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Chemical Kinetics
Chapter 14
The Rate Law
Rate law – description of the effect of concentration on rate
aA + bB cC + dD
Rate = k [A]x[B]y
reaction is xth order in A
reaction is yth order in B
reaction is (x +y)th order overall
F2 (g) + 2ClO2 (g) 2FClO2 (g)
rate = k [F2][ClO2]
Rate Laws
• Rate laws always determined experimentally
• Reaction order always defined in terms of reactant (not product) concentrations
• Order of a reactant is not related to the stoichiometric coefficients
1
Concentration and Initial Rates
NH4+(aq) + NO2
−(aq) N2(g) + 2 H2O(l)
Double [NH4+] with [NO2
−] constant: x = 1Rate doubles
Assume: rate = k [NH4+]x[NO2
−]y
Double [NO2−] with [NH4
+] constant: Rate doubles y = 1
Therefore rate law is rate = k [NH4+][NO2−]
Table14.2
Determine the rate law and calculate the rate constant for the following reaction from the following data:S2O8
2- (aq) + 3I- (aq) 2SO42- (aq) + I3
- (aq)
Experiment [S2O82-] [I-]
Initial Rate (M/s)
1 0.08 0.034 2.2 x 10-4
2 0.08 0.017 1.1 x 10-4
3 0.16 0.017 2.2 x 10-4
rate = k [S2O82-]x[I-]y
Double [I-], rate doubles (experiment 1 & 2)
y = 1
Double [S2O82-], rate doubles (experiment 2 & 3)
x = 1
k = rate
[S2O82-][I-]
=2.2 x 10-4 M/s
(0.08 M)(0.034 M)= 0.08/M•s
rate = k [S2O82-][I-]
Relation Between Concentration and Time
• Rate law provides rate as a function of concentration
• Need relationship between concentration and time :
• i.e., How do we determine the concentration of areactant at some specific time?
First-Order Reactions
A product rate = −[A]t
rate = k [A]
k = rate[A]
= 1/s or s-1M/sM
=[A]t
= k [A]−
[A] is the concentration of A at any time t
[A]0 is the concentration of A at time t=0
ln[A] = ln[A]o - kt
Integrated
rate law
t
0
A
A
dt k[A]
d[A]
o
kt [A]
[A] ln
o
Which now integrates to:
Consider the process in which methyl isonitrile is converted to acetonitrile
CH3CN
Fig 14.7(a) Data collected for this reaction at 198.9 °C.
First-Order Reactions
CH3NC
Plot of ln P vs time, results in a straight line Therefore,
Process is first-orderk is the negative of the slope: 5.1 10-5 s−1
First-Order Reactions
Fig 14.7
orange red-brown
Decomposition of N2O5
2 N2O5 (in CCl4) → 4 NO2 (g) + O2 (g)
→
Decomposition of N2O5
2 N2O5 (in CCl4) → 4 NO2 (g) + O2 (g)
Plot of ln [N2O5] vs time
Linear plot indicates: 1st order
Second-Order Reactions
A product rate = −[A]t
rate = k [A]2
[A]t
= k [A]2−
[A] is the concentration of A at any time t
[A]0 is the concentration of A at time t=0
1[A]
=1
[A]o
+ kt
One type:
A + B product
Second type:
rate = k [A][B]
Initial
rate law:
Combining the two rate expressions:
Which now integrates to: Integrated
rate law
The decomposition of NO2 at 300°C is described by the equation
NO2 (g) NO (g) + 1/2 O2 (g)
plot of ln[NO2] vs time:
Second-Order Reactions
plot of 1/[NO2] vs time:Fig 14.8
Half-life = time required for one-half of a reactant to react
t½ = t when [A] = [A]0/2
Because [A] at t1/2 is one-half of the original [A],
[A]t = 0.5 [A]0
1st order t1/2 = 0.693/k
2nd order
Fig 14.9
1st order rxn
t½ =1
k[A]o
Half-Life
Summary of the Kinetics of Reactions
Order Rate LawConcentration-Time
Equation Half-Life
0
1
2
rate = k
rate = k [A]
rate = k [A]2
ln[A] = ln[A]o - kt
1[A]
=1
[A]o
+ kt
[A] = [A]o - kt
t½ln2k
=
t½ =[A]o
2k
t½ =1
k[A]o