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# Edexcel A2 Chem: (4.1) Rates of Reaction

experimental methods, rate calculations, orders of reaction, rate equation, rate constant, activation energy
by

## J Amuah-Fuster

on 17 June 2015

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#### Transcript of Edexcel A2 Chem: (4.1) Rates of Reaction

When hydrogen peroxide solution reacts with iodide ions in aqueous acid, iodine is liberated.

H2O2 (aq) + 2H+ (aq) + 2I- (aq) 2H2O (l) + I2 (aq)

The following table gives some experimental results for the reaction.

Determine the order of reaction with respect to each reactant.
Using your answer to question 1, write the overall rate equation and calculate the value of the rate constant, k.

A proposed mechanism for this reaction is:
H2O2 + I- H2O + IO- (slow)
H+ + IO- HIO (fast)
HIO + H+ + I- I2 + H2O (fast)

Is this mechanism consistent with the rate equation?

The rate equation for the reaction

The value of the rate constant, k, varies with temperature as shown in the table:

Plot a graph
of lnk on the vertical axis against 1/temperature, on the horizontal axis.

Your graph should be a straight line: its gradient is equal to –E /R.

and use it to find E for this reaction.
Measuring the rate of reaction
Rates: how fast?
Applications of Rate and Equilibria
Unit 4 overview
Specifications
Keywords
Factors affecting the rate of reaction
Lesson Objectives

To know how to measure the rate of reactions using experimental methods.

To determine the order of reaction using the initial rate method.

To calculate activation energy using experimental data [assessment].

To predict reaction mechanisms and the rate determining step.
Half life
time taken for the concentration to halve
Intermediate
A short-lived unstable species in a chemical reaction
Order w.r.t. [A]
the power to which the [A] is raised in the rate equation
Overall order of reaction
The sum of powers to which the concentrations are raised in the rate equation
Oxidation
Loss of electrons
Oxidation state
the hypothetical charge that an atom would have if all bonds to atoms of different elements were 100% ionic
Rate constant (k)
Constant of proportionality in the rate equation
Rate determining step (r.d.s.)
Slowest step
in a multi-step mechanism
Rate equation
Rate of reaction
Rate of change of concentration of reactants or products
Reduction
Transition state
The state of reacting molecules at their position of maximum energy during the course of the reaction. It cannot be isolated.
Gain of electrons
An equation that links reaction rate with the concentration of reactants, it also includes a constant
Thermodynamics
Does a reaction take place?
The rate of a chemical reaction
Thermodynamics

does
a reaction take place?
Kinetics

how fast
does a reaction proceed?
Reaction rate is the
change
in the
concentration
of a
reactant
or a
product
with
time
(mol dm-3/s)
A B
rate = -
[A]
t
rate =
[B]
t
[A] = change in concentration of A over
time period t
[B] = change in concentration of B over
time period t
Because [A]
decreases
with time, [A] is
negative
.
Kinetics
How fast does it happen?
Tangents drawn along the curve are used to calculate the rate of reaction:
time
Time taken
Concentration of A
For a reaction to take place…
…reactant molecules must collide:
with KE greater than or equal to EA;
with the correct orientation.
Neither curve is symmetrical

Both curves start at the origin and finish by approaching the x-axis

The area under both curves is the same

The peak of the T2 (higher temperature) distribution is to the right and lower than the peak of the T1 distribution
Maxwell-Boltzmann distribution of molecular energies
Pressure
Catalyst
Temperature
Particle size
Concentration
Summary starter
Match the factor to its description
Pressure
If all the reactants are all gases then an increase in pressure will increase the rate of reaction. [a homogenous mixture]
The pressure of a system can be increased by reducing the volume of the container or pumping in more of the reactant gases into the container.
Increasing the pressure increases the frequency of collisions.
Concentration
Increasing the concentration will result in an increase in the frequency of collisions.
This increases the frequency of successful collisions and hence the rate of reaction.
Particle size
For reactions involving a solid, a larger surface area results in a faster reaction.
Solid catalysts are made with a large surface area.
Temperature
Increasing the temperature of a reaction has two effects:

Molecules have a
higher average kinetic energy
– more of them have the minimum amount of energy required to produce a successful collision.

Collision frequency also increases
, although this is not as significant as the increase in kinetic energy on the rate of reaction.

Increasing the temperature by
10 degrees
approximately
doubles
the rate of reaction.
Catalyst
Catalysts can be classified as either
homogeneous
or
heterogeneous.
Homogeneous catalysts
A homogeneous catalyst is in the
same phase
as the reactants.
They work by
reacting with one of the reactants
to
form an intermediate
compound. This
intermediate reacts

with the other reactant
and the
catalyst is reformed
.
CH3COOH + C2H5OH CH3COOC2H5 + H2O
H2SO4
The concentrated sulphuric acid (H+) catalyses the reaction between ethanoic acid and ethanol to form the ester, ethylethanoate.
Heterogeneous catalysts
Heterogeneous catalysts are in a
different phase
to the reactants, e.g., iron is the catalyst used in the Haber process to produce ammonia.
The surface area of the catalyst is maximised to further increase the rate of reaction.
Catalysts and the Maxwell-Boltzmann distribution
Catalysts and reaction profile
The alternative route for the reaction has a lower activation.
This is often the reaction profile given for a
catalysed
and
uncatalysed
reaction.
Experimental methods
Change in mass
How may the concentration of 1-chlorobutane be measured?
In this reaction, the concentration of 1-chlorobutane, C4H9Cl, was measured at various times.
Rates of reaction
The
slope
of a line
tangent to the curve
at any point is the
instantaneous rate
at that time.
Rate equations
Experiments are required to find the rate equation (rate law).
It cannot be derived from the stoichiometric equation.

General form of rate equation:

[A], [B]
-
concentration of reactants

(in
mol dm
or
atm
[pressure units])
k

rate constant
; units vary
m, n
– reaction
orders
(to the power of)
Lesson 2: Rate equation, Constants & Order of reaction
The
overall

order
of a reaction is the
sum

of the

powers
to which the concentrations of the reactants are raised in the experimentally determined rate equation.

The
partial order of one reactant
is the power to which the concentration of that
specific

reactant
is raised in the rate equation.
Units of the rate constant,
k
The unit for rate is always:
mol dm-3 s-1
(unless its gaseous pressure then its
atm s-1
)
The units of concentration are
mol dm-3
(or
atm
).
The units of the rate constant are then calculated in a similar way as you do for
k
, the equilibrium constant.
Working out orders of reaction from experiments
A series of experiments are carried out, each time
changing the concentration of

only one

reactant
. The
partial orders

can be deduced by comparing the effect of changing the concentration of each reactant on the rate of reaction (see worked example later).
Experimental methods
Try some questions?
Order of a reaction
Factors affecting the rate of reaction
Measuring the rate of reaction
Calculating the rate constant,
k
Pick
one
experiment to substitute into the rate equation:
1.35 x 10-7 = k[0.100]1[0.0050]1
Units:
k
=
mol dm-3 s-1
[mol dm-3][mol dm-3]
= mol-1 dm3 s-1
mol dm-3 s-1 = k[mol dm-3][mol dm-3]
k
= 0.00027 mol-1 dm3 s-1
Reaction 1:
Initial rate method - worked example
Determine the rate equation and calculate k.
Order w.r.t [NH4+]: Compare exp. 2 and 3. As [ ] doubles, rate doubles. Hence order = 1
Order w.r.t [NO2-]: Compare exp. 1 and 2. As [ ] doubles, rate doubles. Hence order = 1

What is the overall order of reaction?
Determine the rate equation and calculate the constant, k.
Determine the rate equation and calculate the constant, k.
Scenario

Equimolar amounts
of 1-chlorobutane and sodium hydroxide in solution were mixed at
29 degrees Celsius
and the
concentration of hydroxide ions was determined
at various times.
Reaction mechanisms and the
rate determining step
The molecularity of a process tells how many molecules are involved in the process.
The rate equation for an elementary step is written directly from that step.
SN2 mechanism
(an example of a single step reaction)
SN2 mechanism has
no intermediate
; reaction follows
second-order kinetics
(first order with respect to each reactant):

A transition state is formed but the two bonds are of equal strength.
Transition state
Each of these processes is known as an
elementary reaction
or elementary process.
Multi-step reactions
Many reactions take place in more than one step, via intermediate compound, ions or radicals.
e.g., SN1 mechanism: hydrolysis of a tertiary halogenoalkane with aqueous sodium hydroxide.
SN1 mechanism
SN1 mechanism has two steps: (i) heterolytic fission of the C-X bond to form a carbocation; (ii) nucleophile forms a covalent bond with the carbocation.
First step is the rate limiting step
; kinetics of the reaction would show
first order with respect to the halogenoalkane
and
zero order with respect to the OH-
:

Rate = k[haloalkane]
slow
fast
intermediate
SN1 mechanism; rate = k[haloalkane]
First step has a greater activation energy and thus is the rate limiting (determining) step
The rate-determining step
The rate determining step is the one that
features the species mentioned in the overall rate equation
. Any reactant that is
zero order cannot be in the rate-determining step
.

Plot a grap
h of concentration of hydroxide ion on the vertical axis against time on the horizontal axis.

Find
two successive value
s for the
half-lif
e.

What is the
order of the reactio
n?
Give a reaso
n.

Wh
overall order
for this reaction and
not just the partial order
of OH- ions
?
Graph
Calculating overall order from half-lives
A graph of
concentration of reactant
is plotted against
time
.

The concentration of the reactant must fall to less than 25 % of its initial value to allow

at least

two half-lives

to be measured.
Generally, as temperature increases, so does the reaction rate.
This is because
k
(rate constant) is temperature dependent.
The value of k also depends on the
complexity of the geometry of the molecules (i.e. orientation)
activation energy of reaction (high E means low k)
Effect of temperature on the rate constant
If the value of the rate constant is measured at different temperatures, a graph can be plotted of ln k (
y-axis
) against 1/T (
x-axis
).
The graph is a
straight line
with a
of
–E /R
, allowing the activation energy to be calculated.
Relationship between
k
,
temperature
and
E
– the
Arrhenius equation
R
=
gas constant
(8.31 J K-1 mol-1),
T
is
temperature
in Kelvin,
A
is a
constant
Calculating activation energy, E
A
A
A
The two humps reflect an alternative pathway.
Catalysts do not alter the distribution but reduce the activation energy required for a successful reaction.
More of the particles have the minimum amount of energy to react.
Catalysts are specific to reactions.
From initial rates of reaction
From half-lives
zero order reaction
,
decreasing
half-life.
1st order reaction
, half-life is
constant
.
2nd order reactions
have
increasing
half-lives.
The order of reaction deduced from the graph is the
overall order
of the reaction and
not the partial order
of the reactant.
If we ensure that the
concentration of only one of the reactants is a limiting factor
(
i.e. other reactants are in excess
), then we can observe its effect on the rate.
From slope of a rate-concentration graph
where
:
rate
is the
initial rate of reaction
k
is the

rate constant
[A]
is the

concentration of reactant A

when the initial rate was measured
m
is the

order of reaction with respect to 'A'
in the reaction equation
Experimental methods for determining the rate of reaction
Titration
Samples of a
fixed volume
are taken from the reaction mixture at
regular intervals
.
Samples are immediately ‘
quenched
’ to
stop the reaction
in the sample from continuing, (use
sodium hydrogen carbonate
to
quench
a reaction using
acid
(neutralises hydrogen ions).
The
concentration
of a reactant or product can then be determined by titration with a suitable reagent.
Mean titre
is
proportional
to
concentration
of reactant or product in sample.
Colorimetry
Infrared (IR)
spectroscopy
Concentration of reactant or product can be followed by measuring
absorption peaks
The higher the concentration, the stronger the absorption peak
Polarimetry
If the reactant or product has
optical activity
– concentration determined by the
extent
to which the plane of polarisation of plane-polarised light is
rotated
.
‘Clock’ reactions
decomposition of sodium thiosulfate using acid to produce a precipitate of sulfur
.
pH measurements
Volume of gas evolved
Recording the mass of the reaction at regular intervals.
This cannot always be used if the gas evolved is dense (it will not escape from the reaction flask).
Worked Example
Titration
pH measurements
Electrical conductivity
A plot of
concentration vs. time
for this reaction yields a curve like this.
rate =
Plot a graph
of the results
Use the graph to calculate the rate of reaction at
t=350.0s
and
t=700.0s
The sequence of events that describes the actual process by which reactants become products is called the
reaction mechanism
.
Reactions may occur all at once or through several discrete steps.
Rate = k[haloalkane][Nu]
Recall that rates of reaction may be expressed by empirical rate equations of the form: rate = k[A]m[B]n, where m and n are 0, 1 or 2.

Define the terms rate constant and order of reaction and understand that these are experimentally determined.

Deduce rate equations from given experimental initial rate data.

Recall that reactions with a large activation energy will have a small rate constant.

learners will be expected to be familiar with the Arrhenius equation but not recall it.

Understand that many reactions take place in several steps, one of which will be rate-determining step.

Understand that it is sometimes possible to deduce information regarding the mechanism of a chemical reaction from kinetic data.

Understand that many reactions proceed through a transition state.

Present and interpret the results of kinetic measurements in graphical form.

Define the term half-life and recall that this is constant for any given first-order reaction
.
Learning Outcomes
Rate = k[A] [B]
(
concentration
units are in
mol dm
)
m
n
SUMMARY
Reaction orders and, thus, rate laws must be
determined

EXPERIMENTALLY!!!
Note: m ≠ a and n ≠ b
Overall order = sum of individual orders
Rate constant is
independent
of concentration.
aA + bB cC + dD
This is the
instantaneous rate
of reaction when the chemicals are
first mixed
together.
Half-life is the
time taken
for the concentration of a reactant to
reach half its value
.
Concentration vs time for a zero order reaction
Introduction
dilute
concentrated
a
a
a
They work by
reactants onto their surface
this causes a
weakening
and breaking of bonds forming an intermediate
compound. This
intermediates react

together
and the
reforming the catalyst
.
Question
Question 2
Question 4
Question 1
How would you change the conditions to control the following reaction rates?
slowing down
the souring of milk

speeding up
the fermentation of sugar into ethanol and carbon dioxide

slowing down
the reaction of iron with air and water

slowing down
the rate of carbon dioxide formation in the reaction between calcium carbonate and hydrochloric acid
Why would measuring the change in mass not work as a suitable method for the reaction between magnesium and dilute hydrochloric acid?
a)
b)
Which method, a) or b), do you think is likely to give more accurate results? Why?
If the gas released were soluble, which method would be more suitable and why?
Reaction
Select and describe a suitable experimental technique for following a given reaction.
Learning Objectives
more area for reactants to be in contact
increased number of collisions due to less space for gaseous particles to move
speed up reaction by lowering activation energy
more reactant particles available, means more frequent collisions
more kinetic energy given to particles, so more likely to collide with sufficient energy to react
Sketch a Maxwell-Boltzmann distribution for two temperatures, T1 and T2, where T2 is HIGHER than T1
In other words, ...
=
Monotonous, but... very informative!!
Record the volume of gas produced during a reaction at preset time intervals, e.g. every 30 seconds.
oxidation of iodide ions by Hydrogen peroxide
useful if the reactant or product is
c
o
l
o
u
r
e
d
Using pH to measure how the concentration of hydrogen or hydroxide ions changes during a reaction.
Not very effective due to the
logarithmic scale
in which pH is measured
Electrical Conductivity
If the number of positive
and
negative ions in the reactants
OR
the products changes, this will affect the ability of the reaction mixture to conduct electricity.
Conductivity is proportional to concentration
Measure the
volume of gas
at 30 second intervals using a delivery bung, gas syringe and stop clock.

Remove 10 ml aliquots at regular (2-3 min) intervals and quench reaction using sodium hydrogen carbonate.
Titrate
against iodine using thiosulfate.
OR, use
colorimetry
to measure the amount of coloured iodine left in sample

Remove 10 ml aliquots at regular (2-3 min) intervals and quench reaction using ice-cold water.
Titrate
against hydroxide using acid.

Measure the
change in pressure
as the reactans have 4 gaseous molecules while products have only 3. pressure decreases over time proportional to rate of reaction.

Use 'disappearing cross' method to measure time taken cross to no longer be visible through sulfur precipitate.
OR, use
colorimetry
to measure the amount of coloured iodine left in sample
Hint: Think about the density of the products.
One of the products, hydrogen, is very light. Therefore, weighing balances would need to be very precise (0.001g) to record the mass of hydrogen lost over time
Method a will be more accurate as the gas syringe has more precise measurements with less margin for error when reading it.

If the gas were soluble in water, then the gas syringe mod would be more suitable as it does not involve water for the gas to dissolve in amongst its set up.
lower
the
temperature
,
reduce
lactose sugars (
reactant
)

increase

temperature
(up to optimum),
increase
sugar
concentration

remove
air and / or water (
reactants
) using oil/paint

lower
acid
concentration
,
reduce surface area
of carbonate,
lower temperature
of reaction
Mechanisms
(
rate
units are in
s
)
-1
-3
-3
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