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Practical guidance1 How fast ? rates
Methods of investigating reaction rates
Methods
Concentrationtime graphs
A concentrationtime graph shows either how the concentrationof a product increases with time, or how the concentration of a
reactant falls with time. The gradient (slope) of a concentration
time graph at any point measures the rate of a reaction at that
time.
One practical method to monitor the changes in concentration
over time is to remove samples from the reaction mixture and
then to stop the reaction in the samples by rapidly cooling or by
changing the p.
Another method can be used if the reaction produces a gas.!igure " shows the apparatus that can be used to study the rate
of reaction between marble chips and dilute hydrochloric acid.
#arble and acid are added to the $as%. The reaction is allowed to
proceed for a short while to saturate the solution with carbon
dioxide, then the bung is put in place and timing starts.
Typically the marble chips are in excess. The reaction slows
down and stops as the hydrochloric acid gets less concentratedand then is &nally used up altogether.
The total volume of gas collected when the reaction stops ' V&nal.
This &nal volume is proportional to the hydrochloric acid
concentration when the bung was put in place and timing
started. The greater the concentration of acid at the start the
more gas will eventually form.
At any time t after the start of timing the volume of gas collected
is Vt. This varies with the amount of acid that has reacted by that
time. Vtincreases as tincreases while the acid concentration
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%igure 1
Apparatus to collect andmeasure the gas given
off during a reaction.
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Practical guidance1 How fast ? rates
falls. o (V&nalVt) is proportional to the concentration of
hydrochloric acid at time t.
o plotting (V&nalVt) against t gives a concentrationtime graph
(!igure ) for the experiment.
Initial-rate methods
*etermining the initial rate for a %inetics experiment is often
important.
One way to &nd the initial rate is to draw a tangent at the start ofa concentrationtime graph and use it to calculate the gradient at
time +ero.
This can be laborious and there is a useful short cut that
simpli&es the design of rate experiments.
!igure shows two plots of the amount of product formed with
time. -ine " shows the formation of a product under one set of
conditions. An amount of product xforms in time t". -ine shows
the formation of the same product under a dierent set of
conditions. The same amount of product xforms in the longer
time t.
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%igure 2
Concentrationtime
graph for the reaction ofmarble chips with acid.
%igure &
Two plots showing the
formation of a product with
time, for the same reaction
under different conditions.
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Practical guidance1 How fast ? rates
The average rate of formation of product on line " '"t
x
The average rate of formation of product on line ')t
x
/f xis %ept the same, it follows that the average rate near the
start t
1
This means that it is possible to arrive at a measure of the initialrate of a reaction by measuring how long the reaction ta%es toproduce a small, &xed amount of product, or use up a small, &xedamount of reactant.
This techni0ue can be used to study the rate of reaction of
magnesium with an acid. The acid has to be in signi&cant excess
so that its concentration does not change during the reaction.
The procedure is to measure the time for a small, &xed mass of
magnesium ribbon to dissolve completely. The experiment is
repeated with the same mass of metal and volume of acid but
with varying acid concentrations.
The approach can also be used to study the reaction of sodium
thiosulfate with acid. This reaction slowly produces a precipitate
of sulfur. A simple but eective procedure is to measure the time
ta%en for enough sulfur to form to obscure a cross underneath
the $as% containing the reaction mixture. /t is reasonable to
assume that the same amount of sulfur is needed to hide thecross each time.
Clock reactions
A variant on the initial1rate method is to use a 2cloc% reaction3, so
called because the reaction is set up to produce a sudden colour
change after a certain time when it has produced a &xed amount
of one reactant.
The reaction of peroxodisulfate(4/) ions with iodide ions can be
set up as a cloc% reaction5
O67(a0) 8 /7(a0) O97(a0) 8 /(a0)
A small, %nown amount of sodium thiosulfate ions is added to the
reaction mixture, which also contains starch indicator. At &rst the
thiosulfate reacts with any iodine, /, as soon as it is formed,
turning it bac% to iodide ions, so there is no colour change. At the
instant when all the thiosulfate has been used up, free iodine is
produced and this immediately gives a deep blue1blac% colour
with the starch. /f t is the time for the blue colour to appear after
mixing the chemicals, then once again ":tis a measure of the
initial rate of reaction.
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Practical guidance1 How fast ? rates
Investigating orders of reaction
Purpose
This example shows how the 2cloc%3 method for determining
initial rates can be used to &nd the reaction orders in the rate
e0uation for the oxidation of bromide ions by bromate(4) ionsunder acid conditions5
;
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Practical guidance1 How fast ? rates
All-the-reactants-kept-constant-except-one procedure
hen studying this reaction it would be impossible to interpret
the data if all the concentrations of the three reactants were
allowed to vary together. To ma%e it possible to analyse the
results, the procedure is to carry out three distinct series ofexperiments. /n each series, the initial concentration of one of
the reactants is varied systematically while the concentrations of
the other reactants are %ept constant.
Finding the order with respect to bromide ions
!igure 9 shows how a series of six runs with six dierent
mixtures can give a set of values for the initial rate of reaction
for six dierent bromide ion concentrations, while all the other
concentrations are %ept the same.
Run Volume of
0.01mol dm3KBr/cm3
Volume of
water/cm3Run Volume of
0.005mol dm3
KBrO3/cm3
Volume of
solution ofacid andmethyl
orange/cm3
Volume of
0.000 10 mol dm3
henol/cm3
1 10.0 0.0 1 10.0 15.0 5.0
2 .0 2.0 2 10.0 15.0 5.0
! ".0 #.0 ! 10.0 15.0 5.0
# 5.0 5.0 # 10.0 15.0 5.0
5 #.0 ".0 5 10.0 15.0 5.0
" !.0 $.0 " 10.0 15.0 5.0
Bote that in bea%er < the volumes and concentrations are the
same for all six runs. /n bea%er A, however, the volume of the
potassium bromide ion solution varies but the total volume is
%ept the same by adding enough water to ensure that the volume
of the reaction mixture is the same for each run.
!or each run, the contents of bea%ers A and < are mixed and
timing started. Timing stops when the pin% colour of theindicator disappears.
After each run the temperature of the mixture is recorded to
ensure that it stays the same throughout the series of
experiments.
Finding the orders with respect to bromate(V) and hydrogen ions
Another set of experiments investigates the eect of
systematically changing the bromate(4) ion concentration. /n this
case bea%er A contains a range of mixtures of potassium
bromate(4) and water, while bea%er < always contains the same
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%igure 4
%i&tures for e&ploring the
effect of bromide ion
concentration on the initial
rate of reaction.
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Practical guidance1 How fast ? rates
volumes of the solutions of potassium bromide, acid with methyl
orange and phenol.
A &nal set of experiments investigates the eect of changing the
concentration of hydrogen ions. /n these runs bea%er A contains
a series of mixtures of acid and water while bea%er < contains,each time, the same volumes of solutions of potassium
bromate(4), potassium bromide and phenol solution.
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Practical guidance1 How fast ? rates
Results and analysis
The table of results shows the time for the indicator colour to
disappear for the series of experiments to investigate how the
initial rate varies with the bromide ion concentration. As
explained earlier, ":tis a measure of the initial rate. The
temperature of the solutions was ".; C.;DE.
Volume of Br!"a#$/cm3as in %igure &
10.0 '.0 (.0 5.0 &.0 3.0
t's 22.5 2".0 !#.0 !$.5 #.0 "5.0
1't/102s1 #.## !.5 2.(5 2."$ 2.0 1.5#
)a*le 1
Time ta)en for indicator colour to disappear and the initial rate.
ince the concentrations of bromate(4) and hydrogen ions wereconstant, the rate e0uation simpli&es to5
>ate ' constant ?
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Practical guidance1 How fast ? rates
A similar analysis of the results from the second set of
experiments produces a similar straight1line graph showing that
the reaction is also &rst order with respect to bromate(4) ions.
A plot of rate against hydrogen ion concentration for the third
series of results does not produce a straight line. The reaction isnot &rst order with respect to hydrogen ions.
/n this set of experiments the rate e0uation simpli&es to5
>ate ' constant ?8@r
Ta%ing into account the form of the results, this becomes5
t
"' constant (volume of acid)r
Ta%ing logs of both sides of this e0uation gives5
log
t
"' log (constant) 8 rlog (volume of acid)
Hlotting log
(":t) against log (volume of acid) gives a straight1line
graph with
gradient r.
The gradient of the graph in !igure = is ".6. /t may be that the
order with respect to hydrogen ions is I however, there are
reactions with orders that are not whole numbers.
The complete set of results suggests that the rate e0uation is5
>ate ' k?
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Practical guidance1 How fast ? rates
Measuring activation energies
Purpose
>eaction rates vary with temperature because the value of the
rate constant, k, varies with temperature. The Arrheniuse0uation describes the relationship between kand temperature,
T.
ln k' R
Ea
T
"8 constant
Eais the activation energy for the reaction, Tthe temperature on
the Felvin scale andRthe gas constant. A plot of lnkagainst ":T
gives a straight1line graph. The gradient of the line is Ea:R.
This example shows how the 2cloc%3 method for determininginitial rates can be used to &nd the activation for the oxidation of
iodide ions by peroxodisulfate(4/) ions.
O67(a0) 8 /7(a0) O97(a0) 8 /(a0)
The investigation can be extended to study the catalytic eect of
d1bloc% element ions on the reaction. Jective catalysts provide
an alternative pathway for the change with a lower activation
energy.
Method
/n this series of experiments the concentrations of the reactants
are %ept constant while the temperature of the reaction mixture
is varied systematically over an appropriate range of values.
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%igure +utline of a procedure for investigating how the rate of a reaction varies
with temperature.
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Practical guidance1 How fast ? rates
The reaction mixture includes starch solution. Adding a small,
measured amount of sodium thiosulfate as well means that at the
start any iodine formed is immediately reduced bac% to iodide
ions. Once all the thiosulfate has been used up the free iodine
formed gives a sudden blue1blac% colour with the starch.
Results
The table shows a typical set of results from a series of runs with
temperatures in the range C E and ;; E. The table includes
calculated values for ln (":t) and
"CCC:TF7"corresponding to the variables in the Arrhenius
e0uation.
)emerature* T/K !0! !0( !12 !1 !2#
)ime* t* for the +luecolour to aear/s
20# 1! 115 $5 55
ln,"1/t$ 5.!2 #.(! #.$5 #.!2 #.01
1000 /K1T
!.!0 !.2# !.21 !.1# !.0(
)a*le 2K -esults for a series of runs at different temperatures.
Analysis
A plot of ln (":t) against ":Tgives a straight line which has a
negative gradient. The magnitude of the slope wor%s out to be
=.=
"C
F.
o R
Ea ' =.= "CF
ence
Ea' =.= "CF 6." L F7"mol7"
The activation energy,Ea' ;.M %L mol7".
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Note
*hen using the +rrhenius
equation, temperatures
must be in !elvin.
Multiplying the values of1Tby a constant factor
ma!es them easier to plot
without affecting the
gradient of the resulting
graph.
Note
&he general equation for
a straight line ta!es the
form#y$ mx% c
where mis the gradient of
the line and ca constant.
*ith the usual axes, the
gradient is positive if the
line slopes up from left to
right and negative if it
slopes down.
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Practical guidance1 How fast ? rates
%igure ,
Arrhenius plot to determine the activation energ+ for a reaction.
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Practical guidance1 How fast ? rates
-ractical s!ills
Planning
>ates of reaction vary with concentration, particle si+e of any
solids, temperature and the presence of catalysts. ith so many
variables it is important to have a plan that varies one factor at a
time while %eeping the other variables constant.
One approach to %inetics experiments is to concentrate on the
initial rate. On mixing the reagents at the start all the
concentrations are %nown. Eloc% reactions are a variant on the
initial1rate method.
Checklist
hen planning rate experiments ma%e sure that you5
explain the design of your experiment and state which factors
you will vary and which variables you will control
show how you have used the trial tests and:or the e0uation for
the reaction to decide on the concentrations and 0uantities to
use
list the apparatus you need and draw a labelled diagram to
show how it will be used
give step1by1step instructions for carrying out the experiment
indicate the measurements you plan to ta%e
explain how you will analyse your results, showing what
graphs you will plot and why
identify any ha+ards and state how you will reduce the ris%s
from them.
An alternative approach is to follow the change in concentration
of one reactant until it is nearly used up, with all the other
reactants present in such large excess that their concentrations
do not change to a signi&cant extent. Nou can then plot a
concentrationtime graph for the one reactant with varying
concentration, and plot tangents to the curve to measure the
gradient, and hence the rate, at a succession of concentrations.
ometimes it is easier to follow the formation of a product, for
example, by collecting and measuring the volume Vof a gas, and
then use the fact that, as explained earlier, (V&nal7 Vt) is
proportional to the concentration of one of the reactants at time
t.
Always carry out some preliminary tests to &nd out (by
experiment) a suitable range of concentrations or temperatures
that will give you a reasonable range of results in times that you
can measure with suicient accuracy.
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Practical guidance1 How fast ? rates
rite out the balanced e0uation and use it to estimate suitable
0uantities to use. /f, for example, you are planning to study a
reaction that produces a gas you will need to ensure that you will
not produce more gas than you can sensibly collect and measure.
The balanced e0uation also allows you to chec% the extent towhich concentrations will vary during an experimental run. /f
studying the time for a measured amount of metal to dissolve in
an acid, you need to chec% that your acid is in suiciently large
excess for its concentration not to vary before all the metal is
used up.
Nou should show which measurements are critically important in
determining the &nal result. Nou should decide when to use a
burette or pipette to measure volumes of solutions and when to
use a measuring cylinder.
Implementing
Nou have to be well organised and practically competent to get
good results from %inetics experiments. Nou must be able to
measure volumes and times accurately. /f you are following a
reaction over a period of time you have to be alert to ta%e a
succession of readings with appropriate precision at regular
intervals.
ome techni0ues are demanding, such as removing samples from
a reaction mixture with a pipette, stopping the reaction in some
way and then titrating the sample to measure the concentration
of a reactant.
/t is important to measure the temperature of a reaction mixture
to ensure that it does not vary substantially. /f the reaction is
exothermic this may aect an experiment that you are trying to
carry out at constant temperature.
Analysing and drawing conclusions
Nou will usually need to set out your results in a neat table with
extra rows or columns to calculate 0uantities such as ":t or (V&nal7 Vt). Always label the columns and rows clearly and give the
units for physical 0uantities.
/n any %inetics experiment you are li%ely to have to draw and
interpret one or more graphs. These can include plots of5
concentration against time the gradient at any point is the
rate at that time
rate against concentration a straight line through the origin
for a &rst order reaction, a hori+ontal line for a +ero order
reaction
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Practical guidance1 How fast ? rates
log(rate) against log(concentration) with a gradient that
e0uals the order with respect to the particular reactant
ln(rate) against ":T the gradient is used to calculate the
activation energy.
After plotting appropriate graphs from your results you shouldshow how they lead to your conclusions about the orders of
reaction or the activation energy, giving any wor%ing in full.
Always remember the units for physical 0uantities.
Nour analysis should include estimates of the main sources of
measurement uncertainty together with a value for the overall
uncertainty.
valuation
Commenting on the reliaility o! dataNou should review your &ndings and identify any anomalous
results. Nou should then discuss your estimates of measurement
uncertainty and comment on whether the degree of uncertainty
casts signi&cant doubts on your conclusions.
Comparing outcomes with e"pectations
hen studying some reactions you may be able to &nd
information about the expected order of reaction or the accepted
value for the activation energy. /f so, you should discuss how your
&ndings compare with the results reported elsewhere.
Identi!ying possile impro#ements
Nou should ta%e a critical loo% at the design of the experiment
and the practical methods involved. Aim to suggest
improvements to minimise errors and increase reliability.
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