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Concentration and Chemical Reaction Rate

Skills to develop

  • Explain chemical reaction rates
  • Explain the concentration effects on reaction rate
  • Define the order of a reaction with respect to a reactant
  • Define the overall order of a chemical reaction
  • Define the rate constant of a chemical reaction
  • Determine the order of a reaction by experiment
  • Concentration and Chemical Reaction Rate

    In the introduction to chemical kinetics, we have already defined chemical reaction rates. Rates of chemical reactions depend on the nature of the reactants, the temperature, the presence of a catalyst, and concentration. This page discusses how the concentration affect the chemical reaction rates. Concentration effect is important because chemical reactions are usually carried out in solutions.

    Chemical Reaction Rates

    The reaction rates of chemical reactions are the amounts of a reactant reacted or the amount of a product formed per unit time, (moles per second). Often, the amount can be expressed in terms of concentrations.
                 amount reacted
                  or produced
         Rate = --------------- units: g/s, mol/s, or %/s
                 time interval
    
    At certain conditions, the rates are functions of concentrations. Depending on the time interval between measurements, the rates are called
    average rate: rate measured between long time interval
    instantaneous rate: rate measured between very short interval
    initial rate: instantaneous rate at the beginning of an experiment

    However, a more realistic representation for a reaction rate is the change in concentration per unit time, either the decrease of concentration per unit time of a reactant or the increase of concentration per unit time of a product. In this case, the rate is expressed in Mol/(L sec).

                concentration change of
                a reactant or product
         Rate = ----------------------- units: g/(M s), M/s, ppm/s etc
                      time interval
    

    Measuring Reaction Rate

    To measure a reaction rate, we usually monitor either a product or a reactant for its change. Any physical characteristic related to the quantity or concentration of a product or reactant can be monitored. Some of the characteristics to be monitored are:
          change in pressure,
          change in color (spectroscopic measurement),
          temperature for exothermic or endothermic reaction, and
          presence of certain key substance,

    The change can be plotted on a graph, and from the graph, we can get the average rate or the instantaneous rate by either graphical method or using computer for the data analysis.

    Rate Constants and the Orders

    Usually, the rate of a reaction is a function of the concentrations of reactants. For example, the rate of the reaction 2 NO + O2 = 2 NO2
    has the form:
    Rate = k [O2] [NO]2
    The rate is proportional to the concentration of O2, usually written as [O2] and is proportional to the square of [NO], or [NO]2. The orders of 1 and 2 for [O2] and [NO] respectively has been determined by experiment, NOT from the chemical equation. The total order of this reaction is 3 (=2+1).

    Note the rates and order in the following example reactions:

    H2 + I2 = 2 HI,
    Rate = k [H2] [I2],
    Total order 2.

    H2 + Br2 = 2 HBr,
    Rate = k [H2] [Br2]1/2,
    Total order 1.5.

    In particular, note that orders are NOT determined from the stoichiometry of the reaction equation.

    Rates as Functions of Reactant Concentrations

    The order with respect to (wrt) a reactant are determined experimentally by keeping the concentration of other reactants constant, but vary the concentration of one of the reactant, say A in a general reaction a A + b B + c C = products If concentrations of B and C are kept constant, you can measure the reaction rate of A at various concentrations. You can then plot the rate as a function of [A]. For a zeroth order reaction, you will get a horizontal line, because rate = k     (a horizontal line)
    
      rate
         |      /
         |     /rate = k [A]
         |    /
         |- -/- - - - - rate = k
         |  /
         | /
         |/_________________ 
         0   1   2   3   4  [A]
    
    For a first order reaction, the plot is a straight line (linear), as shown above, because rate = k [A]     (a straight line) Note that rate = k when [A] = 1.

    For a second order reaction, the plot is a branch of a prabola, because

    rate = k [A]2
    
      rate
         |      .
         |       rate = k [A]2 
         |     .   (a branch of 
         |          a parabola)
         |    .
         | - . - - - - - -
         |  .
         |._________________ 
         0   1   2   3   4  [A]
    

    For a reaction with an infinite order, the plot is a step function. The rate is small, almost zero, when [A] less than 1. When [A] is greater than or equal to 1, then the reaction rate is very large. This model applies to nuclear explosion, except that [A] = 1 is actually the critical mass of the fission material.

    rate = k [A]00
    
    
      rate
         |       (order = infinity)
         |   |   rate = k [A]00
         |   |   (a vertical line)
         |   |
         |   |
         |   |
         |   |
         |...|_________________ 
         0   1   2   3   4  [A]
    
    Is there a chemical process like this? Well, we all know that one of the key conditions in an atomic bombs is to have a critical mass of the fission material, 235U or 239Pu. When such a mass is put together, the reaction rate increases dramatically, leading to an explosion. Thus, this model seems to apply, however, the mechanism for the fission reaction is not discribed by the order of the fission material.

    Variation of Rate, Rate Constant, and Order of a Reaction

    If only [A] is varied in experiments, and the order wrt [A] is n, then the rate has the general expression, rate = k [A]n In this expression, k is the specific rate constant, or the rate when [A] = 1.00. Again, the order n is not necessarily an integer, but its most common values are 0.5 (1/2), 1, 2, or 3. Cases in which n is a negative number are rare.

    Mathematical models for the effect of concentration on rates are interesting. In general, the rate of a reaction of order n with respect to A can be represented by the equation:

    y = k xn,       (n = various values including 0.5, 1, 2, 3, ...)
    Plots of equations for various values of n illustrate the dependence of rate on concentration for various orders.

    Evaluation of order by Experiments

    For a chemical reaction, we often determine the order with respect to a reagent by determine the initial rate. When more than one reactants are invovled, we vary the concentrations in a systematic way so that the effect of concentration of one of the reactants can be measured.

    For example, if a reaction involving three reactants, A, B, and C, we vary [A] from experiment 1 to experiment 2 and find out how the rate varies. Similarly, we vary concentrations of B or C in other experiments, keeping others constant, and investigate its effect. The example below illustrates the strategy for such an approach.

    Example

    Derive the rate law for the reaction A + B + C => products from the following data, where rate is measured as soon as the reactants are mixed.
    Experiment1234
    [A]o0.1000.2000.2000.100
    [B]o0.1000.1000.3000.100
    [C]o0.1000.1000.1000.400
    rate0.1000.8007.2000.400

    Solution
    Assume the orders to be x, y, and z respectively for A, B, and C, we have

    rate = k [A]x [B]y [C]z From experiment 1 and 2, we have:
    0.800   k 0.2x  0.1y  0.1z
    ----- = ---------------
    0.100   k 0.1x  0.1y  0.1z
    
    Thus, 8 = 2x; and x = ln8 / ln2 = 3

    By similar procedures, we get y = 2 and z = 1. Thus, the rate law is:

    rate = k [A]3 [B]2 [C]

    Discussion
    Note the following relationships:

    x = yz
    ln x = z ln y
    z
    = ln x / ln y

    Summary

    The variation of reaction rates as functions of order and concentrations are summarized in the form of a Table below.

      Differential
    rate law
    Plot of rate vs
    [A]
    0th
    order
    - d[A]/dt = khorizontal
    line
    first
    order
    - d[A]/dt = k[A]straight line with
    slope = k
    second
    order
    - d[A]/dt = [A]2a branch of
    parabola
    order
    = infinity
    - d[A]/dt = k [A]oo rate = 0 when [A] < 1
    rate = infinite when [A] > 1
    a vertical line at [A] = 1

    Confidence Building Questions

    ©cchieh@uwaterloo.ca