Integrated Rate Equation Volumemeasurement Colorimetry Physical Method Physical Chemistry: Chemical...

IntegratedIntegrated

Rate EquationRate Equation

VolumeVolume

measurementmeasurement

ColorimetryColorimetry

Physical Method

Physical Chemistry:Physical Chemistry: Chemical KineticsChemical Kinetics

C. Y. Yeung (CHW, 2009)

AL CHEM REVIEW

Chemical Method

DifferentialDifferential


Chemical MethodChemical Method for Studying for Studying

the Variation ofthe Variation of [A][A] withwith TimeTime

C. Y. Yeung (CHW, 2009) p.01

Chemical Method = …Chemical Method = …

Monitoring the change of Monitoring the change of conc. along with time by:conc. along with time by:

sampling,sampling,

quenching, andquenching, and

titrationtitration

p.02

Example 1:Example 1:

RR CCOO

OR’OR’(aq)(aq) ++ OHOH--(aq)(aq) RR CC

OO

OO--(aq)(aq) ++ R’OHR’OH(aq)(aq)

Step1:Step1: Known amountsKnown amounts of ester and NaOH in be of ester and NaOH in beakers are placed in a thermostatic bath at akers are placed in a thermostatic bath at known temperatureknown temperature..

Step2:Step2: Start the reaction by mixing the reactants Start the reaction by mixing the reactants rapidly. The rapidly. The timetime is noted. is noted.

Step3:Step3: At At regular time intervalsregular time intervals, , a fixed volume a fixed volume of tof the mixture is pipetted into about 5 volumes he mixture is pipetted into about 5 volumes of ice-water to of ice-water to quenchquench the reaction. the reaction.

p.03

Example 1 (continued):Example 1 (continued):

RR CCOO

OR’OR’(aq)(aq) ++ OHOH--(aq)(aq) RR CC

OO

OO--(aq)(aq) ++ R’OHR’OH(aq)(aq)

Step4:Step4: Remaining [OHRemaining [OH--]] in the reaction mixture i in the reaction mixture is determined by titration against s determined by titration against standarstandard HCld HCl using using phenolphthaleinphenolphthalein..

Step5:Step5: Repeat steps 3 and 4 to obtain Repeat steps 3 and 4 to obtain variation of variation of [OH[OH--] against t] against t..

p.04

Example 2:Example 2:

2H2H22OO22(aq)(aq) ++ OO22(g)(g)

Step1:Step1: Known amountsKnown amounts of H of H22OO22 is mixed with a is mixed with a

small amount of MnOsmall amount of MnO22(s) catalyst in a (s) catalyst in a

beaker placed in a thermostatic bath at beaker placed in a thermostatic bath at known temperatureknown temperature..

Step2:Step2: At At regular time intervalsregular time intervals, , a fixed volume a fixed volume of tof the mixture is pipetted into excess dilute Hhe mixture is pipetted into excess dilute H22SS

OO44(aq) to (aq) to quenchquench the reaction by the reaction by removing tremoving t

he MnOhe MnO22(s) catalyst(s) catalyst..

MnOMnO22(s)(s)

2H2H22O(l)O(l)

p.05

Example 2 (continued):Example 2 (continued):

Step4:Step4: Remaining [HRemaining [H22OO22]] in the reaction mixture in the reaction mixture

is determined by titration against is determined by titration against standarstandard KMnOd KMnO44(aq)(aq)..

Step5:Step5: Repeat steps 3 and 4 to obtain Repeat steps 3 and 4 to obtain variation of variation of [H[H22OO22] against t] against t..

2H2H22OO22(aq)(aq) ++ OO22(g)(g)MnOMnO22(s)(s)

2H2H22O(l)O(l)

5H5H22OO22 + 2MnO + 2MnO44-- + 6H + 6H++ 2Mn 2Mn2+2+ + 8H + 8H22O + 5OO + 5O22

p.06

p.07

< COLORIMETRY >< COLORIMETRY >< < COLORCOLORIMETRY >IMETRY >

Physical MethodPhysical Method for Studying for Studying

the Variation ofthe Variation of [A][A] withwith TimeTime

Examples:Examples:

BrBr22 + HCOOH + HCOOH 2Br 2Br-- + 2H + 2H++ + CO + CO22

HH22OO22 + 2I + 2I-- + 2H + 2H++ II22 + 2H + 2H22OO

Colorimetry = …Colorimetry = …


measuring the variation of measuring the variation of absorbanceabsorbance by colorimeter by colorimeter

p.08

absorbance absorbance [coloured substanc [coloured substance]e][colour intensity][colour intensity]

Procedures:Procedures:

(I) Calibration of Colorimeter(I) Calibration of Colorimeter

Step1:Step1: Use distilled water as sample, the Use distilled water as sample, the absorbance absorbance is set to zerois set to zero..

p.09

Calibration of Colorimeter + MeasurementCalibration of Colorimeter + Measurement

Step2:Step2: A A standard solutionstandard solution of Br of Br22(aq) [e.g. 1.0M] is put i(aq) [e.g. 1.0M] is put i

nto the sample cell in the colorimeter.nto the sample cell in the colorimeter.

Step3:Step3: Record the Record the absorbanceabsorbance of 1.0M Br of 1.0M Br22(aq).(aq).

Step4:Step4: Repeat steps 2 and 3 with Repeat steps 2 and 3 with different [Brdifferent [Br22(aq)](aq)]..

Step5:Step5: Plot a Plot a Calibration CurveCalibration Curve of “Absorbance” v of “Absorbance” versus “[Brersus “[Br22(aq)]”.(aq)]”.

Calibration of ColorimeterCalibration of Colorimeter (continue) (continue)

[Br[Br22(aq)](aq)]

AbsorbanceAbsorbance

p.10

Put the BrPut the Br22 containing reaction mixture in containing reaction mixture in

the sample cell and put into the colorimeter.the sample cell and put into the colorimeter.

p.11(II) Measurement(II) Measurement

Step1:Step1:

Start the stop watch to monitor the variation Start the stop watch to monitor the variation of absorbance with time.of absorbance with time.

Step2:Step2:

timetime


BrBr22 + HCOOH + HCOOH 2Br 2Br-- + 2H + 2H++ + CO + CO22

p.12

timetime


[Br[Br22(aq)](aq)]


Time

[Br2]

t1

A1

A1

[Br2]t1

t1

[Br2]t1

Measurement Calibration

Monitoring the change of conc. Monitoring the change of conc.

along with time …along with time …

p.13

AnotherAnother Physical Method … Physical Method …


measuring the volume of measuring the volume of gas formed by syringegas formed by syringe

p.14

Mg + 2HCl Mg + 2HCl MgCl MgCl22 + + HH22

Example:Example:

(no colour change!)(no colour change!)

Rate Eqn.Rate Eqn. & & Order of RxnOrder of Rxn

p.15

Rate Equation Rate Equation (Rate Law)(Rate Law)

the mathematical equation relating ththe mathematical equation relating the e rate of rxnrate of rxn to the to the [reactants][reactants]..

3A + 2B 3A + 2B C C

p.16

Examples:Examples:

raterate [A][A]xx[B][B]yy

order of rxn w.r.t. [A]order of rxn w.r.t. [A]

order of rxn w.r.t. [B]order of rxn w.r.t. [B]

p.17

raterate = =rate constantrate constant

(varies with temp.!!)(varies with temp.!!)

kk[A][A]xx[B][B]yy

Therefore, the rate equation shows that:Therefore, the rate equation shows that:

rate of rxn is affected byrate of rxn is affected by [reactants] [reactants]

rate of rxn is affected byrate of rxn is affected by temperature temperature

* usually, order of reaction = * usually, order of reaction = 0, 1 0, 1 oror 2 2..

p.18

If [B] and temp. are kept constant, when [A] If [B] and temp. are kept constant, when [A] doubles, rate of reaction increases 4 times. doubles, rate of reaction increases 4 times.

How to do it?How to do it?[A] [B] Initial

rate

Expt. 1 [A]01 [B] Rate1



….. ….. ….. …..

kept constantkept constant

tt

[A][A]

[A][A]0303

[A][A]0202

[A][A]0101

initial rate methodinitial rate method

Repeat expt. with constant [A] and different [B], find n!Repeat expt. with constant [A] and different [B], find n!

Plot Plot raterate vs vs [A] [A] ::

p.19Determination of k, m and n Determination of k, m and n

by by graphical methodgraphical method

rate = k’ [A]rate = k’ [A]mm

[A] [B] Initial rate




….. ….. ….. …..

raterate

[A][A]

m = 0m = 0

m = 1m = 1

m = 2m = 2

Only m could be found!Only m could be found!

p.20rate = k’ [A]rate = k’ [A]mm

log (rate) = m log [A] + log k’log (rate) = m log [A] + log k’

log (rate)log (rate)

log [A]log [A]

y = mx + cy = mx + c

m = 0m = 0

m = 1m = 1

m = 2m = 2

log k’log k’

i.e. Both k (=k’/[B]) and m could be found!i.e. Both k (=k’/[B]) and m could be found!

Key PointsKey Pointsp.21

Rate Equation shows that the rate of rxn Rate Equation shows that the rate of rxn is affected by is affected by conc. (order)conc. (order) & & temp (k)temp (k)..

Find the order of rxn (m, n) by Find the order of rxn (m, n) by Initial RatInitial Rate Method e Method (many combinations of [A] & [B]!)(many combinations of [A] & [B]!)

Plot Plot log (rate) = m log[A] + log k’log (rate) = m log[A] + log k’, , both both mm, , k’k’ and and kk could be found. could be found.

Integrated Rate EquationIntegrated Rate Equation

p.22

p.23

[A] = - k’t + [A][A] = - k’t + [A]00

Zeroth OrderZeroth Order RxnRxn

Monitor the variation of Monitor the variation of conc.conc. along with along with timetime by Chemical / Physical Method, by Chemical / Physical Method,

Time t1 t2 t3 t4

[A] [A]1 [A]2 [A]3 [A]4

[A][A]

tt

[A][A]00 slope = - k’slope = - k’

To study Integrated Equation, To study Integrated Equation, e.g. :e.g. :

During the reaction, both [A] and [B] During the reaction, both [A] and [B] decrease!decrease!

p.24

large excess of [B]large excess of [B] should be used.should be used.

[A] = -k’t + [A][A] = -k’t + [A]00 (zeroth order)(zeroth order)

In order to ensure that the decreasing In order to ensure that the decreasing rate is due to decreasing [A], not [B] …rate is due to decreasing [A], not [B] …

i.e. keep [B] as “effectively constant”.i.e. keep [B] as “effectively constant”.

p.25

Time t0 t1 t2 t3 ….

[A] [A]0 [A]1 [A]2 [A]3 ….

ln[A] ln [A]0 ln [A]1 ln [A]2 ln [A]3 ….

ln [A] = - k’t + ln [A]ln [A] = - k’t + ln [A]00

ln [A]ln [A]

tt

ln [A]ln [A]00 slope = - k’slope = - k’

First OrderFirst Order RxnRxn

p.26

Time t0 t1 t2 t3 ….

[A] [A]0 [A]1 [A]2 [A]3 ….

[A]-1 [A]0-1 [A]1

-1 [A]2-1 [A]3

-1 ….

[A][A]-1-1

tt

[A][A]00-1-1

slope = k’slope = k’

[A][A]-1-1 = k’t + [A] = k’t + [A]00-1-1

Second OrderSecond Order RxnRxn

p.27

Summary … Summary … 3 Integrated Rate Eqns3 Integrated Rate Eqns

ln [A] = - k’t + ln [A]ln [A] = - k’t + ln [A]00

m = 0m = 0

m = 1m = 1

m = 2m = 2 [A][A]-1-1 = k’t + [A] = k’t + [A]00-1-1

[A] = - k’t + [A][A] = - k’t + [A]00

p.28

Kinetics Expt.:Kinetics Expt.: Decomposition of HDecomposition of H22OO22

Flask AFlask A(150cm(150cm33 water) water)

10cm10cm33 1.00 mol dm 1.00 mol dm-3-3 HH22OO22

50cm50cm33 borate buffer borate buffer

10cm10cm33 diluted diluted KMnOKMnO44

start stop watch!start stop watch!

10cm10cm33 sample sample(around 5 mins)(around 5 mins)

10cm10cm33 1.0M 1.0M HH22SOSO44Flask BFlask B

Titrate against Titrate against dilutedilute KMnO KMnO44

What happens in Flasks A and B …?What happens in Flasks A and B …?

p.29

Flask AFlask A

HH22OO22 + 2OH + 2OH-- O O22 + 2H + 2H22O + 2eO + 2e-`-`

MnOMnO44-- + 2H + 2H22O + 3eO + 3e-- MnOMnO22 + 4OH + 4OH--

× 3× 3

× 2× 2

3H3H22OO22 + 2MnO + 2MnO44-- 3O 3O22 + 2H + 2H22O + 2OHO + 2OH-- + 2 + 2MnOMnO22

2H2H22OO22 O O22 + 2H + 2H22OOMnOMnO22

Flask BFlask B

MnOMnO22 is killed by H is killed by H22SOSO44..

2MnO2MnO44-- + 5 + 5HH22OO22 + 6H + 6H++ 2Mn 2Mn2+2+ + 8H + 8H22O + 5OO + 5O22

p.30

Date Treatment …Date Treatment …

For 1For 1stst order rxn, ln [A] = - k t + ln [A] order rxn, ln [A] = - k t + ln [A]00

ln ([A]ln ([A]00/[A]) = k t/[A]) = k t

As vol. of MnOAs vol. of MnO44-- used used [A], [A],

ln (Vln (V00/V) = k t/V) = k t

If a If a straight linestraight line is plotted [ln(V is plotted [ln(V00/V) vs t] /V) vs t]

1st order1st order, and , and slope = kslope = k!!

Set Conc. + Collect Data + Plotting Order of Rxn + “k”

Chemical KineticsChemical Kinetics

IntegratedIntegrated


VolumeVolume

measurementmeasurement

ColorimetryColorimetry

Physical MethodChemical Method

DifferentialDifferential


p.31

One Combination? One Combination? (Continuous (Continuous

Method)Method)Many Many

Combinations? Combinations? (Initial Rate Method)(Initial Rate Method)

Physical/Physical/ChemicalChemicalMethod?Method?

Differential /Differential /Integrated Rate Eqn?Integrated Rate Eqn?

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