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Chapter 14

Chapter 14: Chemical Kinetics

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: $ln[A]_t = -kt + ln[A]_0$
    • $ln(\frac{[A]_t}{[A]_0}) = -kt$
    • $[A]_t = \frac{1}{2}[A]_0$
    • $ln(\frac{\frac{1}{2}[A]_t}{[A]_0}) = -kt$
    • $-ln(2) = -kt_{\frac{1}{2}}$
    • $t_{\frac{1}{2}}$
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