required to make the reaction go from products to reactants
  • Change in energy is just final minus initial
  • Frequency factor ($A$)
    • Number of times R approaches Ea barrier per unit of time
  • Exponential factor ($\frac{-Ea}{RT}$)
    • Fraction of molecules with energy to get over the barrier
  • Two-point form of the Arrhenius equation
    • $ln(A) = ln(k_1) + \frac{Ea}{R}(\frac{1}{T_1}) = ln(k_2) + \frac{Ea}{R}(\frac{1}{T_2})$
  • The collision model (A)
    • Need 2 properly oriented molecules with sufficient energy to get over the barrier
    • Orientation factor
      • The reactants need to be oriented properly
    • Collision frequency (z)
      • Collision rate = $z[A][B]$
    • Reaction rate = orientation factor * collision rate * exponential factor

Reaction Mechanisms

  • Series of molecular steps to get from reactants to products
    • Elementary steps
      • Individual molecular event
    • Reaction intermediate
      • Made in one step and consumer in another
        • Never seen in an equation
  • Rates laws for elementary steps: molecularity
    • Unimolecular: one reactant (Rate = $k[O_3]$)
    • Bimolecular: two reactants (Rate = $k[O_3][O]$)
    • Termolecular: three reactants (exceedingly rare) (Rate = $k[O]^2[M]$)
  • Assumptions
    1. Elementary reactions can be reversible
    2. Intermediates cannot be in the overall reaction or the overall reaction law
    3. Rate determining step is the slowest step
  • Conditions for a plausible mechanism
    1. The elementary steps must sum to the overall reaction
    2. The rate law from the mechanism must match the experimentally determined rate law
    3. Molecularity must make sense
      • Look out for this
      • Only have termolecular if there is NO other option
  • Slow first step, fast second step
    • Rate is based on the first step
    • The overall rate law is based on the slowest step
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