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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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    G. Hill and A. Hunt 2009 de!cel "he#istr$ for A2

    %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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