© University of South Carolina Board of Trustees Chapt. 13 Kinetics Sec. 1 Define ‘Rate’

© University of South Carolina Board of Trustees R  P  [R] tt tt slope

© University of South Carolina Board of Trustees Reaction Rate: Good

© University of South Carolina Board of Trustees Average vs Instantaneous Rates  [R] tt dt d [R] Average Instantaneous

© University of South Carolina Board of Trustees Reaction Rate: Better  Use the instantaneous rate

© University of South Carolina Board of Trustees Reaction Rate: Even Better ●Use the instantaneous rate  Make product or reactant measurements interchangeable

© University of South Carolina Board of Trustees Reaction Rate: Best ●Use the instantaneous rate ●Make product or reactant measurements interchangeable  Correct for stoichiometry

© University of South Carolina Board of Trustees Example: Stoichiometry and Rates In an electrolysis cell, electric current forces water to decompose into its elements, producing hydrogen at the rate of 0.12 mol/L-s. 2 H 2 O  2 H 2 + O 2 a) What is the rate of formation of oxygen? b) What is the rate of disappearance of water? c) What is the reaction rate?

© University of South Carolina Board of Trustees Chapt. 13 Kinetics Sec. 2 Define ‘Rate Law’

© University of South Carolina Board of Trustees Rate and Concentration vs Time rate at 0 s rate at 20 s rate at 40 s

© University of South Carolina Board of Trustees Rate Law Most Common Form ●reactants only ● x, y small integers or simple fractions (0,1/2, 1, 3/2, 2,...) ● x  a ; y  b (Not K eq ) rate = k [A] x [B] y Definitions ● k = rate constant ● x = order in A y = order in B ● x + y = overall order a A + b B  products

© University of South Carolina Board of Trustees Chapt. 13 Kinetics Sec. 2 Data  k Method of Initial Rates

© University of South Carolina Board of Trustees [A] vs t Data  Rate Law  Method of Initial Rates (Sec. 13.2) Trial and Error with Common Laws (Sec. 13.3)

© University of South Carolina Board of Trustees Define Initial Rate initial rate initial conc. Assume rate and concentration are constant over initial time period

© University of South Carolina Board of Trustees Example: Method of Initial Rates Initial rates are given below for the reaction F 2 + 2ClO 2  2FClO 2 Determine the rate law.

© University of South Carolina Board of Trustees (1) Use Ratios Initial rates are given below for the reaction F 2 + 2ClO 2  2FClO 2 Determine the rate law.

© University of South Carolina Board of Trustees (2) [F 2 ] const  y Initial rates are given below for the reaction F 2 + 2ClO 2  2FClO 2 Determine the rate law.

© University of South Carolina Board of Trustees (3) [ClO 2 ] const  x Initial rates are given below for the reaction F 2 + 2ClO 2  2FClO 2 Determine the rate law.

© University of South Carolina Board of Trustees (4) Find k Choose any set Initial rates are given below for the reaction F 2 + 2ClO 2  2FClO 2 Determine the rate law.

© University of South Carolina Board of Trustees Trial[NO] M [H 2 ] M Initial Rate M/sM/s x x x10 -2 Student Problem Write the rate law for the reaction given the following data 2NO + 2H 2  N 2 + 2H 2 O

© University of South Carolina Board of Trustees Chapt. 13 Kinetics Sec. 3 Common Rate Laws

© University of South Carolina Board of Trustees Common Rate Laws A  products a) First-order Rate = k [A] b) Second-order Rate = k [A] 2 c) Zero-order Rate = k [A] 0 = k

© University of South Carolina Board of Trustees Common Rate Laws A  products a) First-order Rate = k [A] b) Second-order Rate = k [A] 2 c) Zero-order Rate = k [A] 0 = k

© University of South Carolina Board of Trustees 1 st -Order Rate Law Differential Form Rate = k [A]( t )

© University of South Carolina Board of Trustees 1 st -Order Rate Law Differential Form Rate = k [A]( t ) Integral Forms [A]( t ) = [A] 0 e - kt

© University of South Carolina Board of Trustees [A] = [A] 0 exp(- k t)

© University of South Carolina Board of Trustees Concentration at a Later Time C 12 H 22 O 11 + H 2 O  C 6 H 12 O 6 + C 6 H 12 O 6 sucrose glucose fructose This reaction is 1 st order with a rate constant of 6.2 x10 -5 s -1. If the initial sucrose concentration is 0.40 M, what is the concentration after 2 hrs (7200 s)?

© University of South Carolina Board of Trustees Time to Reach a Concentration C 12 H 22 O 11 + H 2 O  C 6 H 12 O 6 + C 6 H 12 O 6 sucrose glucose fructose This reaction is 1 st order with a rate constant of 6.2 x10 -5 s -1. If the initial sucrose concentration is 0.40 M, at what time does the concentration fall to 0.30 M ?