Chemical Kinetics of bromate-bromide reaction Introduction

Chemical Kinetics of bromate-bromide reaction
Introduction
Chemical reactions occur all the time and interfere in our everyday life in countless aspects. In
order to understand how reactions (or in general, processes) take place, it is essential to study
chemistry. For any process there are two main fields of study: Thermodynamics which is
concerned with the direction a process will take and all the energy changes between the initial
and final states and Kinetics which deals with how fast a certain process will be.
In general, chemical reactions occur through the breaking and formation of chemical bonds
between atoms in the compounds involved in the reactions. Experimental investigation reveals
that different reactions take place at different speeds, or rates. In this context the term “rate” is
taken to mean the quantity of a specific reactant which disappears or product which appears in
unit time at a given temperature. Reaction rates thus expressed have units (mole-1 s-1). For
example, the following reaction
𝑎𝐴+𝑏𝐵 →𝑐𝐶+𝑑𝐷
(1)
will have the following rates’ relationships
−1 𝑑[𝐴]
𝑎
𝑑𝑑
=
−1 𝑑[𝐵]
𝑏
𝑑𝑑
=
1 𝑑[𝐶]
𝑐 𝑑𝑑
=
1 𝑑[𝐷]
𝑑 𝑑𝑑
(2)
And any expression of these is related to the rate of a reaction as a whole.
If a chemical reaction is to take place between two reactive species, these species must collide
with each other in order that bond breaking-forming can take place and lead to the formation of
products. There are different factors affecting number and effectiveness of such collisions such
as number of reactant molecules in the reaction vessel, the temperature at which the reaction is
taking place and the various orientations of the molecules during the collisions. These factors, as
a result, will have their effect on the rate of the reaction.
Effect of Concentration on Reaction Rates
Rates of reactions are affected by changing the concentrations of reacting species since
increasing the concentration will lead to higher number of collisions. The quantitative influence
of concentration on the rate is best determined experimentally and it can be shown that for
kinetically simple cases, the rate is proportional to some power of the concentration of a given
reactant. For example, for our earlier reaction between A and B it might be shown in separate
experiments that,
𝑅𝑅𝑅𝑅 ∝ [𝐴]𝑥
𝑎𝑎𝑎
𝑅𝑅𝑅𝑅 ∝ [𝐵]𝑦
where x and y are the order of reaction rate corresponding to reactant A and order of reaction rate
corresponding to reactant B. the overall order of the reaction is x+y. the order of the reaction –
especially for simple kinetics – is related to the number of species in the rate determining step
(RDS) which is the slowest step in the reaction mechanism.
We can therefore conclude that for such a reaction,
𝑅𝑅𝑅𝑅 = 𝑘[𝐴]𝑥 [𝐵]𝑦
(3)
Where k is the constant of proportionality and is called the rate constant for the reaction.
Effect of Temperature on Reaction Rates
The rates of most reactions are known to increase significantly with rising temperature. A good
rule of thumb is that the rate roughly doubles for every 10 oC rise. There are exceptions to this
but on the whole it is a fair guide. In 1889 Arrhenius proposed that the temperature dependence
of the rate of reaction is governed by the equation which now bears his name,
𝑘 = 𝐴𝑒 −𝐸𝑎 ⁄𝑅𝑅
(4)
Where k is the rate constant, Ea is the activation energy, R is the gas constant and T the
temperature in degrees Kelvin. The pre-exponential term A is the property of the particular
reaction related to the collision frequency of the reactive species. We might thus expect A to be
itself temperature dependent and this is indeed the case. However, in equation (4), the
dependence of k on temperature is dominated by the strong exponential term, so, in the analysis
of experimental data, the dependence of A on temperature is usually ignored as a first
approximation.
Equation (4) can be rewritten in logarithmic form,
𝑙𝑙𝑙 = 𝑙𝑙𝑙 −
𝐸𝑎
𝑅𝑅
(5)
A graph of lnk against 1/T is therefore expected to be linear with negative slope given by –Ea/R.
Measurement of a reaction rate at various temperatures therefore provides us with a means of
determining the activation energy for the reaction.
The reaction to be studied in this experiment is between bromate and bromide ions in acidic
medium and occurs according to the equation. In an acidic medium the bromated ion oxidizes the
bromide ion to give bromine and water as the following reaction
𝐵𝐵𝑂3− + 5 𝐵𝐵 − + 6 𝐻 + → 3 𝐵𝐵2 + 3 𝐻2 𝑂
This reaction is relatively slow and as a result the kinetics of this reaction can be studied using
simple methods. The only difficulty in studying this reaction is how to determine the
concentration changes for this reaction. One method overcome this difficulty is introducing other
reaction by which exact amounts can be determined.
If a small known quantity of phenol and an indicator are added to the reaction mixture, the
liberated bromine will react very quickly with the phenol to produce tribromophenol:
𝐶6 𝐻5 𝑂𝑂 + 𝐵𝐵2 → 𝐵𝐵𝐵6 𝐻2 𝑂𝑂 + 𝐻 + + 𝐵𝐵 −
Once all phenol has been brominated a slight excess of Br2 is sufficient to immediately
decolorize the methyl orange indicator. Thus the quantity of phenol added to the reaction
represents the amount of 𝐵𝐵𝑂3− consumed during the time elapsed between the mixing of the
reactants until the disappearance of the indicator. The overall reaction becomes:
The rate equation of the bromate-bromide reaction takes the form:
−𝑑[𝐵𝐵𝑂3− ]
𝑑𝑑
= 𝑘[𝐵𝐵𝑂3− ]𝑥 [𝐵𝐵 − ]𝑦 [𝐻 + ] 𝑧
(6)
In this experiment the order with respects to the bromate, bromide and H+ will be determined. In
addition the rate constant at two different temperatures will be evaluated to calculate the
activation energy of this reaction,
Experimental:
Determination of the reaction orders
The method of initial rates is used to determine the order for each reactant. This method involves
measuring the rate of reaction at very short times before any significant changes in
concentrations of reactants occur. Two or more kinetic experiments are examined in which only
one reactant concentration is change while the other remains constant and then investigate the
change in the rate of the reaction.
Experimentally, prepare the following mixtures in two test tubes using accurate volume
measuring glassware:
Test tube 1
𝐵𝐵𝑂3−
Test tube 2
0.33 M
𝐵𝐵 −
0.62 M
𝑁𝑁𝑁𝑂3
Water
1
10.0 mL
10.0 mL
20.0 mL
2
10.0 mL
20.0 mL
3
20.0 mL
4
10.0 mL
#
𝐻+
Phenol
Methyl
0.50 M
0.06 M
orange
25 mL
20.0 mL
10.0 mL
5.0 mL
7.0 mL
28 mL
20.0 mL
10.0 mL
5.0 mL
10.0 mL
14.0 mL
21 mL
20.0 mL
10.0 mL
5.0 mL
10.0 mL
0.0 mL
25 mL
40.0 mL
10.0 mL
5.0 mL
0.50 M
As an example, for the first run, mix the amounts of reagents indicated in the two test tubes,
inside the fume hood mix the content of the two tubes and start the stopwatch. Once the pink
color of the methyl orange disappears stop the stop watch and record the time. Dispose of all
solutions in the waste bottle inside the fume hood. In the same manner perform the other trials.
Examining the table, we can see that trials 1+2 used to determine the exponent y for 𝐵𝐵 − , trials
1+3 used to determine the exponent x for 𝐵𝐵𝑂3− and trials 1+4 used to determine the exponent z
for 𝐻 + .
Determination of the activation energy of the reaction
Repeat the first trial in the previous part a two other temperature, such as in ice bath (T= 0oC)
and in thermostatic water bath set at T= 35 oC. Doing so, you will end up with trial one
performed at T= room temp, 0 oC and 35 oC.
Determination of the Specific rate constant
In order to determine the specific rate constant, prepare the following mixtures in two test tubes
using accurate volume measuring glassware. These mixtures are identical except for the amount
of the phenol added. Mix the contents of the two test tubes and measure the time required to
decolorization to occur.
Test tube 1
Run
𝐵𝐵𝑂3−
Test tube 2
0.33 M
𝐵𝐵 −
0.62 M
𝑁𝑁𝑁𝑂3
0.50 M
1
10.0 mL
10.0 mL
2
10.0 mL
3
𝐻+
Phenol
Methyl
0.50 M
0.06 M
orange
20.0 mL
20.0 mL
4.0 mL
5.0 mL
31.0 mL
10.0 mL
20.0 mL
20.0 mL
6.0 mL
5.0 mL
29.0 mL
10.0 mL
10.0 mL
20.0 mL
20.0 mL
8.0 mL
5.0 mL
27.0 mL
4
10.0 mL
10.0 mL
20.0 mL
20.0 mL
10.0 mL
5.0 mL
25.0 mL
5
10.0 mL
10.0 mL
20.0 mL
20.0 mL
12.0 mL
5.0 mL
23.0 mL
#
Water
Calculations:
Exponents of the rate equation
Calculate the initial concentrations of the reactants. Each mole of 𝐵𝐵𝑂3− reacts with bromide 𝐵𝐵 −
and acid to give 3 moles of bromine (Br2). Now each mole of bromine Br2 reacts with one mole
of phenol C6H5OH producing bromophenol. Assume the concentration of phenol to be 1.0 M,
then the methyl red will be decolorized when a/3 M of 𝐵𝐵𝑂3− are consumed. Assuming that in
the initial stages of the reaction the decrease in 𝐵𝐵𝑂3− concentration is linear, we can write:
𝑅𝑅𝑅𝑅 =
−𝑑[𝐵𝐵𝑂3− ]
𝑑𝑑
=
(𝑎/3)
𝑡
= 𝑘[𝐵𝐵𝑂3− ]𝑥 [𝐵𝐵 − ]𝑦 [𝐻 + ] 𝑧
(7)
where t is the time (in seconds) needed for the decolonization of the indicator, and a is the initial
concentration of 𝐵𝐵𝑂3− . Assuming that the exponents are small whole numbers, use the results of
your experiments to find x, y and z and write the whole rate equation for this reaction. Comment
on the rate equation and suggest a suitable mechanism for the reaction depending on this rate
equation.
Specific rate constant
In order to obtain the specific rate constant (k), we need to represent amounts 𝐵𝐵𝑂3− consumed
with time. A plot of 0.033-(a/3) vs time helps to obtain an initial value for
−𝜕[𝐵𝐵𝑂3− ]
𝜕𝜕
. The initial
rate can be determined as the slop of the straight line tangent to the curve at the beginning of the
curve (see the Figure 1). Knowing the initial concentrations of the reactants and the rate equation
(order of each reactant) the value of k can be calculated. Finally, the sodium nitrate is added to
the mixtures to have a constant ionic strength for all experiments, you should calculate the ionic
strength of your reaction mixtures and state it with your answer. Question: do you think that k
could vary by varying the ionic strength?
Figure 1: schematic graph representing the relation between the amount of bromate consumed
with time.
Activation energy
According to Arhenius equation (2), there is an exponential relationship between the rate
constant and temperature. Taking the logarithm form (equation (3)) plot lnk vs 1/T where T in
Kelvin, we should obtain a linear line with slope equal –Ea/R and the intercept is lnA. Obtain
both Ea and A for such a graph. Show that under the conditions used in this experiment, the value
of t is inversely proportional to the specific rate constant k.
Chemical Kinetics of bromate-bromide reaction
Data sheet
Name :
Partner’s name:
Lab section:
Part A: Estimating the reaction order
Volume of
Volume of
Volume of
𝑩𝑩𝑶𝟑−
𝑩𝑩−
𝑵𝑵𝑵𝑶𝟑
(
)M
(
)M
(
)M
Ambient temperature=
Volume of
Water
Volume of
Volume of
Volume of
𝑯+
Phenol
Methyl
(
)M
(
)M
ºC
Time
orange
1
2
3
4
Part B: Estimating activation energy
Volume of
Volume of
Volume of
𝑩𝑩𝑶𝟑−
𝑩𝑩−
𝑵𝑵𝑵𝑶𝟑
(
)M
(
)M
(
)M
temperature 2=
Volume of
Water
Volume of
Volume of
Volume of
𝑯+
Phenol
Methyl
(
)M
(
)M
ºC
Time
orange
1
temperature 3=
Volume of
Volume of
Volume of
𝑩𝑩𝑶𝟑−
𝑩𝑩−
𝑵𝑵𝑵𝑶𝟑
(
)M
(
)M
(
)M
Volume of
Water
Volume of
Volume of
Volume of
𝑯+
Phenol
Methyl
(
)M
(
)M
ºC
Time
orange
1
Part C: Estimating the rate constant
Volume of
#
(
𝑩𝑩𝑶𝟑−
)M
Volume of
(
𝑩𝑩
−
)M
Volume of
(
𝑵𝑵𝑵𝑶𝟑
)M
Ambient temperature=
Volume of
Water
Volume of
(
𝑯
+
)M
Volume of
Volume of
Phenol
Methyl
(
)M
orange
1
2
3
4
Instructor’s signature:
Date:
ºC
Time