http://lawrencekok.blogspot.com

Prepared by Lawrence Kok

Tutorial on Rate Law, Rate Expression, Order of Reaction, Initial Rate and Half Life .

Reaction Rates / Kinetics

• Chemical rxn, reactant consumed, product formed• Amt reactant decrease ↓ , Amt product increase ↑

• Rate follow stoichiometric principles A → B

• For every ONE A breakdown = ONE B will form• Rate decomposition A = Rate formation of B

dtBd

dtAd ][][

2NO2 → N2O4

• Two mole NO2 decompose = One mole N2O4 form

• NO2 used up is twice as fast as N2O4 produced

dtONd

dtNOd ][12

][1 422

dtHId

dtId

dtHd

2][][1][1 22

H2 + I2 → 2HI

• One mole H2 decompose = TWO mole HI form• Rate H2 and I2 decomposition the same but only half the rate HI formation

Amt/Conc Amt/Conc

Time Time

Reactants Product

(Reactants)• X decrease/consume ↓ over time

(Products)• Y increase/form ↑over time

Rate of Decrease of X• Decrease ↓ Conc X /time• Decrease ↓ Vol X /Time• Decrease ↓ Abs X /Time

Rate of Increase of Y• Increase ↑ Conc Y /time• Increase ↑ Vol Y /Time• Increase ↑ Abs Y /Time

Amt/Conc/Vol/Abs X

Time

Amt/Conc/Vol/Abs Y

X

Y

Time

Gradient= rate change at time,t Gradient= rate change at time,t

Instantaneous rate time, t1

Initial rate, t = 0

Initial rate, t = 0

Instantaneous rate time, t1

X → Y

Click here notes

Graphical Representation of Order :ZERO, FIRST and SECOND order

ZERO ORDER FIRST ORDER SECOND ORDER

Rate – 2nd order respect to [A]Conc x2 – Rate x 4Unit for k Rate = k[A]2

Rate = kA2

k = M-1s-1

Rate

Conc reactant

Rate

Conc reactant Conc reactant

Conc Conc Conc

Time Time Time

Time

Conc reactant

Rate

Time

ln At

Time

1/At

ktAA ot ][][

Rate = k[A]0

Rate independent of [A]Unit for k Rate = k[A]0

Rate = kk = Ms-1

Rate vs Conc – Constant

Conc vs Time – Linear

Rate = k[A]1

Rate - 1st order respect to [A]Unit for k Rate = k[A]1

Rate = kAk = s-1

Rate vs Conc - proportional

Conc vs Time

ktAAeAA

ot

ktot

]ln[]ln[][][

[A]t

[A]o

ktAA ot

][1

][1

ln Ao

1/Ao

Conc at time t Conc at time t

Order of rxn found using THREE mtds

Initial Rate mtd(Multiple Single Runs)

Conc Vs Time Mtd (Half Life)

Conc Vs Time Mtd(Whole Curve/Tangent)Multiple Single Runs

Vary/Keep certain conc fixedWasteful as multiple runs

needed

Monitor decrease in conc reactantUsing Half Life to determine order

Monitor decrease conc of single reactantUsing gradient/ tangent at diff conc

Conc x2 – rate x2 - 1st orderConc x2 – rate x4 – 2nd orderConc x2 – rate 0 – zero order Convert Conc Vs Time to Rate vs Conc

Rate Vs Conc – Linear – 1st OrderInitial Rate taken, time 0 Draw tangent at time 0

Half Life directly prop to Conc

Half Life inversely prop to Conc

Expt ConcA

ConcB

Initial rate

1 0.01 0.02 2

2 0.01 0.04 4

3 0.02 0.02 4

Conc

TimeExpt 2

Expt 1

Conc reactant

Time

Zero order

Conc reactant

TimeHalf Life constant

1st order

2nd order

Conc reactant

Time

Gradient at diff conc

Conc

Rate

Rxn : A + B → AB

Find order A (fix conc B ) Let Rate = k[A]x[B] y

Rate = k[A]2 [B]1

2nd order respect to A 1st order respect to B

Using Initial rate for order of rxn

Find order B (fix conc A) Let Rate = k[A]x[B] y

2806.0log652.0lg

806.0652.00713.00575.0

1026.11021.8

2.1.

2.1.

2

3

xx

ConcConc

RateRate

x

x

x

1649.0log652.0lg

649.0652.00333.00216.0

1026.11021.8

3.1.

3.1.

2

3

yy

ConcConc

RateRate

y

y

y

Expt ConcA

ConcB

Initial rate

1 0.0575 0.0216

8.21 x 10-3

2 0.0713 0.0216

1.26 x 10-2

3 0.0575 0.0333

1.26 x 10-2

Expt ConcF2

ConcCIO2

Initial rate

1 0.10 0.01 1.2 x 10-3

2 0.10 0.04 4.8 x 10-3

3 0.20 0.01 2.4 x 10-3

Rxn : F2 + 2CIO2 → 2FCIO2

Find order CIO2 (fix conc F2 ) Let Rate = k[F2]x [CIO2] y

Find order F2 (fix conc CIO2) Let Rate = k[F2]x [CIO2] y

1st order respect to CIO2 1st order respect to F2

Rate = k [CIO2]1 [F2]1

144

01.004.0

102.1108.4

1.2.

1.2.

3

3

y

ConcConc

RateRate

y

y

y

122

10.020.0

102.1104.2

1.3.

1.3.

3

3

x

ConcConc

RateRate

x

x

x

To calculate k

Expt 1 : Ini rate = 1.2 x 10-3, [F2] = 0.10M, [CIO2] = 0.01MRate = k[F2]1[CIO2]1

1.2 x 10-3 = k[0.10]1[0.01]1, k = 1.2 M-1s-1

To calculate k

Expt 1 : Ini rate = 8.21 x 10-3, [A] = 0.0575, [B] = 0.0216Rate = k[A]2[B]1

8.21 x 10-3 = k[0.0575]2[0.0216]1, k = 115

Rxn : 2CIO2 + 2OH- → CIO3- + CIO2

- + H2O

Find order CIO2 (fix conc OH- ) Let Rate = k[CIO2]x[OH-]y

Expt 1 : Ini rate = 8 x 10-3 , [CIO2] = 0.025M, [OH-] = 0.046MRate = k[CIO2]2[OH-] 1

8 x 10-3 = k[0.025]1[0.046]1, k = 278.3M-1s-1

Find order OH- (fix conc CIO2 ) Let Rate = k[CIO2]x[OH-]y

2nd order respect to CIO2 1st order respect to OH-

Rate = k[CIO2]2[OH-]1

Using Initial rate for order of rxn

To calculate k

24.1log96.1lg

4.196.1025.0035.0

1000.81057.1

1.2.

1.2.

3

2

xx

ConcConc

RateRate

x

x

x

122

046.0092.0

1057.11014.3

2.3.

2.3.

2

2

y

ConcConc

RateRate

y

y

y

Expt ConcOH

ConcCIO2

Initial rate

1 0.046 0.025 8 x 10-3

2 0.046 0.035 1.57 x 10-3

3 0.096 0.035 3.14 x 10-3

Rxn : Br2 + 2NO → 2NOBr

Find order Br2 (fix conc NO ) Let Rate = k[Br2]x[NO]y

Find order NO (fix conc Br2 ) Let Rate = k[Br2]x[NO]y

Expt ConcBr2

ConcNO

Initial rate

1 0.1 0.1 12

2 0.2 0.1 24

3 0.1 0.2 48

121

21

2.01.0

2412

2.1.

2.1.

x

ConcConc

RateRate

x

x

x

221

41

2.01.0

4812

3.1.

3.1.

y

ConcConc

RateRate

y

y

y

2nd order respect to NO1st order respect to Br2

Rate = k[Br2]1[NO]2

Expt 1 : Ini rate = 12Ms-1, [Br2] = 0.1M, [NO] = 0.1MRate = k[Br2]1[NO]2

12 = k[0.1]1[0.1]2 , k = 12,000 M-1min-1

To calculate k

Conc Vs Time / Conc Vs Rate for Order Rxn: 2A → B + C

Plot Conc A vs Time for order, initial rate and rate constant, kRxn: 2N205 → 4N02 + 02

Plot Rate vs Conc for order and rate constant, k

Conc vs Time Mtd• Half Life A -constant = 80s • 1st order respect to [A]• Formula for 1st order half life

Conc vs Rate Mtd• Straight Line – 1st order respect to [N205]• Rate = k[N205 ], k = gradient = 7.86 x 10-6 s-1

Time 0 40 80 120 160 200 240

Conc 0.8 0.58 0.40 0.28 0.20 0.14 0.10

Conc

Time

80s 80s 80s

13

2/1

1066.880693.0

693.0

sk

kt

Conc Rate/10-5

0.94 1.26

1.40 1.52

1.79 1.93

2.00 2.10

2.21 2.26

Conc

Rate

rate constant

Rate Law / Rate Expression

Rxn: aA + bB → cC + dD• Stoichiometry eqn : Show mole ratio of

reactant/product• Rate eqn : Eqn relate rate with

conc of reactant : How conc reactant affect rate

Rxn eqn = k[A]x[B]y x = order respect to [A] y = order respect to [B] (x +y) = overall order k = rate constant

Order must be determined experimentally , NOT derived from stoichiometry coefficients

Gradient = k

Using Initial rate and Half Life for order

Hydrolysis of ester by OH- : Ester + OH- → X + YRxn done using two diff OH- conc.Run 1 – [OH- ] – 0.20M Run 2 – [OH-] – 0.40MPlot Conc ester vs Time. Find order and initial rate

Find order for OH- (fix conc ester)Let Rate = k[OH-]x [ester] y

Find order for ester (Using Half Life )Using expt 2 : Conc ester vs timeHalf Life Ester t1/2 = 12 m(constant)1st order respect to ester

Rate = k[OH-]1 [ester]1

For EXPT 2 :• Ini rate = 8.00, [OH-]= 0.4M, [ester]

= 100M• Rate = k[OH-]1 [ester]1

• 8.00 = k[0.4]1[100]1 • k = 0.2M-1min-1

Half life : 100 → 50→ 25 (12 min)• Ini Rate expt 1 – Gradient time

0 = 4.00 • Ini Rate expt 2 – Gradient time

0 = 8.00

1st order respect to OH -

Conc ester

TimeExpt 2- [OH] = 0.40M

Expt 1 - [OH] = 0.20M

Compare Expt 1 and 2

121

21

40.020.0

00.800.4

2.1.

2.1.

x

ConcConc

RateRate

x

x

x

Conc ester

Time

Expt 1 - [OH] = 0.20MExpt 2- [OH] = 0.40M

Gradient, rate = 4.00

Gradient, rate = 8.00

12 m 12 m

RBr + OH- → ROH + Br-

Rxn done using TWO diff conc OH-

Expt 1 – [OH- ] – 0.10M Run 2 – [OH- ] – 0.15MPlot Conc RBr vs time. Find order and initial rate

Determine order for OH- (fix conc RBr)Let Rate = k[OH-]x [RBr] y

Find order RBr (using half life)Using expt 2 : Conc vs timeHalf Life RBr t1/2 = 78 m

Rate = k[OH-]1 [RBr]1

• For expt 1 Initial rate = 5.25, [OH-] = 0.10M, [RBr] = 0.01M• Rate = k[OH-]1 [RBr]1

• 5.25 = k[0.10]1[0.01]1 • k = 5250 M-1min-1

Half life : 0.01 → 0.005 → 0.0025 = 78 mIni Rate expt 1 – Gradient time 0 = 5.25 Ini Rate expt 2 – Gradient time 0 = 8.00

1st order with respect to OH -

Rate = k[OH-]1 [RBr]1

Using Initial rate and Half Life for order

165.065.015.010.0

00.825.5

2.1.

2.1.

x

ConcConc

RateRate

x

x

x

Expt 1 Expt 2Time/m [RBr]/M

in [OH] = 0.10

[RBr]/Min [OH] =

0.15

0 0.0100 0.0100

40 0.0079 0.0070

80 0.0062 0.0049

120 0.0049 0.0034

160 0.0038 0.0024

200 0.0030 0.0017

240 0.0024 0.0012 Expt 1 - [OH] = 0.20M

Expt 2- [OH] = 0.15M

Time

Conc RBr

78s 78s

Gradient, rate = 8.00

Gradient, rate = 5.25

1st order with respect to RBr

Ester + H2O → CH3CO2H + C2H5OHRxn done using TWO diff HCI concExpt 1 : [HCI] – 0.10M Expt 2 :[HCI] – 0.20MPlot Conc Ester vs time. Find order and rate of rxn

Find order HCI (fix conc Ester)

Rate = k[HCI]1[Ester]1

1st order respect to HCI

Using Initial rate and Half Life for order

Expt 1 Expt 2Time/m [Ester]/M

in [HCI] = 0.1

[Ester]/Min [HCI] =

0.2

0 0.200 0.200

25 0.152 0.115

50 0.115 0.067

75 0.088 0.038

100 0.067 0.022

120 0.051 0.013

Time

Conc Ester

Gradient, rate = 1.9

Conc Ester

Time

Gradient, rate = 3.8

Find order Ester (use half life)Half life Ester -> 0.200 → 0.100 → 0.050 = 31 m

31 m 31 m

1st order respect to Ester

15.05.02.01.0

8.39.1

2.1.

2.1.

x

ConcConc

RateRate

x

x

x

Ini rate Expt 1 – Gradient time 0 = 1.90Ini rate Expt 2 – Gradient time 0 = 3.80

Expt 1 Expt 2

Half life is 31 min (constant)Ini rate Expt 1 – Gradient time 0 = 1.90Ini rate Expt 2 – Gradient time 0 = 3.80

C3H8 + 5O2 → 3CO2 + 4H2O2H2 + O2 → 2H2ORate O2 decrease ↓ is 0.23Ms-1, what is rate of H2O formation/increases ↑

Rate C3H8 decrease ↓ is 0.30Ms-1, what is the rate of 02 decrease ↓

Rxn Rates / Kinetics

122

22

2

46.0)23.0(2][

2][

2][1

1][1

2][

1][1

2][1 22

MsdtOd

dtOHd

dtOHd

dtOd

dtOHd

dtOd

dtHd

1832

832

283

5.1)30.0(5][

5][

1][1

5][1

3][1

5][1

1][1 2

MsdtHCd

dtOd

dtHCd

dtOd

dtCOd

dtOd

dtHCd

Benzenediazonium chloride, unstable, decomposes to produce N2 gas shown belowC6H5N2

+CI- + H2O → C6H5OH + N2 + HCI

Vol of N2 was collected over timeVol of gas produced N2 in time t is proportional to amt C6H5N2

+CI- used upV∞ α [C6H5N2

+CI- ] at start(V∞ - Vt ) α [C6H5N2

+CI- ] remaining at time tPlot of (V∞ - Vt ) vs time = Plot of conc vs time

Time/t 0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 ∞

Vt = Vol N2

0 14 28 41 54 65 76 87 96 104

112

120

127

133

139

219

(V∞ – Vt)/ cm3

219

205 191

178

165

154

143

132

123

115

107

99 92 86 139

0

Find rate at diff conc

Time

Plot of (V∞ - Vt ) vs time = Conc vs time (V∞ - Vt ) Time

ConcV∞ - Vt

Rate/Slope

0 219 16.5

4 165 12.1

7 132 10.0

14 80 6.22

21 47 3.84 (V∞ - Vt )

Rate

Plot Rate vs Concslope = rate

Acknowledgements

Thanks to source of pictures and video used in this presentation

Thanks to Creative Commons for excellent contribution on licenseshttp://creativecommons.org/licenses/

Prepared by Lawrence Kok

Check out more video tutorials from my site and hope you enjoy this tutorialhttp://lawrencekok.blogspot.com