CH112 FA10 LRSVDS 1
Dr. Lori Stepan Van Der Sluys
Section 002, MWF 9:05-9:55 am
Email: [email protected]
Office Hours:
! "Email for appointment or
! "______________________________
REQUIRED MATERIALS
Required: Brown, LeMay, Bursten & Murphy; Chemistry: The Central
Science, 11th ed., 2009.
Required: Chem 112 FA09 Student Packet
Required: non-programmable scientific calculator
Optional: Volume 2 for Chem 112; partial text
Optional: Wilson Solutions to Exercises in Chemistry, The Central Science,
11th ed.
CH112 LRSVDS Kinetics 2-3 2
Chemical Kinetics part 1: Reaction Rates Overview of Kinetics •"Rates of reaction
average rates instantaneous rates
•"Dependence of rate on concentration
rate constant
rate laws order of the reaction
•"Dependence of rate on time
First order
Second order
Half-life
•"Dependence of rate on temperature
Activation Energy Ea Activated Complex
Arrhenius Equation
•"Reaction Mechanisms
•"Catalysis and Enzymes
CH112 LRSVDS Kinetics 2-3 3
EXPRESS REACTION RATES
“What is the rate of this reaction?”
We can express the rate of reaction in terms of:
1.
2.
Rate = OR
Stoichiometry of a reaction tells us how these are related.
In General: aA + bB ! cC + dD
reactants products
(a, b, c, d are stoichiometric coefficients)
!
rate = "1
a
# A[ ]#t
= "1
b
# B[ ]#t
= +1
c
# C[ ]#t
= +1
d
# D[ ]#t
!
"#[C
4H
9Cl]
# t
C4H9Cl(aq) + H2O(l) ! C4H9OH(aq) + HCl(aq)!
!
+"[C
4H
9OH]
" t
CH112 LRSVDS Kinetics 2-3 4
Reaction Rates and Stoichiometry
!" A + B ! C
1." Given the rate of disappearance of A is 5M/s, what is the
rate of appearance of C?
2." What is the rate of disappearance of B?
!" 2A + B ! C
1." Given the rate of disappearance of A is 5M/s, what is the
rate of appearance of C?
2." What is the rate of disappearance of B?
CH112 LRSVDS Kinetics 2-3 5
Example Problem
2HI(g) ! H2(g) + I2(g) If 6 moles of HI in a 1 L flask are converted to I2 and H2 in 1 min., What is the rate of disappearance of HI?
What is the rate of appearance of H2?
1." Twice the rate of disappearance of HI?
2." 1/2 the rate of disappearance of HI?
HINT: is rate of appearance of H2 greater than or less than the rate of
disappearance of HI?
!
rate ="# HI[ ]#t
=
!
rate =+" H
2[ ]"t
=
CH112 LRSVDS Kinetics 2-3 6
WAYS TO MEASURE REACTION RATES
N2O4(g) ! 2NO2(g)
1 mole gas 2 moles gas
a) For gas reactions, can measure P or V changes if "ngas = +1, then [N2O4] # PN2O4 and [NO2] # PNO2
rate = "PNO2 = - "PN2O4
2"t "t
b)! Spectroscopic methods; are the colors different?
N2O4(g) colorless NO2(g) red-brown
Measure light absorption vs. time; Absorbance # [NO2]
rate = " [NO2] 2"t
•" Wavelength used corresponds to wavelength of light that is absorbed by the species of interest.
•" This is a general method since we can use any wavelength of light
CH112 LRSVDS Kinetics 2-3 7
FOUR FACTORS THAT AFFECT REACTION RATES
1.! The physical state of the reactants
2. The Concentration of reactants
3. The Temperature
4.! The Presence of a catalyst
CH112 LRSVDS Kinetics 2-3 8
Rate Law: the relationship between the _________
of a reaction and _________________ of its
reactants.
EFFECT OF CONCENTRATION
ON RATE
Rate varies as concentration varies:!
CH112 LRSVDS Kinetics 2-3 9
Rate Laws
For a general reaction:
aA + bB ! cC + dD reactants products
rate = -"[A] OR -"[B] OR +"[C] OR +"[D]
"t "t "t "t
The rate law is:
k is the rate constant •"
•"
x and y exponents are _____________ (Must be ! 0, not
necessarily integers)
Order of reaction = ________________ (Overall order of reaction = x + y)
CH112 LRSVDS Kinetics 2-3 10
Simple Rate Laws
For the following reaction, any of the following could be the rate
law, if it matches the experimental data:!
A + B ! C!
1.! If Rate = k[A]!
2.! If Rate = k[B]!
3.! If Rate = k[A][B]!
CH112 LRSVDS Kinetics 2-3 11
Reaction Orders
2 NO(g) + 2H2(g) ! N2(g) + 2H2O(g)
Rate =
Given the Rate Law: rate = k[NO]2[H2]
1." What order is the reaction in H2?
2." What order is the reaction in NO?
3." What is the overall reaction order?
CH112 LRSVDS Kinetics 2-3 12
DETERMINING THE RATE LAW
Method of “initial rates”:
Initially, we know [A] and [B] (and [C] = [D] =____)
initial rate = k1[A]ox [B]o
y
Strategy:
1.! Vary [A]0 and [B]0
2.! measure the initial rates
3.! observe the effect
CH112 LRSVDS Kinetics 2-3 13
Sample problem: data given for the reaction: A + B ! Z
[A]0 [B]0 initial rate
1) 1.0M 1.0M 0.8x10-2 M/s
2) 2.0 1.0 1.6x10-2
3) 2.0 2.0 6.4x10-2
4) 1.0 2.0 3.2x10-2 Rate = k [A]x [B]y
1.!What is x?
2.!What is y?
3.!What is the overall reaction order? 4.!What is the Rate Law?
5.!What is k? What are the units?
CH112 LRSVDS Kinetics 2-3 14
FYI
Solution to Sample Problem
1.! Compare Rate 1 to Rate 2
!
R1
R2
=k A[ ]
1
a
B[ ]1
b
k A[ ]2
a
B[ ]2
b=
A[ ]1
a
A[ ]2
a=
1M[ ]a
2M[ ]a
=1
2
!
Rate 1
Rate 2=
R1
R2
= 0.8 "10
#2M /s
1.6 "10#2
M /s =
1
2
Using the rate laws to compare rates:
a must be one for the relationship above to be true
!
" 1
2
#
$ % &
' (
a
= 1
2
Recall that [B] in trials 1 and 2 does not change so the ratio of ([B]1/[B]2 )b = 1
regardless of the value of the exponent.
CH112 LRSVDS Kinetics 2-3 15
FYI
Solution to Sample Problem continued
2. Compare Rate 2 to Rate 3
Using the rate laws to compare rates:
b must be two for the relationship above to be
true
!
Rate 2
Rate 3=
R2
R3
= 1.6 "10
#2M /s
6.4 "10#2
M /s =
1
4
!
R2
R3
=k A[ ]
2
a
B[ ]2
b
k A[ ]3
a
B[ ]3
b=
B[ ]2
b
B[ ]3
b=
1M[ ]b
2M[ ]b
=1
4
!
" 1
2
#
$ % &
' (
b
= 1
4
CH112 LRSVDS Kinetics 2-3 16
Determination of Rate Laws
aA + bB ! zZ
rate = k[A]x[B]y
Are x and y the same as a and b?
NOTE: Rate Law MUST be determined experimentally.
Exponents CANNOT be predicted from the overall reaction.
experiment $ rate law % mechanism
(exponents x, y)
Examples of Rate Laws:
CH112 LRSVDS Kinetics 2-3 17
Summary: Using experimental data to determine the rate law
!"Observe the effect of changing the initial concentration of the reactants on the initial rate of the reaction.
!" In most reactions the exponents are 0, 1, or 2 (can be a fraction or negative.)
!" Change in concentration of zero order reactants has no effect on the rate.
!" Doubling the concentration of first order reactants ___________ the rate.
!" Doubling the concentration of second order reactants increases the rate by 22=4 (____________ the rate).
!" Tripling the concentration of second order reactants increases the rate by 32=________.
!" For third order reactants, doubling the concentration increases the rate by 23=_______.
CH112 LRSVDS Kinetics 2-3 18
Using experimental data to determine the rate law
The following data were collected for the rate of disappearance of NO in the reaction below:
2 NO(g) + O2(g) ! 2NO2(g)
Exp [NO] [O2] Initial Rate (M/s)
1 0.0126 M 0.0125 M 1.41 & 10-2
2 0.0252 M 0.0250 M 1.13 & 10-1
3 0.0252 M 0.0125 M 5.64 & 10-2
(a)" What is the order in NO?
(b)" What is the order in O2?
(c)" What is the rate law for the reaction?
(d) What are the units of the rate constant?
CH112 LRSVDS Kinetics 2-3 19
Continued: Data were collected for the rate of
disappearance of NO in the reaction:
2 NO(g) + O2(g) ! 2NO2(g)
(e) What is the rate of disappearance of [O2] at the concentrations given in experiment 1?
Exp [NO] [O2] Initial Rate (M/s)
1 0.0126 M 0.0125 M 1.41 & 10-2
CH112 LRSVDS Kinetics 2-3 20
Summary
Measure the instantaneous rate of a reaction: this is a number!
Measure
the rate of loss
of a reactant
Or . . . the rate of appearance
of a product
Repeat the experiment to determine the concentration
dependence: Obtain the Rate Law
Differential rate Law: gives rate as a function of
concentration
CH112 LRSVDS Kinetics 2-3 21
Study Rate Law as a function of time We are studying a chemical reaction; for example
aA ! products
Measure the rate as a function of concentration
rate = -"[A] = k[A]x (the differential rate law)
" t
This is a differential equation; Integration gives [A] as a function of t
Differential Rate Law for 1st order reaction (x = 1):
Integrate to get:
or:
Rearrange:
(Different forms of the same equation)
CH112 LRSVDS Kinetics 2-3 22
FYI
If "[A] ! d[A] as "t ! 0 then
!
rate = "# A[ ]#t
= k A[ ] (First order rate law)
rearrange
!
" A[ ]A[ ]
= # k"t
!
d A[ ]A[ ]
= " kdt
Integrate: at t = 0, [A] = [A]0
!
d A[ ]A[ ]A[ ]
0
A[ ]
" = # k dt
0
t
"
ln A[ ] # ln A[ ]0 = ln
A[ ]A[ ]
0
= # kt
Integrated first order rate law: concentration as a
function of time
CH112 LRSVDS Kinetics 2-3 23
The Integrated First Order Rate Law
is a Linear Equation
ln[A] = - k t + ln[A]o
This is in the form of:
y = m x + b y = b =
x = m =
A plot of__________vs. ________ gives a straight line for
first order reactions.
time!
ln[A]! slope = -k!
ln[A]o!
CH112 LRSVDS Kinetics 2-3 24
CH3'N(C: CH
3 ' C ( N:
!
[A] = [A]0e"kt
PA
= P0e"kt
!n [A] = !n[A]0 - k t
!n (PA) = !n(P0) - k t
Make two plots using the reaction data:
CH112 LRSVDS Kinetics 2-3 25
INTEGRATED RATE LAW
2nd order reaction
2nd order reaction (x = 2):
differential
rate law
Integrate to get:
integrated 2nd
order rate law !
rate ="# A[ ]#t
= k A[ ] 2
!
1
A[ ]= k t +
1
A[ ] 0
[A]!
t!
CH112 LRSVDS Kinetics 2-3 26
FYI
If "[A] ! d[A] as "t ! 0 then !
rate = "# A[ ]#t
= k A[ ]2 Second order rate law
rearrange
!
" A[ ]
A[ ]2
= # k"t
!
d A[ ]
A[ ]2
= " kdt
Integrate: at t = 0 [A] = [A]0
!
"d A[ ]
A[ ]2
A[ ]0
A[ ]
# = k dt
0
t
#
1
A[ ] "
1
A[ ]0
= kt
Integrated second order rate law: concentration as a
function of time
CH112 LRSVDS Kinetics 2-3 27
NO2(g) ! NO(g) + ! O2(g)
Step 1: Measure [NO2] as a function of time
Collect data Calculate these
Time(s) [NO2](M) ln [NO2] 1/[NO2]
0.0 0.01000 - 4.610 100
50.0 0.00787 - 4.845 127
100.0 0.00649 - 5.038 154
200.0 0.00481 - 5.337 208
300.0 0.00380 - 5.573 263
Example : What is the rate law?
0
0.001
0.002
0.003
0.004
0.005
0.006
0.007
0.008
0.009
0.01
0 100 200 300 400 500 600
TIME (SEC)
[NO
2]
(M)
CH112 LRSVDS Kinetics 2-3 28
Step 2 to Determine Order of Reaction:
Plot ln [NO2] vs. time Plot 1/[NO2] vs. time
Is either plot linear?
What is the rate law?