Name_______________________
Integrated Rate Law
notes
14.3- The Change of Concentration with Time
1.
2.
Differential- Data table contains RATE AND
CONCENTRATION DATA. Uses “table logic” or algebra to
find the order of reaction and rate law
Integrated- Data table contains TIME AND
CONCENTRATION DATA. Uses graphical methods to
determine the order of the given reactant. K=slope of
best fit line found through linear regressions
a. Can be used when we want to know how long a
reaction has to proceed to reach a
predetermined concentration of some reagent
Graphing Integrated Rate Law
• Time is always on x axis
• Plot concentration on y axis of 1st graph
• Plot ln [A] on the y axis of the second graph
• Plot 1/[A] on the y axis of third graph
• You are in search of a linear graph
Zero order ReactionsUse A  B as an example. What happens when we double
[A], what happens to the rate of reaction that is zero order?
So when we plot our data table and get a negative straight
line it is ____________order!!
First-Order ReactionAB in a reaction.
①Write the rate expression for reactant A. (sec. 1 stuff)
②Write the rate law for reactant A. (sec 2 stuff)
Describe a First Order reaction.
Sketch a graph with rate on Y and concentration on X axisLabel axis!!
So does the concentration affect rate? Y/N_________
What would the rate law be for a zero order?
Sketch a graph with rate on Y and concentration on X axisLabel axis!!
Sketch a graph with concentration on Y and time on X axisLabel axis!!
Sketch a graph with concentration on Y and time on X axisLabel axis!!
We can manipulate the data to provide a straight line plot.
Change how we plot concentration.
Take equations ① and ② and smash them together.
How do you use this equation to solve for concentration?
Using calculus to integrate the rate law for a first-order
process gives us.
Practice Exercise
The decomposition of dimethyl ether, (CH3)2O, at 510 ºC is a
first-order process with a rate constant of 6.8  10–4 s–1:
(CH3)2O(g)  CH4(g) + H2(g) + CO(g)
If the initial pressure of (CH3)2O is 135 torr, what is its
pressure after 1420 s?
Using calculus to integrate the rate law for a first-order
process gives us.
Second-Order ReactionDescribe a second-order reaction.
Where,
[A]0 is the initial concentration of A.
[A]t is the concentration of A at some time, t, during the
course of the reaction.
Sketch a graph with rate on Y and concentration on X axisLabel axis!!
Integrated Law for 1st order is
Relate this equation to the slope.
Therefore, if a reaction is first-order, a plot of ln [A] vs. time
will yield a straight line, and the slope of the line will be -k.
Let’s look at the integrated 1st order equation.
Sample problem 14.5
The decomposition of a certain insecticide in water at 12 C
follows first-order kinetics with a rate constant of 1.45 yr1. A
quantity of this insecticide is washed into a lake on June 1,
leading to a concentration of 5.0  107 g/cm3. Assume that
the average temperature of the lake is 12 ºC.
(a) What is the concentration of the insecticide on June 1 of
the following year?
Sketch a graph with concentration on Y and time on X axisLabel axis!!
We can manipulate the data to provide a straight line plot.
Change how we plot concentration.
How do you use this equation to solve for concentration?
Using calculus to integrate the rate law for a first-order
process gives us.
(b) How long will it take for the insecticide concentration to
decrease to 3.0  10–7 g/cm3?
What does second order reactions depend on?
Sample Exercise 14.7
The following data were obtained for the gas-phase
decomposition of nitrogen dioxide at 300 ºC,
Time (s)
[NO2], M
0.0
0.01000
50.0
0.00787
100.0
0.00649
200.0
0.00481
300.0
0.00380
ln [NO2]
1/ [NO2]
Is the reaction first or second order in NO2? Fill in Blanks!
Let’s graph the ln[NO2] to see if its 1st order
Practice with graphs- After creating regression graphs of
various reactions; provide the rate order for each graph.
Is your graph linear?______ then it is/isn’t ________ order.
What order is this reaction and what formula would I use to
calculate various times/concentrations?
Let’s graph the 1/[NO2] to see if its 2nd order
What order is this reaction and what formula would I use to
calculate various times/concentrations?
Is your graph linear?______ then it is/isn’t ________ order.
Summary on Integrated Rate Laws
What order is this reaction and what formula would I use to
calculate various times/concentrations?