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Kinetics Study of Base Catalysed Diacetone
Alcohol Depolymerisation
David Hewett
Simon Langton Grammar School for Boys

Abstract
The theory accompanying the depolymerisation of diacetone alcohol in the presence of hydroxide ions is explored, and a possible reaction mechanism is proposed.
The kinetic study of the reaction is carried out using a dilatometer, and the rate law
is found to represent a two reactant system in which the reaction is first order with
respect to both diacetone alcohol and hydroxide ions. Subsequent calculations of
the rate constant for a variety of temperatures and a resulting Arrhenius plot gave
the activation enthalpy to be 61.1 kJ mol 1 . Experimental limitations are considered, the implementation of materials, equipment and procedures is evaluated, and
experimental uncertainties are calculated.

1

Contents
1 Investigation Aims

5

2 Introduction

5

3 Theory
3.1 Kinetics . . . . . . . . . . . . . . . . . . . . . . . . . .
3.2 Rate Law . . . . . . . . . . . . . . . . . . . . . . . . .
3.2.1 Determining the Rate Law . . . . . . . . . . .
3.2.2 Determination of k - The Integrated Rate Law
3.3 Activation Enthalpy . . . . . . . . . . . . . . . . . . .
3.3.1 Determining the Reaction Mechanism . . . . .
4 Methods
4.1 Reagents . . . . .
4.2 Equipment . . .
4.3 Procedure . . . .
4.4 Risk Assessment

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5 Analysis
5.1 Use of statistical methods and graph plotting software
5.2 Determining the Rate Law . . . . . . . . . . . . . . . .
5.3 Determination of k - The Integrated Rate Law . . . .
5.4 Activation Enthalpy . . . . . . . . . . . . . . . . . . .
5.5 Determining the Reaction Mechanism . . . . . . . . .
5.6 Conclusions . . . . . . . . . . . . . . . . . . . . . . . .

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6 Evaluation
6.1 Limitations of practical procedures . . . . . . . . . . . . . . . . . . . . . .
6.2 Experimental Uncertainties . . . . . . . . . . . . . . . . . . . . . . . . . .
6.2.1 Uncertainty associated with the meniscus height scale . . . . . . .
6.2.2 Uncertainty associated with volumetric flasks, pipettes and burettes
6.2.3 Uncertainty associated with the timing of data recording . . . . .
6.2.4 Uncertainty associated with temperature measurement . . . . . . .
6.3 Evaluation of materials, equipment and practical procedures . . . . . . . .
6.4 Proposed experimental improvements . . . . . . . . . . . . . . . . . . . .

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55
55
55
56

7 Appendix
7.1 0.1M 6 hours at
7.2 0.1M 6 hours at
7.3 0.1M 6 hours at
7.4 0.1M 6 hours at
7.5 0.1M at 30 C .
7.6 0.1M 6 hours at

58
58
61
66
70
76
79

25
25
25
25
. .
35

C . . . . . . . . .
C (first repeat) . .
C (second repeat)
C (third repeat) .
. . . . . . . . . . .
C . . . . . . . . .
2

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7.7
7.8
7.9
7.10
7.11
7.12
7.13
7.14
7.15
7.16
7.17

0.1M
0.1M
0.1M
0.1M
0.2M
0.2M
0.2M
0.3M
0.3M
0.4M
0.4M

at 40 C . . . . . . . . .
6 hours at 45 C . . . .
at 50 C . . . . . . . . .
at 50 C (repeat) . . . .
at 25 C . . . . . . . . .
at 25 C (first repeat) .
at 25 C (second repeat)
at 25 C . . . . . . . . .
at 25 C (repeat) . . . .
at 25 C . . . . . . . . .
at 25 C (repeat) . . . .

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83
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90
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97
99
102
105
107
110
113

List of Figures
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20

The Maxwell-Boltzmann distribution curve [1]. . . . . . . . . . . . . . . .
The expected curve for the variation of rate of reaction as a function of
[OH ] for a reaction which is first order with respect to OH . . . . . . .
The expected curve for the change in meniscus height as a function of time.
The expected curve for the variation in rate of reaction as a function of
the concentration of a zero order reactant. . . . . . . . . . . . . . . . . . .
The expected curve for the variation in rate of reaction as a function of
the concentration of a first order reactant. . . . . . . . . . . . . . . . . . .
The expected curve for the variation in rate of reaction as a function of
the concentration of a second order reactant. . . . . . . . . . . . . . . . .
The experimental setup. . . . . . . . . . . . . . . . . . . . . . . . . . . . .
A plot of the data shown in Table 1, with regression lines including the
anomalous data point (red) and excluding it (blue) shown. . . . . . . . . .
A plot of log(rate) against log([OH ]) . . . . . . . . . . . . . . . . . . . .
A plot of the results for the reaction run using 0.1M NaOH at 40 C. h1 h
and the gradient of the curve have been calculated for di↵erent times t. .
A plot of the data shown in Table 2. . . . . . . . . . . . . . . . . . . . . .
A logarithmic plot of log(rate) against log([DAA]) at 40 C . . . . . . . .
The e↵ect of a change in concentration of diacetone alcohol on the rate
of reaction of the reaction run using 0.1M at 50 C. . . . . . . . . . . . . .
A plot of the data shown in Table 3. . . . . . . . . . . . . . . . . . . . . .
A plot of log(rate) against log([DAA]) at 50 C. . . . . . . . . . . . . . . .
Change in h1 h as a function of time at 40 C. . . . . . . . . . . . . . .
Change in h1 h as a function of time at 50 C. . . . . . . . . . . . . . .
Change in the natural logarithm of h1 h as a function of time at 40 C.
Change in the natural logarithm of h1 h as a function of time at 50 C.
Change in the natural logarithm of h1 h as a function of time at 25 C.

3

6
8
9
10
11
11
16
20
22
24
26
27
29
31
32
35
36
38
39
41

21
22
23
24
25
26
27

Change in the natural logarithm of h1 h as a function of time at 25 C
(repeat). . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
Change in the natural logarithm of h1 h as a function of time at 30 C.
Change in the natural logarithm of h1 h as a function of time at 35 C.
Change in the natural logarithm of h1 h as a function of time at 45 C.
Change in the natural logarithm of h1 h as a function of time at 50 C
(repeat). . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
The Arrhenius plot - change in the natural logarithm of k as a function
of 1/T. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
An example of poor quality data which was discarded and the reaction
run repeated. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

42
43
44
45
46
48
52

List of Tables
1
2
3
4
5

The e↵ect of a change in concentration of OH on the rate of reaction.
The e↵ect of a change in concentration of diacetone alcohol on the rate
of reaction of the reaction run using 0.1M NaOH at 40 C. . . . . . . . .
The e↵ect of a change in concentration of diacetone alcohol on the rate
of reaction of the reaction run using 0.1M NaOH at 50 C. . . . . . . . .
The mean rate constant, k 0 , at di↵erent temperatures (T). . . . . . . . .
Manipulation of T and k 0 to give 1/T and ln(k), required for the calculation of Ea . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

4

. 18
. 25
. 30
. 47
. 47

1

Investigation Aims

The aims of this investigation are as follows:
• Determine the order of the reaction with respect to each reactant.
• Determine the value of the rate constant k for a variety of temperatures.
• Determine the activation enthalpy of the reaction.
• Discuss to what extent the results obtained support or oppose the proposed reaction mechanism.

2

Introduction

Diacetone alcohol1 (DAA) dissociates in the presence of hydroxide ions in the following
reaction:

(2.0.1)

It is possible to determine a rate law for Reaction (2.0.2) of the form:
Rate =

d[DAA]
= k[DAA]a [OH ]b
dt

(2.0.2)

where a and b are constants determined by experiment, and k is a rate ‘constant’ to be
found. As the reaction involves the formation of two products from one reactant, the
volume of the reaction mixture increases as the reaction proceeds. The progress of the
reaction may be monitored by carrying out the reaction in a dilatometer and recording
the change in volume of the reaction mixture as a function of time [2]. Temperature,
the concentration of diacetone alcohol and the concentration of hydroxide ions will all
be varied and their e↵ects on the reaction rate considered. The resultant rate law will,
along with the activation enthalpy to be calculated, be used to support or oppose a
proposed reaction mechanism for Reaction (2.0.1).
1

IUPAC name: 4-hydroxy-4-methylpentan-2-one

5

3

Theory

3.1

Kinetics

Consider the following generalised reaction:
A+B !C+D

(3.1.1)

We know from basic collision theory that in order for Reaction (3.1.1) to proceed, reactant A must collide with reactant B with the correct orientation and sufficient total
kinetic energy [3]. The number of these collisions per unit time can be increased by
changing a number of di↵erent variables, such as temperature, concentration of reactants, or presence of a catalyst2 . In doing so, the rate of the reaction is increased.
• Temperature – in any given reaction mixture, the reactant molecules will be
moving with kinetic energy 12 mv 2 . A variety of kinetic energies will therefore be
observed; these will be dependent on the reactant molecules’ mass and velocity.
It has been shown empirically that this distribution of kinetic energies follows the
Maxwell-Boltzmann distribution curve [4] (Figure 1):

Figure 1: The Maxwell-Boltzmann distribution curve [1].
The kinetic energies of reactant molecules are distributed such that there will be a
clear modal kinetic energy for the temperature of the reaction mixture, and a certain proportion of the molecules will have kinetic energies which exceed the total
kinetic energy needed to react in a collision (the activation energy). By increasing
the temperature of the reaction mixture, this curve shifts to the right, resulting
in a greater proportion of the reactants having kinetic energies greater than the
activation energy. It is therefore more likely at this increased temperature that
in a collision, the molecules will react. There will also be more collisions per unit
2
This particular reaction is an example of homogeneous catalysis and hence the catalysis theory
discussed will be limited to this case.

6

time as the molecules are moving at greater speeds.
• Concentration of reactants – increasing the concentration of reactants, that is,
the number of molecules per unit volume, will increase the number of collisions per
unit time, thus increasing the rate of reaction. More precisely, it is the concentration of the molecules involved in the rate determining step, that is, the step with
the slowest rate should each step take place independently, which will dictate the
rate of reaction. This is because the rate determining step, as the name suggests,
is responsible for the rate of the reaction as a whole, as the steps which follow in
the mechanism are dependent on the products from the rate determining step. Regardless of how fast the other steps in the reaction take place, they do not proceed
until the relatively slow rate determining step is complete. In this investigation,
the concentration of the catalyst, NaOH, was changed.
• Presence of a homogenous catalyst – provides an alternative reaction pathway
with a lower activation energy. This increases the proportion of reactant molecules
whose combined kinetic energies in a collision exceed the activation energy. There
are therefore more successful collisions per unit time and the reaction rate increases. In this case, it is possible that the presence of hydroxide ions leads to
the deprotonation of diacetone alcohol, resulting in an unstable transition state
compound which will go on to form two molecules of acetone.
The rate constant represents the e↵ect of all variables other than the concentration of the
reactants, including temperature (this relationship is given by the Arrhenius equation,
see Section 2.3).

3.2
3.2.1

Rate Law
Determining the Rate Law

The value of b in Equation (2.0.2), that is, the order of the reaction with respect to
hydroxide ion concentration, will be obtained by calculating the initial rate of reaction for
each concentration of NaOH used in the reactions. This ensures that the concentration of
diacetone alcohol will be constant for each reaction at that time. The e↵ect of a change
in hydroxide ion concentration on the initial reaction rate (the gradient of the curve at
t = 0) will then be considered. For example, if [OH ] is increased from 0.1M to 0.2M
and the initial rate doubles, it could be deduced that b = 1 and hence the reaction is
first order with respect to [OH ]. The expected curve is shown below in Figure 2.

7

1

Rate/mol dm3 s

[OH ]/mol dm3
Figure 2: The expected curve for the variation of rate of reaction as a function of [OH ]
for a reaction which is first order with respect to OH .
The value of a in Equation (2.0.2), that is, the order of the reaction with respect to
diacetone concentration, will be calculated by generating curves of meniscus height (h)
against time for the three reactions which run to completion. The remaining concentration of diacetone alcohol will be proportional to h1 h, where h1 is the maximum height
reached by the meniscus and h is the height of the meniscus for any time t. The e↵ect
of a change in diacetone alcohol concentration from t1 to t2 on the reaction rate (the
gradient of the curve at t1 and t2 respectively) will then be considered. The expected
curve is shown below in Figure 3.

8

meniscus height / cm

time / seconds
Figure 3: The expected curve for the change in meniscus height as a function of time.
The order of the reaction with respect to each reactant can be determined perhaps most
easily by considering the shape of the concentration of reactant vs rate plots. Figures 4,
5 and 6 show the plots that would be expected for zero, first and second order reactions
with respect to the reactant in question.

9


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