Chapter 14 Chemical Kinetics Chemical Kinetics CH 14 1
Chemical Kinetics CH 14 1
Chapter 14 Chemical Kinetics
Chemical Kinetics CH 14 2
• Factors affecting chemical reaction• Rate of reaction• Average rate, Instantaneous rate• Rate law• Order of reaction• First order reaction• Second order reaction• Half - life time
Chemical Kinetics CH 14 3
Chemical Kinetics: How fast is the chemical reaction, (i.e. studying of rates of chemical
processes).
Chemical Kinetics CH 14 4
Factors That Affect Reaction Rates 1. Reactant concentration: As the concentration of reactants increases, so does that reactant molecules will collide and rate of reaction increases. 2. Temperature: As temperature increases, the reaction rate increases, reactant molecules have more kinetic energy, move faster, and collide more often and with greater energy. 3. Catalysts: catalyst increases chemical reactions by changing mechanism.
Chemical Kinetics CH 14 5
Speed of a reaction is measured by: the change in
concentration with time.
For a reaction A B
Reaction Rates
t
Bof moles
timein change
Bof moles ofnumber in changerate Average
Chemical Kinetics CH 14 6
Reaction Rates
Rates of reactions can be determined by monitoring the change in concentration of either reactants or products
as a function of time. [A] / t
A B
Chemical Kinetics CH 14 7
At t = 0 (time zero) there is 1.00 mol A (100 red spheres) and no B present = zero.
At t = 20 min, there is 0.54 mol A and 0.46 mol B. At t = 40 min, there is 0.30 mol A and 0.70 mol B. Calculating average rate:
Reaction Rates
mol/min 023.0min 0min 20
mol 0 mol 46.0min 0min 20
0at Bof moles20at Bof moles
Bof molesrate Average
ttt
Chemical Kinetics CH 14 8
For the reaction:
A B There are two ways of measuring rate:
1. The speed at which the products appear (i.e. change in moles of B per unit time), or
2. The speed at which the reactants disappear (i.e. the change in moles of A per unit time).
Reaction Rates
t
A
t
][A of molesA respect to withrate Average
Chemical Kinetics CH 14 9
Example: Reaction of butyl chloride to give butanol.
Average rate decreases as the reaction goes on.
Chemical Kinetics CH 14 10
The average rate of the reaction over each interval = the change in concentration divided by the change in time:
Average Rate, M/s
C4H9Cl(aq) + H2O(l) C4H9OH(aq) + HCl(aq)
SMx /109.10.00.50
1000.00905.0 4
t
ClHCeaveragerat
]94[
Chemical Kinetics CH 14 11
• Instantaneous rate defines as The rate at any instant in time and it is the slope of the tangent to the curve.
• Average rate: is the change in reactant or product concentration to the change of time.
Instantaneous Rate & Average Rate
Chemical Kinetics CH 14 12
Example:
C4H9Cl(aq) + H2O(l) C4H9OH(aq) + HCl(aq)– If We plot [C4H9Cl] with respect to t.
–The units for average rate are mol/L·s or M/s.
Instantaneous Rate & Average Rate
Chemical Kinetics CH 14 13
Calculate: 1. average rate?SMxeaveragerat /106.1
200
4.0
0200
1.00671.0 4
2. instantaneous rate at Z point?
Average rate= Y2-Y1
X2-X1
ZSMxousrateIns /1067.6
200
4.0
600
030.0tantan 4
Chemical Kinetics CH 14 14
Reaction Rates and Stoichiometry
•What if the ratio is not 1:1?
H2(g) + I2(g) 2 HI(g)
• Only 1/2 HI is made for each H2 used.
Chemical Kinetics CH 14 15
• In General, for the reaction
aA + bB cC + dD
(-) sign because Reactants (decrease) with time
(+) sign because Products (increase) with time
Reaction Rates and Stoichiometry
Chemical Kinetics CH 14 16
• For Example
C4H9Cl(aq) + H2O(l) C4H9OH(aq) + HCl(aq)
tt
OHHCClHCRate 9494
Chemical Kinetics CH 14 17
• For Example
Chemical Kinetics CH 14 18
• In general rates increase as concentrations increase.
NH4+(aq) + NO2
-(aq) N2(g) + 2H2O(l)
Concentration and Rate
Constant
Constant increases
increases
Chemical Kinetics CH 14 19
• From previous table, for the reaction
NH4+(aq) + NO2
-(aq) N2(g) + 2H2O(l)
we note:
as [NH4
+] doubles with [NO2-] constant the rate doubles,
as [NO2-] doubles with [NH4
+] constant, the rate doubles
Concentration and Rate
Chemical Kinetics CH 14 20
Concentration and Rates
The above equation is called the rate law, and k is the rate constant.
For the reaction
Chemical Kinetics CH 14 21
• For a general reaction with rate law
m: order in reactant 1 and n: order in reactant 2.
• The total order of reaction = (m + n + ….)• The total order of reaction = zero, if m = 0, n = 0.
Rate Law
nmk ]2reactant []1reactant [Rate
Chemical Kinetics CH 14 22
Concentration and Rate
• This reaction is
First-order in [NH4+]
First-order in [NO2−]
• The overall reaction order: is the sum of the exponents on the reactants in the rate law.
• The overall order of this reaction= 1+1= 2 ( i.e. second-order).
Chemical Kinetics CH 14 23
AB
Differential Rate Law
Chemical Kinetics CH 14 24
ktt
ktt
t
t
t
tA
A
x
x
eAA
eA
A
ktA
A
ktAA
multiply
ktAA
AAt
ktcA
kdtA
Ad
cxx
dx
t
t
0
0
0
0
0
0
0
][
][
][][
][
][
][
][ln
]ln[]ln[
]ln[]ln[
][][,0
]ln[
][
][
ln
0
0
[A]0: the initial concentration at t = 0.[A]t: the concentration after time, t >0.
Chemical Kinetics CH 14 25
When [A]t is plotted as a function of time, a curve results.• Slope = - k
First Order Reactions
Chemical Kinetics CH 14 26
Straight Line Equation y = mx + bSlope= + mintercept = b
First Order Reactions
Chemical Kinetics CH 14 27
0AlnAln kttA plot of ln[A]t vs t is a straight line. slope = -k intercept = ln[A]0
First Order Reactions
ln[A]t
Chemical Kinetics CH 14 28
• Half-life t1/2: is the time taken for the concentration of
a reactant to drop to half its original value.• For a first order process, when t = t½,
so [A]t = ½[A]0.
kk
t693.0ln
21
21
First Order Reactions
ktA
A t 0][
][ln
Half- life time doesn’t depend on concentration of reactant
Chemical Kinetics CH 14 29
• For a second order reaction with just one reactant.
Second Order Reactions
kdtA
Ad
Akdt
Adrate
2
2
][
][
][][
tA
A
kdtA
Adt
0
][
][2
0][
][
cxx
dx
12
ktAA t
0][
1
][
1
[A] = [A]0 , t=0
0][
1
][
1
Akt
A t
Differential Equation
Chemical Kinetics CH 14 30
Second Order Reactions
The Change of Concentration with Time
0A1
A1 ktt
y = mx + b A plot of 1/[A] vs. t is a straight line with a slope of k. Intercept= 1/[A]0
Chemical Kinetics CH 14 31
0A1
21
kt
For a second-order process, set [A]t=0.5 [A]0 .
Half-Life of Second Order
21
00
][
1
][2
11
ktAA
Chemical Kinetics CH 14 32
The decomposition of NO2 at 300°C is described by the equation
NO2 (g) NO (g) + 1/2 O2 (g)
and yields these data:
Time (s) [NO2], M
0.0 0.01000
50.0 0.00787
100.0 0.00649
200.0 0.00481
300.0 0.00380
Determining the order of chemical reaction
Example
Chemical Kinetics CH 14 33
Graphing ln [NO2] vs. t yields:
Time (s) [NO2], M ln [NO2]
0.0 0.01000 -4.610
50.0 0.00787 -4.845
100.0 0.00649 -5.038
200.0 0.00481 -5.337
300.0 0.00380 -5.573
The plot is not a straight line, so the process is not first-order in [A].
Does not fit:
Determining the order of chemical reaction
Chemical Kinetics CH 14 34
A graph of 1/[NO2] vs. t gives this plot.
Time (s) [NO2], M 1/[NO2]
0.0 0.01000 100
50.0 0.00787 127
100.0 0.00649 154
200.0 0.00481 208
300.0 0.00380 263
• This is a straight line. Therefore, the process is second-order in [NO2].
Determining the order of chemical reaction
Chemical Kinetics CH 14 35
Practice Problems CH.14 in the book