IB Chemistry Order Reaction, Rate Law and Half life

1. 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
dt
Bd
dt
Ad ][][ 


2NO2 → N2O4
• Two mole NO2 decompose = One mole N2O4 form
• NO2 used up is twice as fast as N2O4 produced
dt
ONd
dt
NOd ][1
2
][1 422 


dt
HId
dt
Id
dt
Hd
2
][][1][1 22 




H2 + I2 → 2HI
• One mole H2 decompose = TWO mole HI form
• Rate H2 and I2 decompositionthe 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

2. GraphicalRepresentationof Order :ZERO, FIRST and SECOND order
ZERO ORDER FIRST ORDER SECOND ORDER
Rate – 2nd order respect to [A]
Conc x2 – Rate x 4
Unit 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 = k
k = 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 = kA
k = s-1
Rate vs Conc - proportional
Conc vs Time
ktAA
eAA
ot
kt
ot

 
]ln[]ln[
][][
[A]t
[A]o
kt
AA ot

][
1
][
1
ln Ao
1/Ao
Conc at time t Conc at time t

3. 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 fixed
Wasteful as multiple runs needed
Monitor decrease in conc reactant
Using Half Life to determine order
Monitor decrease conc of single reactant
Using gradient/ tangent at diff conc
Conc x2 – rate x2 - 1st order
Conc x2 – rate x4 – 2nd order
Conc x2 – rate 0 – zero order Convert Conc Vs Time to Rate vs Conc
Rate Vs Conc – Linear – 1st Order
Initial Rate taken, time 0
Draw tangent at time 0
Half Life directly prop to Conc
Half Life inversely prop to Conc
Expt Conc
A
Conc
B
Initial rate
1 0.01 0.02 2
2 0.01 0.04 4
3 0.02 0.02 4
Conc
Time
Expt 2
Expt 1
Conc reactant
Time
Zero order
Conc reactant
Time
Half Life constant
1st order
2nd order
Conc reactant
Time
Gradient at diff conc
Conc
Rate

4. 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
2
806.0log652.0lg
806.0652.0
0713.0
0575.0
1026.1
1021.8
2.
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2.
1.
2
3
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x
x
Conc
Conc
Rate
Rate
x
x
x
1
649.0log652.0lg
649.0652.0
0333.0
0216.0
1026.1
1021.8
3.
1.
3.
1.
2
3
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y
y
Conc
Conc
Rate
Rate
y
y
y
Expt Conc
A
Conc
B
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 Conc
F2
Conc
CIO2
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
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
1
44
01.0
04.0
102.1
108.4
1.
2.
1.
2.
3
3
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y
Conc
Conc
Rate
Rate
y
y
y
1
22
10.0
20.0
102.1
104.2
1.
3.
1.
3.
3
3
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x
Conc
Conc
Rate
Rate
x
x
x
To calculate k
Expt 1 : Ini rate = 1.2 x 10-3, [F2] = 0.10M, [CIO2] = 0.01M
Rate = 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] = 0.0216
Rate = k[A]2[B]1
8.21 x 10-3 = k[0.0575]2[0.0216]1, k = 115

5. 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-
] = 0.046M
Rate = 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 calculatek
2
4.1log96.1lg
4.196.1
025.0
035.0
1000.8
1057.1
1.
2.
1.
2.
3
2
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x
x
Conc
Conc
Rate
Rate
x
x
x
1
22
046.0
092.0
1057.1
1014.3
2.
3.
2.
3.
2
2
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y
Conc
Conc
Rate
Rate
y
y
y
Expt Conc
OH
Conc
CIO2
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
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 Conc
Br2
Conc
NO
Initial rate
1 0.1 0.1 12
2 0.2 0.1 24
3 0.1 0.2 48
1
2
1
2
1
2.0
1.0
24
12
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x
Conc
Conc
Rate
Rate
x
x
x
2
2
1
4
1
2.0
1.0
48
12
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y
Conc
Conc
Rate
Rate
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] = 0.1M
Rate = k[Br2]1[NO]2
12 = k[0.1]1[0.1]2 , k = 12,000 M-1min-1
To calculatek

6. Conc Vs Time / Conc Vs Rate for Order
2A → B + C
Plot Conc A vs Time for order, initial rate and rate constant, k
2N205 → 4N02 + 02
Plot Rate vs Conc for order and rate constant, k
Conc vs Time Mtd
• Half Life A -constant =80s
• 1st orderrespect to [A]
• Formulafor 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
1066.8
80
693.0
693.0



sk
k
t
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

7. Using Initial rate and Half Life for order
Hydrolysis of ester by OH-
: Ester + OH- → X + Y
Rxn done using two diff OH- conc.
Run 1 – [OH- ] – 0.20M Run 2 – [OH-] – 0.40M
Plot 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 (UsingHalf Life )
Using expt 2 : Conc ester vs time
Half 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
Time
Expt 2- [OH] = 0.40M
Expt 1 - [OH] = 0.20M
Compare Expt 1 and 2
1
2
1
2
1
40.0
20.0
00.8
00.4
2.
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x
Conc
Conc
Rate
Rate
x
x
x
Conc ester
Time
Expt 1 - [OH] = 0.20M
Expt 2- [OH] = 0.40M
Gradient, rate = 4.00
Gradient, rate = 8.00
12 m 12 m

8. RBr + OH- → ROH + Br-
Rxn done using TWO diff conc OH-
Expt 1 – [OH- ] – 0.10M Run 2 – [OH- ] – 0.15M
Plot 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 time
Half Life RBr t1/2 = 78 m
Rate = k[OH-]1 [RBr]1
• For expt 1
Ini 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 m
Ini 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
1
65.065.0
15.0
10.0
00.8
25.5
2.
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x
Conc
Conc
Rate
Rate
x
x
x
Expt 1 Expt 2
Time/m [RBr]/M
in [OH] = 0.10
[RBr]/M
in [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

9. Ester + H2O → CH3CO2H + C2H5OH
Rxn done using TWO diff HCI conc
Expt 1 : [HCI] – 0.10M Expt 2 :[HCI] – 0.20M
Plot Conc Estervs 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 2
Time/m [Ester]/M
in [HCI] = 0.1
[Ester]/M
in [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
1
5.05.0
2.0
1.0
8.3
9.1
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x
Conc
Conc
Rate
Rate
x
x
x
Ini rate Expt 1 – Gradient time 0 = 1.90
Ini 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 = 1.90
Ini rate Expt 2 – Gradient time 0 = 3.80

10. C3H8 + 5O2 → 3CO2 + 4H2O2H2 + O2 → 2H2O
Rate 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




Ms
dt
Od
dt
OHd
dt
OHd
dt
Od
dt
OHd
dt
Od
dt
Hd
1832
832
283
5.1)30.0(5
][
5
][
1
][1
5
][1
3
][1
5
][1
1
][1 2




Ms
dt
HCd
dt
Od
dt
HCd
dt
Od
dt
COd
dt
Od
dt
HCd
Benzenediazonium chloride, unstable, decomposes to produce N2 gas shown below
C6H5N2
+CI- + H2O → C6H5OH + N2 + HCI
Vol of N2 was collected over time
Vol of gas produced N2 in time t is proportional to amt C6H5N2
+CI- used up
V∞ α [C6H5N2
+CI- ] at start
(V∞ - Vt ) α [C6H5N2
+CI- ] remaining at time t
Plot 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 Conc
V∞ - 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