Rate Laws Worksheet - Answer Key

 

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  1. Kinetics is the study of the rates of reaction.

    2.  

  2. What is a Rate Law?

    The equation that defines the rate of a particular reaction at a particular temperature.  

      3.  

    • How is a rate law determined?

      It must be experimentally determined.

     

     

  3. What are the two types of rate law and what does each compare?

      4.  

    • Differential Rate Law

      This rate compares how the rate of the reaction changes as the concentrations change.

      •  

    • Integrated Rate Law

      This rate compares how the concentrations change with time.

     

     

  4. The general appearance of a differential rate law is:

    Rate = k [Reactant]n

      5.  

    • Where k represents the rate constant. 

        •  

      • What are the units for k?

        k units = .  L n-1  .
                        moln-1 s

       

    • Where n represents the order of reaction.

        •  

      • If n=1 this is said to be a first order reaction.

        •  

      • If n=2 this is said to be a second order reaction.

        •  

      • If n=0 this is said to be a zero order reaction.

       

    • If there is more than one reactant in a rate law you must add their n values to determine the overall order of the reaction.

     

     

  5. For a zero order reaction

      6.  

    • What does zero order tell us with respect to concentration & rate?

      When a reaction is zero order with respect to some species a change in its concentration has no effect on the rate of reaction (the rate remains unchanged).

      •  

    • Differential Rate Law

      Rate = k

      •  

    • Integrated Rate Law

      [A] = -kt + [A]o

        •  

      • How can we utilize this information?

        An important point about the format of the equation is that a reaction is zero order if a graph of [A] vs. t yields a straight line.

       

    • Half Life Equation

      t1/2 = [A]o
      2k

     

     

  6. For a first order reaction

      7.  

    • What does first order tell us with respect to concentration & rate?

      In a first order case, the rate will change by the same factor that the concentration of the reactant changes.

      •  

    • Differential Rate Law

      The general appearance of the first order rate law looks like:

      Rate = k [A]

      •  

    • Integrated Rate Law

      ln [A] = -kt + ln[A]o                                    

        •  

      • What format is this equation written in?  How can we utilize this information?

        The important thing about the format of the equation is that a reaction is first order if a graph of ln[A] vs. t yields a straight line.

       

    • Half Life Equation

      t1/2 = 0.693
      k

     

     

  7. For a second order reaction

      8.  

    • What does second order tell us with respect to concentration & rate?

      In the second order case the change in the rate of reaction is equal to the factor of concentration change squared.

      •  

    • Differential Rate Law

      The general appearance of the second order rate law looks like:

      Rate = k [A]2

      •  

    • Integrated Rate Law

        1 . = kt +   1 .
      [A]              [A]o

        •  

      • What format is this equation written in?  How can we utilize this information?

        The important thing about the format of the equation is that you can tell if a reaction is second order if a graph of 1/[A] versus t yields a straight line.       

       

    • Half Life Equation

      t1/2 =    1    .
      k[A]o

     

     

  8. Determine the differential rate law and rate constant for

    2NO(g) + Cl2(g)    → 2NOCl(g)
    given:

    [NO]o             [Cl2]o               Initial Rate
    0.10 M          0.10 M          0.18 M/min
    0.10 M          0.20 M          0.36 M/min
    0.20 M          0.20 M          1.45 M/min


Rate = k [NO]2[Cl2]
k = 180 M-2 min-1

 

     

  1. Determine the rate law for

     

    2NO(g) + O2(g)    →2NO2(g)

    given:

     

    [NO]o             [Cl2]o               Initial Rate

     

    1.66 x 10-9    1.66 x 10-9    3..32 x 10-11
    1.98 x 10-9    1.66 x 10-9    2.99 x 10-10
    4.15 x 10-9    4.15 x 10-9    5.20 x 10-10

    Rate = k [NO]2[O2]

    2.  

     

  2. A certain reaction has the following general form

    aA    →bB

    At a particular temperature and [A]0=2.80 x 10-3 M concentration versus time data were collected and a plot of 1/[A] versus time resulted in a straight line with a slope value of  +3.60 x 10—2 L/mol*min
    • Determine the differential and integrated rate laws and the value of the rate constant.

      Differential Rate Law:
      Rate = k[A]2
      Integrated Rate Law:
        1 . = kt +   1 .
      [A]              [A]o

      k = 3.60 x 10-2 M-1 min-1                      

      •  

    • Calculate the half-life for this reaction.

      t1/2 = 9921 min

      •  

    • How much time is required for the concentration of A to decrease to 2.50 x 10-3M?

      t = 1109 minutes

     

  1. The decomposition of hydrogen peroxide was studied and the following data was obtained:

     

    Time (s)         [H2O2] (M)
    0                      1
    120                 0.91
    300                 0.78
    600                 0.59
    1200              0.37
    1800              0.22
    2400              0.13
    3000              0.082
    3600              0.05
    • Determine the integrated rate law, the differential rate law, and the value of the rate constant.        

      Differential Rate Law:       Rate = k[H2O2]
      Integrated Rate Law:         ln[H2O2] = -kt + ln[H2O2]o
      k = 0.00083

      •  

    • Calculate the [H2O2] at 4000. s after the start of the reaction.

      0.0362 M
  1. A first order reaction is 75.0% complete in 320. s.
    • What are the first and second half-lives for this reaction?

      160s per half life

      •  

    • How long does it take for this reaction to be 90.0% complete?

      t = 531 s

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