AP Chem Kinetics
4.14.2- integrated rate laws, half life
Remember order of reaction?
• Rate = k[A]m[B]n
• Overall reaction order = m+ n
• Remember that rate has units of mol L-1s-1
(M/s)
Two types of rate laws
• Differential rate law- what we did so far
– Shows how the rate of reaction is dependent on
concentration (m and n)
– Uses initial rates of reaction occurring at varying conc.
and sees how the rate changes due to conc.
• Integrated rate law
– Shows how conc. depends on time
– Conc. are measured at various times and data is
plotted. We see how integrated rate law fits the data
(gives us a straight line)
Why do I need to integrate????
• The slope of this graph isn’t that useful in
predicting concentrations of reactants over long
periods of time
• I can find average rate from entire graph (not
super accurate)
• Or using tangent I can find Instantaneous rate
• But it would be nice if I had a graph with a linear
relationship so at any point on graph I can find
conc. or time or make predictions
• I want to integrate rate to make a linear graph
so I have a constant rate. I can then use y=mx+b
to make find conc. of reactants at various times
• Want straight line so we can use y=mx+b to
predict information
• Not all graphs give us a straight line slope so we
may need to manipulate to get in y=mx+b form.
• Zero order, 1st order, 2nd order graphs are
predictable
tangent
Zero order reactions
• A rxn that is zero order has a rate law
in which exponents of all reactants
are zero
• Equation: Rate =k
• This type of reaction doesn’t depend
on concentration of any reactant. The
rate is constant.
• Slope = D[A]
DT
Rate = k
The slope is negative …therefore
Slope of line = -k
The graph is already linear- I don’t need
to manipulate the data to “integrate”
the rate
Integrate the zero rate law
(to get y= mx +b FORM)
y = mx +b FORM
[A]t = -kt +[A]0
1st order Reaction
(probably most impt b/c also deal with ½ life of rxn)
• Any rate law when
the sum of the
exponents is a first
order reaction
• Equation: rate = k[A]
• So as reaction
progresses, the
amount of A
decreases and the
rate decreases
Integrate data to linearize graph…
so we can have it in y=mx+b form
Can use to get info
at any point
Can find avg rate,
instaneous rate,
This one is an integrated graph f
or 1st order rxn. Plot ln[A] vs time
Integrated first order law
y
= mx+ b
ln[A]t = -kt + ln[A]0
kt = ln([A]0 /[A] t)
Integrated rate law example
• A certain first order reaction has a rate constant
of 4.5 x 10 -3 s -1. How much of 50.0 x 10 -3 molar
sample will be left after 75.0s?
Integrated rate law example 2
The decomposition of a 0.1000M sample of N2O5 is
first order and has a k of 6.93x10-3s-1. What will the
concentration of N2O after 150s have passed?
2nd order reactions
• Equation: rate = k[A]2 or k[A][B]
• Integrated:
1/[A]t = kt + 1/[A]0
Slope = +k
Recap
order
Rate law
Integrated rate law
O
Rate = k
[A]t = -kt +[A]0
Straight
line plot
[A] vs t
1
Rate = k[A]
ln[A]t = -kt +ln[A]0
ln[A] vs t
2
Rate = k[A]2
1/[A]t = kt + 1/[A]0
1/ln[A] vs t
• Stop video here
• Re-Start at 19:35 to finish ½ life part of
PowerPoint
Last Topic in Kinetics
• Half – life = amount of time it takes for half
the sample to decay (if talking about
radioactivity) or be consumed by the reaction
(reaction rates)
• Radioactivity is not on ap test so we will only
talk about ½ life as it pertains to reaction rates
½ life only applies to 1st order reactions
• 1st order
reactions
• Notice the graph
is before
integrated form
Half life = t1/2
t1/2 =0.693/k
Example 1
• What is the half life of a reaction that has a
first order rate constant of 2.6 x 10-4s-1?
Example 3
• In the first order reaction D
products its is
found that 90% of the original amount of
reactant D decomposes in 140 minutes. Find
the half of the decomposition reaction.