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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
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