Integrated Rate Laws !
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The differential rate laws we have seen
thus far lack an essential element
necessary for answering the question,
“How long is this going to take?” In other
words, the rate laws do not have a time
variable. By applying calculus, a new set of
useful formulas can be obtained as shown below.!
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Pre-lab:!
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Go to the class website, look at the Kinetics page and view the podcast: “Integrated Rate Laws”.!
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1.
Explain how integrated rate laws allow for a graphical way to determine the order of a
decomposition reaction.!
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2. Solve the problem:!
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For a first order process: A —-> products, if the initial concentration of A is 1.0 M and
k = 0.0234 s-1, how long will it take for the concentration of A to become 0.010 M?!
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The Kinetics of the Rusting of Steel Wool: An Application of Integrated Rate Laws
The Reaction:
4 Fe(s) + 3 O2 (g) ! 2 Fe2O3 (s)
In this investigation, we will collect data using a Vernier pressure sensor connected to a small
test tube containing the reactants. Logger Pro will be used to plot total pressure in the tube
as a function of time. With this data, you will be able to create other graphs and determine
the rate law and k for this reaction.
The pressure sensor will measure total pressure in the tube. You need to create a column
that would be the poxygen. How is ptotal related to poxygen?
1. Once you have this set up, use the table above and create columns for the
appropriate integrated rate law plots and use them to determine the appropriate
order with respect to O2 for the rate law for the reaction. Use the correlation
coefficient to determine the most linear graph.
(a) Determine the initial rate of the reaction from using your graphs in both units of
atm/min and M/min. To obtain the rate in units of M/min, you’ll need to use the
ideal gas law to convert pressure to M. ( P = MRT )
(b) Write 4 rate laws for this reaction, including k, with units, for each:
2.
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The differential rate law in terms of pO2
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The differential rate law in terms of [O2]
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The integrated rate law in terms of pO2
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The integrated rate law in terms of [O2]
Print out the following graphs or copy them into Word file:
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poxygen vs. time
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ln poxygen vs. time
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1/poxygen vs. time
3.
Use your data to determine the half-life of this reaction. How could the rate of this
reaction be changed? Offer two specific suggestions and explain the chemical basis for
how they would work.
4. Use your rate law to determine the time it would take 30% of the oxygen in a 0.0300 L
test-tube to react with a large piece of steel wool if there is 0.0010 moles of oxygen in
the test tube initially.
5. Complete problems from chapter 14: 43, 44, 46, 107
6. Follow up problem:
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