© university of south carolina board of trustees chapt. 13 kinetics sec. 1 define ‘rate’
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Chapt. 13KineticsSec. 1
Define ‘Rate’
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R P
D[R]
Dt
D[R]Dt
slope
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Reaction Rate: Good[ ]R
rate of reactiont
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Average vs Instantaneous Rates
D[R]
Dt
dtd[R]
Average
Instantaneous
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Reaction Rate: Better
Use the instantaneous rate
[ ]Rrate of reaction
dt
d
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Reaction Rate: Even Better
● Use the instantaneous rate
Make product or reactant measurements interchangeable
[ ] [ ]P Rrate of reaction
d d
dt dt
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Reaction Rate: Best
● Use the instantaneous rate
● Make product or reactant measurements interchangeable
Correct for stoichiometry
1 [ ] 1 [ ]
P R
P Rrate of reaction
d d
dt dt
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Example: Stoichiometry and Rates
In an electrolysis cell, electric current forces water to decompose into its elements, producing hydrogen at the rate of 0.12 mol/L-s.
2 H2O 2 H2 + O2
a) What is the rate of formation of oxygen?
b) What is the rate of disappearance of water?
c) What is the reaction rate?
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Chapt. 13Kinetics
Sec. 2Define ‘Rate Law’
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Rate and Concentration vs Time
rate at 0 s
rate at 20 s
rate at 40 s
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Rate Law
Most Common Form
● reactants only
● x, y small integersor simple fractions(0,1/2, 1, 3/2, 2, ...)
● x a; y b (Not Keq)
rate = k [A]x [B]y
Definitions
● k = rate constant
● x = order in Ay = order in B
● x+y = overall order
aA + bB products
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Chapt. 13Kinetics
Sec. 2Data k
Method of Initial Rates
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[A] vs t Data Rate Law
Method of Initial Rates (Sec. 13.2)
Trial and Error with Common Laws (Sec. 13.3)
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Define Initial Rate
initial rateinitial
conc. Assume rate and concentration are constant over initial time period
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Example: Method of Initial Rates
Initial rates are given below for the reaction
F2 + 2ClO2 2FClO2
Determine the rate law.Trial [F2]
(mol/L) [ClO2]
(mol/L) Initial Rate
(mol/L-s)
1 0.10 0.010 1.2x10-3
2 0.10 0.040 4.8x10-3
3 0.20 0.010 4.8x10-3
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(1) Use Ratios
Trial [F2](mol/L)
Rel.conc.
[ClO2](mol/L)
Rel.conc.
InitialRate
Rel.rate
1 0.10 1 0.010 1 1.2x10-3 1
2 0.10 1 0.040 4 4.8x10-3 4
3 0.20 2 0.010 1 4.8x10-3 4
Initial rates are given below for the reaction
F2 + 2ClO2 2FClO2
Determine the rate law.
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(2) [F2] const y
Trial [F2](mol/L)
Rel.conc.
[ClO2](mol/L)
Rel.conc.
InitialRate
Rel.rate
1 0.10 11 0.010 1 1.2x10-3 1
2 0.10 11 0.040 4 4.8x10-3 4
3 0.20 2 0.010 1 4.8x10-3 4
Initial rates are given below for the reaction
F2 + 2ClO2 2FClO2
Determine the rate law.
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(3) [ClO2] const x
Trial [F2](mol/L)
Rel.conc.
[ClO2](mol/L)
Rel.conc.
InitialRate
Rel.rate
1 0.10 1 0.010 11 1.2x10-3 1
2 0.10 1 0.040 4 4.8x10-3 4
3 0.20 2 0.010 11 4.8x10-3 4
Initial rates are given below for the reaction
F2 + 2ClO2 2FClO2
Determine the rate law.
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(4) Find k
Trial [F2](mol/L)
Rel.conc.
[ClO2](mol/L)
Rel.conc.
InitialRate
Rel.rate
1 0.10 1 0.010 11 1.2x10-3 1
2 0.10 1 0.040 4 4.8x10-3 4
3 0.20 2 0.010 11 4.8x10-3 4
Choose any set
Initial rates are given below for the reaction
F2 + 2ClO2 2FClO2
Determine the rate law.
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Trial [NO]M
[H2]M
Initial RateM/s
1 0.057 0.130 4.50x10-3
2 0.057 0.260 9.00x10-3
3 0.11 0.130 1.80x10-2
Student Problem
Write the rate law for the reaction given the following data
2NO + 2H2 N2 + 2H2O
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Chapt. 13Kinetics
Sec. 3Common Rate Laws
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Common Rate Laws
A products
a) First-orderRate = k [A]
b) Second-orderRate = k [A]2
c) Zero-orderRate = k [A]0 = k
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Common Rate Laws
A products
a) First-orderRate = k [A]
b) Second-orderRate = k [A]2
c) Zero-orderRate = k [A]0 = k
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1st-Order Rate Law
Differential Form
Rate = k [A](t)
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1st-Order Rate Law
Differential Form
Rate = k [A](t)
Integral Forms
[A](t) = [A]0 e-kt
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[A] = [A]0 exp(-k t)
Time0 2 4 6 8 10
[A]
0
1
2
3
4
5
6Time [A]
0.00 5.001.00 3.352.00 2.253.00 1.514.00 1.015.00 0.686.00 0.457.00 0.308.00 0.209.00 0.14
10.00 0.09
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Concentration at a Later Time
C12H22O11 + H2O ® C6H12O6 + C6H12O6 sucrose glucose fructose
This reaction is 1st order with a rate constant of 6.2 x10-5 s-1. If the initial sucrose concentration is 0.40 M, what is the concentration after 2 hrs (7200 s)?
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Time to Reach a Concentration
C12H22O11 + H2O ® C6H12O6 + C6H12O6 sucrose glucose fructose
This reaction is 1st order with a rate constant of 6.2 x10-5 s-1. If the initial sucrose concentration is 0.40 M, at what time does the concentration fall to 0.30 M?