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The equation for a straight line is:. Compare this equation to the rearranged first order rate-law. Enrichment - Rate Equations to Determine Reaction Order . Enrichment - Rate Equations to Determine Reaction Order . Now we can interpret the parts of the equation as follows:

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enrichment rate equations to determine reaction order2
Enrichment - Rate Equations to Determine Reaction Order
  • Now we can interpret the parts of the equation as follows:
    • y can be identified with ln[A] and plotted on the y-axis.
    • m can be identified with –ak and is the slope of the line.
    • x can be identified with t and plotted on the x-axis.
    • b can be identified with ln[A]0and is the y-intercept.
enrichment rate equations to determine reaction order3
Enrichment - Rate Equations to Determine Reaction Order
  • Example 16-9: Concentration-versus-time data for the thermal decomposition of ethyl bromide are given in the table below. Use the following graphs of the data to determine the rate of the reaction and the value of the rate constant.
enrichment rate equations to determine reaction order5
Enrichment - Rate Equations to Determine Reaction Order
  • We will make three different graphs of the data.
  • Plot the [C2H5Br] (y-axis) vs. time (x-axis)
    • If the plot is linear then the reaction is zero order with respect to [C2H5Br].
  • Plot the ln [C2H5Br] (y-axis) vs. time (x-axis)
    • If the plot is linear then the reaction is first order with respect to [C2H5Br].
  • Plot 1/ [C2H5Br] (y-axis) vs. time (x-axis)
    • If the plot is linear then the reaction is second order with respect to [C2H5Br].
enrichment rate equations to determine reaction order6
Enrichment - Rate Equations to Determine Reaction Order
  • Plot of [C2H5Br] versus time.
    • Is it linear or not?
enrichment rate equations to determine reaction order7
Enrichment - Rate Equations to Determine Reaction Order
  • Plot of ln [C2H5Br] versus time.
    • Is it linear or not?
enrichment rate equations to determine reaction order8
Enrichment - Rate Equations to Determine Reaction Order
  • Plot of 1/[C2H5Br] versus time.
    • Is it linear or not?
enrichment rate equations to determine reaction order9
Enrichment - Rate Equations to Determine Reaction Order
  • Note that the only graph which is linear is the plot of ln[C2H5Br] vs. time.
    • Thus this is a first order reaction with respect to [C2H5Br].
  • Next, we will determine the value of the rate constant from the slope of the line on the graph of ln[C2H5Br] vs. time.
    • Remember slope = y2-y1/x2-x1.
enrichment rate equations to determine reaction order10
Enrichment - Rate Equations to Determine Reaction Order
  • From the equation for a first order reaction we know that the slope = -a k.
    • In this reaction a = 1.
enrichment rate equations to determine reaction order11
The integrated rate equation for a reaction that is second order in reactant A and second order overall.

This equation can be rearranged to:

Enrichment - Rate Equations to Determine Reaction Order
enrichment rate equations to determine reaction order12
Compare the equation for a straight line and the second order rate-law expression.

Now we can interpret the parts of the equation as follows:

y can be identified with 1/[A] and plotted on the y-axis.

m can be identified with a k and is the slope of the line.

x can be identified with t and plotted on the x-axis

b can be identified with 1/[A]0 and is the y-intercept.

Enrichment - Rate Equations to Determine Reaction Order
enrichment rate equations to determine reaction order13
Enrichment - Rate Equations to Determine Reaction Order
  • Example 16-10: Concentration-versus-time data for the decomposition of nitrogen dioxide are given in the table below. Use the graphs to determine the rate of the reaction and the value of the rate constant
enrichment rate equations to determine reaction order15
Enrichment - Rate Equations to Determine Reaction Order
  • Once again, we will make three different graphs of the data.
  • Plot [NO2] (y-axis) vs. time (x-axis).
    • If the plot is linear then the reaction is zero order with respect to NO2.
  • Plot ln [NO2] (y-axis) vs. time (x-axis).
    • If the plot is linear then the reaction is first order with respect to NO2.
  • Plot 1/ [NO2] (y-axis) vs. time (x-axis).
    • If the plot is linear then the reaction is second order with respect to NO2.
enrichment rate equations to determine reaction order16
Enrichment - Rate Equations to Determine Reaction Order
  • Plot of [NO2] versus time.
    • Is it linear or not?
enrichment rate equations to determine reaction order17
Enrichment -Rate Equations to Determine Reaction Order
  • Plot of ln [NO2] versus time.
    • Is it linear or not?
enrichment rate equations to determine reaction order18
Enrichment - Rate Equations to Determine Reaction Order
  • Plot of 1/[NO2] versus time.
    • Is it linear or not?
enrichment rate equations to determine reaction order19
Enrichment - Rate Equations to Determine Reaction Order
  • Note that the only graph which is linear is the plot of 1/[NO2] vs. time.
  • Thus this is a second order reaction with respect to [NO2].
  • Next, we will determine the value of the rate constant from the slope of the line on the graph of 1/[NO2] vs. time.
enrichment rate equations to determine reaction order20
Enrichment - Rate Equations to Determine Reaction Order
  • From the equation for a first order reaction we know that the slope = a k
    • In this reaction a = 2.
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