Integrated Rate Law

Rate laws can be converted into equations that tell us what the concentration of the reactants or products are at any time

Calculus required to derive the equations but not to use them

Rate = k With calculus it can be changed to an

equation that relates the starting conc ([A]o) to the conc at any other time (t)

[A] = -kt + [A]o

Zero Order

Plot of [A] vs t is linear with a slope equal to k

Graph

Find the conc of a reactant at some time after the reaction started

Find the time required for a given fraction of a sample to react

Find the time required for a reactant to reach a certain concentration

Uses of Equation

Rate = k[A]

ln[A] = - kt + ln[A]o

First Order Reactions

Plot of ln[A] vs t is linear

Graphs

The first order constant for the hydrolysis of a certain insecticide in water at 12°C is 1.45/yr. A quantity of this insecticide is washed into a lake in June, leading to an overall concentration of 5 x 10-7 g/cm3 of water. Assume that the effective temp of the lake is also 12°C. A) what is the conc of the insecticide in June of the following year? B) How long will it take for the conc of the insecticide to drop to 3.0 x 10-7

g/cm3 ?

Example

The decomposition of dinitrogen pentoxide is studied over time and the results are given in in the table on pg.573.a) Verify if this is a first order reaction.b) Calculate the value of the rate constantc) Find the concentration after 150 sec.

Example

Time required for the concentration of a reactant to decrease to halfway between its initial and final values

Time when [A]= ½ [A]o

t1/2 = .693/k

Half Life

What is the half life of the insecticide in the lake from the previous example?

Example

Rate = k[A]2

1/[A] = kt + 1/[A]o Plot of 1/[A] vs t is linear

Second Order Reactions

Plot of 1/[A] vs t is linear

Graph

The following data was obtained for the decomposition of nitrogen dioxide. Is the reaction first or second order? What is the rate constant? Time (s) [NO2] 0 .0100 50 .0079 100 .0065 200 .0048 300 .0038

Example