Title: Lesson 3 Rate Law and Reaction
Order
Learning Objectives:
– Know that rate law can only be derived from experimental data
– Understand the concept of reaction order
– Identify reaction order from appropriate graphs
– Complete an experiment to determine the order of a reaction with respect
to the concentration of acid.
Recap

On the same axes, sketch the Maxwell-Boltzmann
distribution for a lower and a higher temperature, and
use this to explain why increasing the temperature
increases the rate of reaction.
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Recap


Excess magnesium, was added to a
beaker of aqueous hydrochloric acid.
A graph of the mass of the beaker
and contents was plotted against
time (line 1).
Mass
1
What change in the experiment
could give line 2?
A.
B.
C.
D.
The same mass of magnesium in
smaller pieces
The same volume of a more
concentrated solution of
hydrochloric acid
A lower temperature
A more accurate instrument to
measure the time
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2
Time
Recap






Which quantities in the enthalpy level
diagram are altered by the use of a catalyst?
A.
B.
C.
D.
I and II only
I and III only
II and III only
I, II and III
II.
III.
II
III
Time
Which statement is true about using sulfuric acid as a catalyst
in the following reaction?
CH3–CO–CH3(aq) + I2(aq)  CH3–CO–CH2–I(aq) + HI(aq)
I.
I
Enthalpy
The catalyst increases the rate of reaction.
The catalyst lowers the activation energy for the reaction.
The catalyst has been consumed at the end of the chemical
reaction.
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A.
B.
C.
D.
I and II only
I and III only
II and III only
I, II and III
Ch 1.1
Finding the rate
A2
In this reaction, the
concentration of butyl
chloride, C4H9Cl, was
measured at various
times, t.
How do you find reaction rates?
C4H9Cl(aq) + H2O(l)  C4H9OH(aq) + HCl(aq)
Finding the rate
The average rate of the reaction over each
interval is the change in concentration divided
by the change in time:
C4H9Cl(aq) + H2O(l)  C4H9OH(aq) + HCl(aq)
A2
How do you find reaction rates?
Ch 1.1
Finding the rate
How do you find reaction rates?
Ch 1.1
A2
Finding the rate
A2
What do
you notice
about the
average
rate?
The average rate decreases as the reaction proceeds.
Why?
As the reaction goes forward, there are
fewer collisions between reactant molecules.
How do you find reaction rates?
Ch 1.1
Given the following data, what is the average
rate of the following reaction over the time
interval from 54.0 min to 215.0 min?
CH3OH (aq) + HCl (aq) →
Time (min)
0.0
54.0
107.0
215.0
[HCl] (M)
1.85
1.58
1.36
1.02
CH3Cl (aq) + H2O (l)
A2
How do you find reaction rates?
Example
Ch 1.1
Finding the rate
Given: [HCl]54 min = 1.58 M
[HCl]215 min = 1.02 M
Find:
avg. rate of disappearance of HCl
Avg. rate = - D [HCl]
Dt
= - (1.02 M - 1.58 M)
215 min - 54 min
= 0.0035M / min
A2
How do you find reaction rates?
Ch 1.1
Ch 1.1
Finding the rate
A2
• A plot of
concentration vs. time
for this reaction yields
a curve like this.
• The slope of a line
tangent to the curve
at any point is the
instantaneous rate at
that time.
How do you find reaction rates?
C4H9Cl(aq) + H2O(l)  C4H9OH(aq) + HCl(aq)
Finding the rate
Rate laws for the reaction must be
determined experimentally.
Measure the instantaneous reaction rate
at the start of the reaction (i.e. at t = 0)
for various concentrations of reactants.
You CANNOT determine the rate law for the
reaction by looking at the coefficients in the
balanced chemical equation!
A2
How do you find reaction rates?
Ch 1.1
Now look at this example...

An oxidised buckminsterfullerene, C60O3 decomposes into C60O, releasing O2:

The reaction can be measured by change of absorbance of light of a certain
wavelength.

Absorption ∝ [C60O3]
Remember: Rate is
expressed as a
positive value!
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
Rate calculated as a function of time:
Rate decreases over time,
slowing as the concentration of
C60O3 decreases.
This mirrors the absorbance
graph on the previous slide!
Rate must be related to concentration at each time

Rate of reaction plotted against the absorbance of C60O3:
The straight line graph of rate
against absorbance confirms:
Reaction rate ∝ [C60O3]
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Rate expression or Rate law

Reaction rate ∝ [C60O3]

This proportional relationship is converted into an equation by introducing a
constant.

Reaction rate = k[C60O3]

This expression is a first order expression because the concentration is raised to
the power one.

In general, the rate is proportional to the product of the concentrations of the
reactants, each raised to a power.
m and n, are known as the
k = rate constant
orders of the reaction with
respect to reactants A and B.
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Overall order is the SUM of
the individual orders.
The table below gives some examples of
some reaction equations.
There is no predictable relationship
between the co-efficients in the equation
and the values for the order of reaction
with respect to the reactants.
ORDERS OF REACTION CAN
ONLY BE OBTAINED BY
EXPERIMENTAL DATA!
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Solutions
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What is reaction order?

Reaction order describes how changes to the
concentration of reactants affect the rate of a reaction

Assuming temperature and pressure are fixed
0th Order (0o)
1st Order (1o)
2nd Order (2o)
[R] doubled  rate doubled
[R] halved  rate halved
[R] trebled  rate trebled
[R] doubled  rate
quadrupled
[R] halved  rate quartered
[R] trebled  rate x 9
Changing the concentration
does not affect the rate
[R] doubled  rate same
[R] halved  rate same
[R] trebled  rate same
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For example:

Initial [B]
([B]0)
Initial Rate (v0)
1
1.00 M
1.00 M
1.25 x 10-2 M/s
2
1.00 M
2.00 M
2.5 x 10-2 M/s
3
2.00 M
2.00 M
2.5 x 10-2 M/s
Comparing Runs 2 and 3:


[A] doubles but [B] remains fixed
Rate unchanged
The reaction is 1st order w.r.t reactant B

Comparing Runs 1 and 2:



Initial [A]
([A]0)
The reaction is 0th order w.r.t reactant A


Run #
[B] doubles but [A] remains fixed
Rate doubles
Overall the reaction is 1st order
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Another example:
Experiment

Initial rate /
mol (N2) dm–3 s–1
1
0.100
0.100
2.53×10–6
2
0.100
0.200
5.05×10–6
3
0.200
0.100
1.01×10–5
4
0.300
0.100
2.28×10–5
Comparing Runs 1 and 2:


[H2] doubles but [NO] remains fixed
Rate doubles
The reaction is 2nd order w.r.t reactant NO

Comparing Runs 1 and 3:



Initial [H2] /
mol dm–3
The reaction is 1st order w.r.t reactant H2


Initial [NO] /
mol dm–3
[NO] doubles but [H2] remains fixed
Rate quadruples
Overall the reaction is 3rd order (1st order + 2nd order = 3rd order)
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First Order Reactions
Expt
[A] (M)
1
0.50
Rate (M/s)
1.00
x2
2
1.00
x2
2.00
x2
3
2.00
x2
4.00
• First Order Reaction
– Overall reaction order = 1
– Rate = k[A]
As [A]
doubles,
the rate
doubles
[A]  rate
A2
How do you find reaction rates?
Ch 1.1
Expt
Second Order Reactions
Initial [A] (M)
1
3
x2
1.6 x 10-2
0.2
x1
2
Rate (mol dm-3 s-1)
Initial [B] (M )
0.1
0.1
0.2
[A] stays the same
[B] doubles
[A] doubles
[B] stays the same
x2
x1
A2
x2
0.4
-2
3.2
x
10
x4
0.2
6.4 x 10-2
the rate doubles
[B]  rate
the rate is x4
[A]2  rate
How do you find reaction rates?
Ch 1.1
Second Order Reactions
[A] stays the same
[B] doubles
[A] doubles
[B] stays the same
the rate doubles
[B]  rate
the rate is x4
[A]2  rate
What is the rate equation
for this reaction?
Rate = k[A]2 [B]
The reaction is second order in respect of A and
first order in respect of B. The overall reaction
order is 3.
A2
How do you find reaction rates?
Ch 1.1
Second Order Reactions
Initial [X]/M
0.10
x1
X0.50.10
0.05
0.10
x1
x1
Initial [Y]/M
0.10
x1
0.10
0.10
0.40
x4
A2
Initial [Z] / M Initial rate/
mol dm-3 s-1
0.10
x3
x1 0.30
0.10
0.10
x1
2.40 x 10-3
x3
-3
NE 7.20 x 10
2.40 x 10-3x1
3.84 x 10-2
[Z] triples
[X] &[Y] stay the same
the rate trebles
[Z]  rate
[X] halves
[Y] & [Z] stay the same
the rate is
the same
[X]0  rate
[Y] quadruples
[X] & [Z] stay the same
the rate goes
2  rate
[Y]
2
up by 16 (ie 4 )
How do you find reaction rates?
Ch 1.1
Second Order Reactions
[Z] triples
[X] &[Y] stay the same
the rate trebles
[Z]  rate
[X] halves
[Y] & [Z] stay the same
the rate is
the same
[X]0  rate
[Y] quadruples
[X] & [Z] stay the same
the rate goes
2  rate
[Y]
2
up by 16 (ie 4 )
What is the rate equation
for this reaction?
Rate = k[Y]2 [Z]
The reaction is second order in respect of Y and
first order in respect of Z. The overall reaction
order is 3.
A2
How do you find reaction rates?
Ch 1.1
Determination of the order of reaction
Initial rates method
 This involves carrying out separate experiments with
different starting concentrations of A, with other reactants
held constant  effect on [A] can be observed. This can
then be repeated for reactant B.
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Solutions
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Graphical representation of reaction
kinetics


Zero order reaction
Concentration of reactant A does not affect the reaction
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Graphical representation of reaction
kinetics


First-order reaction
Rate is directly proportional to the concentration A
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Graphical representation of reaction
kinetics


Second-order reaction
Rate is directly proportional to the square of
concentration A
Note: The
concentration – time
graph is steeper at the
start and levels off more
(when compared to
first-order graph)
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Parabola shape –
characteristic of
the square
function
Summary
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Rate-Concentration Graphs
1st Order
0th Order
No
effect
Gradient 0
Direct
proportion
Gradient positive and
constant
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2nd Order
Squared
relationship
Gradient positive and
increasing
Concentration-Time Graphs
0th Order
t1/2
t1/2
Half-life decreases
1st Order
t1/2
t1/2
Half-life constant
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2nd Order
t1/2
t1/2
Half-life increases
Constant half life is a feature of only first
order reactions
Constant half life can be used to establish
that a reaction is first order w.r.t that
reactant.
The shorter the half life, the faster the
reaction.
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Rate Graphs in Practice

In the experiment you will follow the progress of a reaction using a
data logger with pH probe

Follow the instructions here.

This will collect so much data that the only realistic way to analyse it
will be by spreadsheet. There is an example here.

Information about R2 values can be found here:
https://www.youtube.com/watch?v=kiCeJHwpYDQ

How to do line equations here:
https://www.youtube.com/watch?v=Ogx7CJ1JD9k
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Review

The order of a reaction tells us the effect on the rate of
changing the concentration of the reactants.

Order can be determined by:



Directly comparing experimental data
The gradient of a rate-concentration graph
The shape of a concentration-time graph
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