Applications of Kinetics Edward A. Mottel Department of Chemistry Rose-Hulman Institute of Technology

6/15/2015 Kinetics Applications  Reading assignment: Zumdahl: Chapter  Comparison of orders of reaction rates of reaction  Half-life  Percentage Completion  Nuclear dating processes

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.

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.

6/15/2015 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.

6/15/2015 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 Time (s) PNO2 (torr) 474 torr

6/15/2015 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 Time (s) PNO2 (torr) 474 torr 237 torr 139 s 118 torr = 278 s

6/15/2015 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.

6/15/2015 NO 2 Decomposition is Second-Order (P NO2 ) t - 1 = 1.52 x (t - t o ) + (P NO2 ) o time until the first half-life t = 139 s Determine the second half-life for NO 2. t = 278 s

6/15/2015 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.

6/15/2015 If 80% of the nitrogen dioxide is decomposed, then 20% remains Time (s) PNO2 (torr) 474 torr 95 torr 555 s Graphical Determination of Percent Completion 2 NO 2 (g)  2 NO(g) + O 2 (g)

Alcohol Evaporation at Room Temperature Time (s) Mass (g) Ethanol y = x R 2 = Determine if the half-life for the evaporation of ethanol is constant.

6/15/2015 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.

6/15/2015 Radioactive Dating 131 I (mg) Percent Reacted ½ 93¾ Period Time (d) Time Change (d) 8.1

6/15/2015 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?

6/15/2015 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

6/15/2015 Carbon-14 Dating  14 C is produced in the upper atmosphere by the bombardment of 14 N with cosmic rays.  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.

6/15/2015 Carbon-14 Dating  What assumptions are implicit in this dating process?

6/15/2015 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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