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Rate Law & Reaction Order 02
Reaction Order: The sum of the powers to which all reactant concentrations appearing in the rate law are raised. Reaction order is determined experimentally: By inspection. From slope of the line, using the appropriote plot: [A] vs. t, ln[A] vs. t, 1/[A] vs. t
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First-Order Reactions 02
Using calculus we obtain the integrated rate equation: ln [A]t = – kt + ln [A]0 y = m x b Plotting ln[A]t against t will give:
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Determining Reaction Order
Reaction: H2O2 → H2O ½ O2 Plot [H2O2] vs. time time [H2O2] ln[H2O2] 1 0.0000 0.705 0.3496 2 0.497 0.6992 3 0.349 1.0527 4 0.246 1.4024 5 0.173 1.7545
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Determining Reaction Order
Reaction: H2O2 → H2O ½ O2 Plot ln [H2O2] vs. time time [H2O2] ln[H2O2] 1 0.000 0.705 -0.349 2 0.497 -0.699 3 0.349 -1.053 4 0.246 -1.402 5 0.173 -1.754
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Determining Reaction Order
Reaction: H2O2 → H2O ½ O2 Plot ln [H2O2] vs. time time [H2O2] ln[H2O2] 1 0.0000 0.705 0.3496 2 0.497 0.6992 3 0.349 1.0527 4 0.246 1.4024 5 0.173 1.7545
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First-Order Reactions 04
Show that the decomposition of N2O5 is first order and calculate the rate constant. Plot: ln[N2O5] vs. t Is it linear?
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First-Order Reactions 06
Half-Life: Time for reactant concentration to decrease by half its original value.
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Second-Order Reactions 01
A Products A + B Products Rate = k[A] Rate = k[A][B] These equations can then be integrated to give: y = m x b Does this form look familiar?
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Second-Order Reactions 01
Rate = k[A]2 y = m x b Plot 1/[A] vs. t
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Second-Order Reactions 02
Half-Life: Time for reactant concentration to decrease by half its original value.
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Second-Order Reactions 03
Iodine atoms combine, form molecular iodine in gas phase: I(g) + I(g) I2(g) The reaction follows second-order kinetics. Rate constant: k = 7.0 x 10–1 M–1s– at 23°C. 1. If initial concentration of I is M, calculate the concentration after 2.0 min. 2. Calculate the half-life at the start of the reaction if the initial concentration of I is 0.60 M.
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Second-Order Reactions 03
Iodine atoms combine, form molecular iodine in gas phase: I(g) + I(g) I2(g) 2nd Order, k = 7.0 x 10–1 M–1s–1 [I]0 = M, Find [I]120
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Second-Order Reactions
Iodine atoms combine, form molecular iodine in gas phase: I(g) + I(g) I2(g) 2nd Order, k = 7.0 x 10–1 M–1s–1 [I]0 = 0.60 M, Find t1/2
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Review – 1st and 2nd Order Reactions
(integrated form)
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Review – Rate Constants
Units for “Rate” will always be M/sec Molarity units will vary, depending on reaction order
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Review – Equations for Kinetics Problems
General Rate Law: rate = k [A]x [B]y First, determine the order of the reaction (find exponents x and y) by inspection or by graphing. Then this equation can be used to calculate the rate constant k.
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Review – Equations for Kinetics Problems
Integrated forms of Rate Laws: 1st Order Reaction: 2nd Order Reaction: Zero Order Reaction: rate = k [A]x [B]y ln[A]t = –kt + ln[A]0 1/[A]t = kt + 1/[A]0 [A]t = -kt + [A]0
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