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Applications of Kinetics Edward A. Mottel Integrated, First-Year Curriculum in Science, Engineering and Mathematics

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Please Sit with Your Group Please be sure each member of your team has a copy of Applications of Kinetics Lecture Notes Todays reporter is the person with the largest pet.

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6/5/2014 Kinetics Applications Comparison of orders of reaction rates of reaction Half-life Percentage Completion Nuclear dating processes

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Orders of Reaction On a graph of concentration versus time, plot zero, first and second order data sets that have the same initial concentration and the same numeric value for the rate constant. Will the lines ever cross? Describe the shape of each line and interpret the line shape.

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Reaction Rate Constants On a graph of concentration versus time, plot a system with the same reaction order, but with three different numeric values for the rate constant. The second rate constant should be twice the first rate constant, and the third rate constant should be ten times the first rate constant. Will the lines ever cross? Describe the shape of each line and interpret the line shape.

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6/5/2014 Half-Life The half-life of a reaction is the time required for a given amount of a reactant to be consumed. Could be a concentration or a pressure. Can be determined either graphically or analytically.

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6/5/2014 Graphical Determination of Half-Life 2 NO 2 (g) 2 NO(g) + O 2 (g) Determine if the half-life for the decomposition of nitrogen dioxide is constant. 02004006008001000 Time (s) 100 200 300 400 500 PNO2 (torr) 474 torr 237 torr 139 s 118 torr 417-139 = 278 s

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6/5/2014 Half-Life and Percentage Completion The half-life equation is derived from the integrated solution of the rate equation. Percentage completion calculations are similar, using appropriate initial and final amounts of reactant.

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6/5/2014 NO 2 Decomposition is Second-Order (P NO2 ) t - 1 = 1.52 x 10 - 5 (t - t o ) + (P NO2 ) o - 1 4740 2 time until the first half-life t = 139 s Determine the second half-life for NO 2. t = 278 s

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6/5/2014 Percentage Completion Use the integrated form of the rate equation to determine the amount of time required for the reaction to be 80% completed from the original reaction conditions. Confirm your answer using the graph.

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6/5/2014 If 80% of the nitrogen dioxide is decomposed, then 20% remains. 02004006008001000 Time (s) 100 200 300 400 500 PNO2 (torr) 474 torr 95 torr 555 s Graphical Determination of Percent Completion 2 NO 2 (g) 2 NO(g) + O 2 (g)

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Alcohol Evaporation at Room Temperature 0 1 2 3 4 5 6 7 8 9 0100200300400500600700800 Time (s) Mass (g) Ethanol y = - 0.0099x + 7.941 R 2 = 0.9991 Determine if the half-life for the evaporation of ethanol is constant.

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6/5/2014 Radioactive Dating First-order kinetic processes have constant half-lives. Can you prove this? Almost all radioactive processes are first-order. This allows "dating" of objects if such a first-order process is occurring.

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6/5/2014 Radioactive Dating 131 I (mg) 100. 50.0 25.0 12.5 6.25 Percent Reacted 0 50 75 87½ 93¾ Period 0 1 2 3 4 Time (d) 0 8.1 16.2 24.3 32.4 Time Change (d) 8.1

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6/5/2014 Radioactive Dating The length of the dating "window" depends on the half-life of the process. A practical limit is about 0.1 to 10 half-lives. How much of a reactant remains after 0.1 half-lives 10 half-lives Why does this dating "window" exist?

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6/5/2014 Radioactive Processes Radioactive Species ReactionHalf-LifeApplications 3H3H 3 H 3 He + 12.3 ytracer studies 14 C5730 y dating of former living artifacts 234 U2.47 x 10 5 y 238 Uage of rocks 14 C 14 N + 234 U 230 Th + 4 He 238 U 234 Th + 4 He 4.51 x 10 9 y

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6/5/2014 Carbon-14 Dating 14 C is produced in the upper atmosphere by the bombardment of 14 N with cosmic rays.

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6/5/2014 Carbon-14 Dating The carbon-14 produced reacts to form carbon dioxide, consumed by plants which are eaten by animals. Every living thing has carbon-14 in it, but the ingestion process stops at death. The ratio of the amount of carbon-14 when measured to the amount expected while alive can be used to estimate the age of the organism.

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6/5/2014 Carbon-14 Dating What assumptions are implicit in this dating process?

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6/5/2014 Atomic Clocks Radioactive dating has been used to estimate the age of rocks. If the age of the earth is about 4.5 x 10 9 years, why does a typical uranium sample contain mostly 238 U and a small amount of 235 U, but virtually no 234 U?

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6/5/2014

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