chapter 13 chemical kinetics. the study of reaction rate is called chemical kinetics. reaction rate...
TRANSCRIPT
The study of reaction rate is called chemical kinetics.
Reaction rate is measured by the change of
concentration (molarity) of reactants or products
per unit time.
Δt
reactantΔreactantreactantr
if
if
tt
Unit:
Molarity of A: [A], e.g. [NO2]: molarity of NO2
Δt
productΔproductproductr OR
if
if
tt
reactants products,
− −
[reactant]↓ and [product]↑
mol·L−1·s−1 ≡ M·s−1
5 122
NO 0.0079 M 0.0100 Mr NO 4.2 10 M s
50 s 0 s-
t
0 s → 50 s:
5 122
NO 0.0065 M 0.0079 Mr NO 2.8 10 M s
100 s 50 s-
t
50 s → 100 s:
2NO2 (g) 2NO (g) + O2 (g)
− = r(NO2)
rate is a function of time
−
5 1NO 0.0035 M 0.0021 Mr NO 2.8 10 M s
100 s 50 s-
t
5 122
O 0.0018 M 0.0011 Mr O 1.4 10 M s
100 s 50 s-
t
50 s → 100 s:
−
2NO2 (g) 2NO (g) + O2 (g)
50 s → 100 s:
= r(NO2)
rate is a function of time
1
2
Δn
Δn
V
nΔ
V
nΔ
]Δ[O
]Δ[NO
Δt]Δ[O
Δt]Δ[NO
)r(O
)r(NO
2
2
2
2
O
NO
O
NO
2
2
2
2
2
2
2NO2(g) 2NO(g) + O2(g)
a A + b B c C + d D
r(A) a
r(B) b
r(A) a
r(C) c
d
r(D)
c
r(C)
b
r(B)
a
r(A) r =
r does not depend upon the choice of species
r(A) r(B) ,
a b
r(A) r(C)
a c
r(N2O5) = 4.2 x 10−7 M·s−1
What are the rates of appearance of NO2 and O2 ?
2N2O5(g) 4NO2(g) + O2(g)
Consider the following balanced chemical equation:
H2O2(aq) + 3 I–(aq) + 2 H+(aq) I3–(aq) + 2 H2O(l)
In the first 10.0 seconds of the reaction, the concentration of I– dropped from 1.000 M to 0.868 M.
(a)Calculate the average rate of this reaction in this time interval.
(b) Predict the rate of change in the concentration of H+ (that is, [H+]/t) during this time interval.
Example 13.1. page 567
Consider the general reaction aA + bB cC and thefollowing average rate data over some time period Δt:
1Δ[A]0.0080 M s
Δt 1Δ[B]
0.0120 M sΔt
1Δ[C]0.0160 M s
Δt
Determine a set of possible coefficients to balance thisgeneral reaction.
0 mileBarnesville
16 miles Griffin
56 miles Atlanta
2:00 pm 2:16 pm 3:16 pm
Average Speed from B to G = 16 miles ÷ 16 min = 1.0 mile/min
Average Speed from G to A = 40 miles ÷ 60 min = 0.7 mile/min
Δl
Δt
0limt
l d l
t d t
Instantaneous speed at green spot
Instantaneous speed contains more information
l
t
Δl
Δt
t
l
Instantaneous speed at the red point = slope of the red solid line =
Barnesville0 mile 0 min
Atlanta56 miles
Griffin20 miles
16 min 76 min
Factors that affect reaction rates
State of the reactants
Concentrations of the reactants
Temperature
Catalyst
a A + b B c C + d D
r = k [A]m [B]n
Differential rate law: how r depends on concentrations
m, n: reaction order, mth order for A, nth order for B(m+n): overall reaction order
m and n must be measured from experiments. They canbe different from the stoichiometry.
k: rate constant: depends on temperature, but not concentrations
1 Δ[A] 1 d[A]
a Δt a dt
(1) 2N2O5(g) 4NO2(g) + O2(g) r = k[N2O5]
(2) CHCl3(g) + Cl2(g) CCl4(g) + HCl(g) r = k[CHCl3][Cl2]1/2
(3) H2(g) + I2(g) 2HI(g) r = k[H2][I2]
(1) 2N2O5(g) 4NO2(g) + O2(g) r = k[N2O5]
(2) CHCl3(g) + Cl2(g) CCl4(g) + HCl(g) r = k[CHCl3][Cl2]1/2
(3) H2(g) + I2(g) 2HI(g) r = k[H2][I2]
Experiment Number
Initial [NH4+] (M) Initial [NO2
−] (M) Initial Rate (M·s−1)
1 0.100 0.0050 1.35 x 10−7
2 0.100 0.010 2.70 x 10−7
3 0.200 0.010 5.40 x 10−7
r = k [NH4+]m [NO2
−]n
NH4+ (aq) + NO2
− (aq) N2(g) + 2H2O(l)
How to find the rate law by experiment: method of initial rates
A very common method to investigate how each factoraffects the whole system:
Change one thing at a time while keep the others constant.
z = f (x,y)
x
z
x
z
y
How does the change of x affect z?
y
z
y
z
x
How does the change of y affect z?
Experiment Number
Initial [NH4+] (M) Initial [NO2
−] (M) Initial Rate (M·s−1)
1 0.100 0.0050 1.35 x 10−7
2 0.100 0.010 2.70 x 10−7
3 0.200 0.010 5.40 x 10−7
r = k [NH4+]m [NO2
−]n
NH4+ (aq) + NO2
− (aq) N2(g) + 2H2O(l)
How to find the rate law by experiment: method of initial rates
(a) Determine the differential rate law
(b) Calculate the rate constant
(c) Calculate the rate when [NO] = 0.050 M and [H2] = 0.150 M
2NO(g) + 2H2(g) N2(g) + 2H2O(g)
Experiment Number
Initial [NO] (M) Initial [H2] (M) Initial Rate (M·s−1)
1 0.10 0.10 1.23 x 10-3
2 0.10 0.20 2.46 x 10-3
3 0.20 0.10 4.92 x 10-3
(a) Determine the differential rate law
(b) Calculate the rate constant
(c) Calculate the rate when [NO] = 0.050 M and [H2] = 0.150 M
2NO(g) + 2H2(g) N2(g) + 2H2O(g)
Experiment Number
Initial [NO] (M) Initial [H2] (M) Initial Rate (M·s−1)
1 0.10 0.10 1.23 x 10-3
2 0.10 0.30 3.69 x 10-3
3 0.30 0.10 1.11 x 10-2
again
Experiment Number
Initial [A] (M) Initial [B] (M) Initial Rate (M·s−1)
1 0.100 0.100 4.0 x 10−5
2 0.100 0.200 4.0 x 10−5
3 0.200 0.100 1.6 x 10−4
A + B C
(a) Determine the differential rate law
(b) Calculate the rate constant
(c) Calculate the rate when [A] = 0.050 M and [B] = 0.100 M
From the data, determine:
(a) the rate law for the reaction
(b) the rate constant (k) for the reaction
EXAMPLE 13.2 Determining the Order and Rate Constant of a Reaction
NO2(g) + CO(g) NO(g) + CO2(g)
Use the data in table to determine
1) The orders for all three reactants 2) The overall reaction order3) The value of the rate constant
r = k [BrO3−]m [Br−]n [H+]p
r1 = k (0.10 M)m (0.10 M)n (0.10 M)p = 8.0 x 10−4 M · s−1
r2 = k (0.20 M)m (0.10 M)n (0.10 M)p = 1.6 x 10−3 M · s−1
r3 = k (0.20 M)m (0.20 M)n (0.10 M)p = 3.2 x 10−3 M · s−1
r4 = k (0.10 M)m (0.10 M)n (0.20 M)p = 3.2 x 10−3 M · s−1
one quiz after lab
Relationship among reaction rates as expressedby different species.
d
r(D)
c
r(C)
b
r(B)
a
r(A) r =
overall reaction order (m+n) unit of k ⇌
Method of initial rates:
table of experimental data rate order, k, rate at otherconcentrations.
a A + b B c C + d D
r = k [A]m [B]n
Differential rate law: how r depends on concentrations
Differential rate law: differential equation
[ ] [ ][ ] [ ]m nA d A
r k A Ba t a dt
How concentration changes as a function of time integrated rate law
A Products
Δ[A] d[A]r = r(A) k[A]
Δt dt
First order reaction differential rate law:
First order reaction integrated rate law:
0ln[A]ktln[A] kt[A]
[A]ln 0 or
integrated rate law: how concentration changes as a function of time.
0ln[A] kt ln[A]
Plot ln[A] vs. t gives a straight line
Slope = −k, intercept = ln[A]0
First order reaction integrated rate law:
y = mx + b
[A] is the molarity of A at t
[N2O5] (M) Time (s)
0.1000 0
0.0707 50
0.0500 100
0.0250 200
0.0125 300
0.00625 400
N2O5(g) 2NO2(g) + ½ O2(g)
Use these data, verify that the rate law is first order in N2O5,and calculate the rate constant.
k = 6.93 x 10−3 s−1
Using the data given in the previous example, calculate [N2O5]
at 150 s after the start of the reaction.
[N2O5] (M) Time (s)
0.1000 0
0.0707 50
0.0500 100
0.0250 200
0.0125 300
0.00625 400
0.0354 M
The half-life of a reaction, t1/2, is the time required for a
reactant to reach one-half of its initial concentration.
[N2O5] (M) Time (s)
0.1000 0
0.0707 50
0.0500 100
0.0250 200
0.0125 300
0.00625 400
The half-life for first order reaction:
kt
2ln2/1
The half-life for first order reaction does NOT depend onconcentration.
A certain first order reaction has a half-life of 20.0 s.
a)Calculate the rate constant for this reaction.
b)How much time is required for this reaction to be 75 %
complete?
kt
2ln2/1 kt
[A]
[A]ln 0
a) k = 0.0347 s−1 b) k = 40.0 s
A Products
2k[A]dt
d[A]
Δt
Δ[A]r(A)
Second order reaction differential rate law:
Second order reaction integrated rate law:
0[A]
1kt
[A]
1
integrated rate law: how concentration changes as a function of time.
Plot 1/[A] vs. t gives a straight line
Slope = k, intercept = 1/[A]0
Second order reaction integrated rate law:
0[A]
1kt
[A]
1
y = mx + b
The half-life for second order reaction:
02/1 ]A[
1
kt
The half-life for second order reaction depends on initial concentration.
A certain reaction has the following general form: A BAt a particular temperature [A]0 = 2.80 x 10−3 M, concentration versus time data were collected for this reaction,and a plot of 1/[A] versus time resulted in a straight line with aslope value of 3.60 x 10−2 M−1·s−1
a)Determine the (differential) rate law, the integrated rate law, and the value of the rate constant.
b) Calculate the half-life for this reaction.
c) How much time is required for the concentration of A to decrease to 7.00 x 10−4 M ?
0[A]
1kt
[A]
1
02/1 ]A[
1
kt
For first order reaction, show that
from the integrated rate law
kt
2ln2/1
0ln[A] kt ln[A]
(show your work, do not copy the question)
A Products
kk[A]dt
d[A]
Δt
Δ[A]r(A) 0
Zero order reaction differential rate law:
Zero order reaction integrated rate law:
0[A]kt[A]
integrated rate law: how concentration changes as a function of time.
Plot [A] vs. t gives a straight line
Slope = −k, intercept = [A]0
Zero order reaction integrated rate law:
0[A]kt[A]
y = mx + b
The half-life for zero order reaction:
kt
2
]A[ 02/1
The half-life for zero order reaction depends on initial concentration.
The decomposition of ethanol on alumina surface C2H5OH(g) C2H4(g) + H2O(g) was studied at 600 K.Concentration versus time data were collected for this reaction, and a plot of [C2H5OH] versus time resulted in a straight line with a slope value of −4.00 x 10−5 M·s−1
a)Determine the (differential) rate law, the integrated rate law, and the value of the rate constant.
b) If the initial concentration of C2H5OH was 1.25 x 10−2 M, calculate the half-life of this reaction.
c) How much time is required for all the 1.25 x 10−2 M C2H5OH to decompose ? 0[A]kt[A]
kt
2
]A[ 02/1
Factors that affect reaction rates
State of the reactants
Concentrations of the reactants
Temperature
Catalyst
A Plot Showing the Exponential Dependence of the Rate Constant on Absolute Temperature
Collision model: molecules must collide to react.
T ↑ v ↑ kinetic energy = ½ mv2 ↑
Not all collisions lead to products
Prentice Hall © 2003 Chapter 14
RTEaef /Fraction of molecules whose Ek > Ea is
T ↑ f ↑ Ea ↑ f ↓
activation energy
212
1 11ln
TTR
E
k
k a
Arrhenius equation
RTEaAek /
RTEapzek / steric factor p ≤ 1
A: frequency factor How k depends on T
T ↑ k ↑ Ea ↑ k ↓
At 550 °C the rate constant for
CH4(g) + 2S2(g) CS2(g) + 2H2S(g)
is 1.1 M·s−1, and at 625 °C the rate constant is
6.4 M·s−1. Using these value, calculate Ea for this reaction.
212
1 11ln
TTR
E
k
k a
Ea = 1.4 x 105 J/mol
The ball can climb over the hill only if its kinetic energy is greaterthan Ep = mgh, where m is the mass of the ball, h is the heightof the hill, and g is gravitational acceleration.
h
(a) The Change in Potential as a Function of Reaction Progress (b) A Molecular Representation of the Reaction
BrNO + BrNO 2NO +Br2
O N Br
exothermic reaction
NO2 + CO NO + CO2
Step 1: NO2 + NO2 NO3 + NO Step 2: NO3 + CO NO2 + CO2 +
NO2 + CO NO + CO2
NO3: intermediate, does notappear in overall reaction
Whole process is called the reaction mechanism.
Each single step is called an elementary reaction/step.An elementary reaction is a single collision.
NO2 NO2 NO3 NO
NO3 CO NO2 CO2
For an elementary reaction
aA + bB cC + dD
r = k[A]a[B]b
Not for overall reaction!
The number of molecules that react in an elementary reaction is called the molecularity of that that elementary reaction (not applicable to overall reaction).
Overall reaction: r = k[A]m[B]n , find m and n by experiments
Ep
Reaction progress
Reactants
Products
∆E
intermediate
Which step is the rate determining step?
exothermic orendothermic?
Ea, 2
Ea, 1
2nd
Factors that affect reaction rates
State of the reactants
Concentrations of the reactants
Temperature
Catalyst
Catalyst is a substance that speeds up a reaction without
being consumed itself.
Catalyst changes the reaction mechanism through a lower
activation energy pathway.
Homogeneous catalyst: same phase as reactants.
3O2(g) 2O3(g)
2NO(g) + O2(g) 2NO2(g)
2NO2(g) 2NO(g) + 2O(g)
2O2(g) + 2O(g) 2O3(g)
light
+
3O2(g) 2O3(g)
NO(g): catalyst; NO2(g), O(g): intermediates
The Decomposition Reaction 2N2O(g) 2N2 (g) + O2 (g) takes place on a Platinum Surface
Heterogeneous catalyst: different phase from reactants.