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Enduring Understanding 4.A: Reaction Rates

  • Chemical reactions vary widely in the speed at which they occur.
  • The reaction rate is defined as the change in concentration of a substance divided by the time interval:
    • Rate = Δ concentration / Δ time

  • Reactions can be examined experimentally to determine their rate. If a reactant or product is colored, it can be followed by spectrometry using Beers Law.
  • Factors that influence a rate of reaction include:
  • Concentration of reactants (except in zero order processes)
  • Pressure (for reactions involving gases)
  • Surface area (for a solid)
  • Temperature (increased temperature = faster reaction)
  • Presence of a catalyst.

  • Example: A reaction in a closed container, A→2B, is monitored for 60 seconds, giving the following results. What concentrations of A and B are present at 90 seconds?
    • Time, seconds [A], mol/L [B], mol/L
    0 2.00 0
    30 1.00 2.00
    60 0.50 3.00
    90 ? ?
  • Every 30 seconds, the concentration of A drops by half and the concentration of B increases by twice the drop in A.
  • Therefore, after 90 seconds, [A] will be 0.25 mol/L and [B] will be 3.50 mol/L.
  • The rate of a chemical reaction can be expressed mathematically by a rate law. For the reaction:
    • A + B → C

  • The rate law for this reaction would take the form rate = k[A]x[B]y
  • k is the specific rate constant, the rate when [A] and [B] are 1.
  • The exponents, x and y, are the order of the reaction with respect to that reactant. The sum of the exponents, x + y, is the overall order of the reaction.
  • If x = 0, doubling [A] has no effect on the rate (zero order)
  • If x = 1, doubling [A] doubles the rate (first order)
  • If x = 2, doubling [A] increases the rate by 22 or four times (second order).
  • Example: For the reaction:
    • O2 + 2NO → NO2
  • The rate equation is k[O2][NO]2
  • If the concentration of O2 doubles, the rate doubles.
  • If the concentration of NO doubles, the rate increases by 22, or quadruples.
  • The overall order of the reaction is 3.
  • Rate laws cannot be determined from the chemical equation; they must be determined experimentally.
  • Sample Question: Give the following data, what is the rate law for the reaction:
    • A + B + C → D

    [A][B][C]Initial Rate (mol/s)
    0.100.100.105.0
    0.200.100.1020.0
    0.200.200.1040.0
    0.200.200.2040.0
  • Doubling [A] quadruples the rate, so the order of A is 2.
  • Doubling [B] doubles the rate, so the order of B is 1.
  • Doubling [C] has no effect on the rate, so the order of C is zero.
  • The rate law must therefore be k[A]2[B]

  • Radioactive decay is an example of a first-order process. The time taken for half of a sample of a radioactive isotope to decay is called the half-life.
  • The amount of a sample remaining after n half-lives is given by the equation:
    • Amount remaining = (1/2n) x original amount




Related Links:
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AP Chemistry Notes
Redox Reactions



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