Chapter Five Rates of Chemical Reaction. Weather can occur ? chemical thermodynamics How fast (reaction rate)? chemical kinetics. Chemical Reaction. 化学反应 速度的快慢 —— 主要决定于反应的 内在机理 。. 反应机理： 化学反应所经历的 途径 或 具体步骤 ， 又 称为 反应历程 。.
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Chapter Five Rates of Chemical Reaction
Weather can occur ?
chemical thermodynamics
How fast (reaction rate)?
chemical kinetics
Chemical
Reaction
1. 2/
3/?
2.
)
51 Rates and Mechanisms of Chemical
Reactions
52 Theories of Reaction Rate
53 Reaction Rates and Concentrations
54 Effect of Temperature on Reaction
Rates
55 Effect of Catalyst on Reaction Rates
51 Rates and Mechanisms of Chemical Reactions
Reaction rate: changes in a concentration of a
product or areactant per unit time.
The rate is defined to be a positive number.
The unit of reaction rate is molL1S1,
molL1min1
or molL1h1 et al
Define reaction rate :
1. Average reaction rate
2N2O5 = 4NO2 + O2
average reaction rate is obtained by dividing the change in concentration of a reactant or product by the time interval over which the change occurs
0 : c1(H2O2) = 15.88103 mol/L
5 : c2(H2O2) = 12.8103 mol/L
So:
H2O2 = H2O + 1/2 O2
aA + bB
cC + dD
This equation can be used to establish the relationship between rate of change of one reactant or product to another reactant or product.
 c
dc
V = lim = 
t
dt
t0
Define reaction rate :
2. Instantaneous reaction rate
2N2O5 = 4NO2 + O2
The instantaneous rate of change at a point is the same as the slope of the tangent line. That is, it's the slope of a curve.
c
c
t
v
t
elementary reaction: is one that the reactants can convert directly into the products in a single step when they act each other. (onestep reaction)
NO2 + CO NO + CO2
NO2 + NO2 NO3 + NO (slow)NO3 + CO NO2 + CO2 (fast)
This means that the rate of the overall reaction is dominatedby the rate of the first reaction, this is the ratedetermining step.
H2(g) + I2(g) 2 HI(g)
I2(g) 2I (fast)
H2+ 2I 2HI (slow)
ratedetermining step.
of two reactants to give an activated complex in an elementary reaction. NO(g) + O3(g) NO2(g) + O2(g)
_termolecular reaction: an elementary reaction involving the simultaneous collision of any combination of three molecules, ions, or atoms.
2 NO + H2 N2 + H2O2
The collision theory is based on the kinetic theory and assumes a collision between reactants before a reaction can take place.
1918 Lewis
The transition state theory suggests that as reactant molecules approach each other closely they are momentarily in a less stable state than either the reactants or the products.
52.1 Collision Theory and Activation Energy
Contents of Collision Theory:
reacting molecules must come so close that they
collide.
"effective" collisions : not every collision
between molecules creates products,
only few collisions between reactant
molecules will react.
product formation can only take place when there are "effective" collisions between reactant molecules involved in the rate determining step of the process.
What constitutes an effective collision?
:
enough energy
proper orientation
HCl NH3
is the molecule have enough energy and can produce effective collision
Ec Ea
Figure:As the activation energy of a reaction decreases, the number of molecules with at least this much energy increases, as shown by the yellow shaded areas.
,
, Ea
Ea
2SO2(g) + O2(g) = 2SO3(g), Ea=251 kJmol1
N2(g) + 3H2(g) = 2NH3(g), Ea=175.5 kJmol1
HCl + NaOH NaCl+H2O, Ea20 kJmol1
Ea
Ea63 kJmol1
40 kJmol1400 kJmol1
(rH)
52.2 The Transition State Theory
Transition state theory (TST) is also called
activated complex theory.
reactants pass through highenergy transition
states before forming products, they are associated in an unstable entity called an activated complex,
then change into products.
Example :NO2(g) + CO(g) NO(g) + CO2(g)
H = Ea,f  Ea,r
=358 kJmol1 132 kJmol1
H = 226kJmol1.
53 Reaction Rates and Concentrations
Chemical reactions are faster when the concentrations of the reactants are increased .
Because more molecules will exist in a given volume. More collisions will occur and the rate ofa reaction will increase.
Each reaction has its own equation that gives its rate as a function of reactant concentrations.
this is called its Rate Law
A rate law shows the relationship between the reaction rate and the concentrations of reactants.
53.1 The Rate Law
The rate of a reaction is proportional to the product of the concentrations of the reactants raised to somepower.
aA + bB cC + dD
v[A]m[B]n
v = k[A]m[B]n
P101
v = k[A]m[B]n
2N2O5g4NO2g O2 (g)
N2O5 NO3NO2
NO2NO3 NO2O2NO
NONO3 2NO2
v = k[A]m[B]n
aA + bB cC + dD
[A], [B] are the concentration of A and B;
mand nare themselves constants for a given reaction, it must be determined experimentally
in general, m and n are not equal to the
stoichiometric coefficientsa and b
53.2 Order of A Reaction
The order of a reaction with respect toone of the reactantsis equal to the power to which the concentration of that reactant is raised in the rate equation.
The sum of the powers to which all reactant concentrations appearing in the rate law are raised is called theoverall reaction order.
For rate equationv = k[A]m[B]n
mis the order of the reaction with respect to A,nis the order of the reaction with respect to B.
m+n isoverall order of the reaction
the exponents m and n are not necessarily related to the stoichiometric coefficients in the balanced equation, that is, in general it is not true that for a A + b B c C + d D, m a and n b
The rate law for the thermal decompositionof acetaldehyde (CH3CHO) CH3CHO(g) CH4(g) + CO(g)has been determined experimentally to bev =k[CH3CHO]3/2and not rate = k[CH3CHO]
Example 51:
Given the following data, what is the rate expression for the reaction between hydroxide ion and chlorine dioxide?
2ClO2(aq) + 2OH(aq) ClO3(aq) + ClO2(aq) + H2O
[ClO2] (mol.L1) [OH] (mol.L1) Rate (mol.L1 s1)
0.010 0.030 6.00104 v1
0.010 0.075 1.50103 v2
0.055 0.030 1.82102 v3
Solution:
v = k[ClO2]m[OH]n
m=?
By inspection, m = 2. The reaction is 2nd order in ClO2
v = k[ClO2]m[OH]n
n=?
By inspection, n = 1
Firstorder reactions
A firstorder reactionis a reaction whose rate depends on the reactant concentration raised to the first power.
A B
the rate equation is
Differential form:
Thus
Integrate the left side from c = c0 to c and the right from t = 0 to t.
Can be rearranged to give:
 { lnc lnc0} = k1( t  0 )
c0 is the initial concentration of c (t =0).
c is the concentration of c at some time t.
or
The characteristics of firstorder reactions
2. The rate constant, k, has units of [time]1.
is the time it takes for the concentration of a reactant A to fall to one half of its original value.
By definition, when t = t1/2, , so
k1
k1
t1/2
t1/2h
0.5
23
2040
14C5580
11gct k1/2.303k1
2k1[]1
k1
3k1
Example 52(a) What is the rate constant k for the firstorderdecomposition of N2O5(g) at 25 if the halflife of N2O5(g) at that temperature is 4.03104 seconds?
Solution: (a)

(b) Under these conditions, what percent of the N2O5 molecules will not have reacted after one day?
Solution: (b)
Putting in the value for k and substitutingt = 8.64104 seconds (one day has 86,400 seconds) gives
Hence
Therefore, 22.6% of the N2O5 molecules will not have reacted after one day at 25.
Example 53SO2Cl2 decomposes to sulfur dioxide and chlorine gas. The reaction is first order. If it takes 13.7 hours for a 0.250mol/L solution of SO2Cl2 to decompose into a 0.117mol/L solution, what is the rate constant for the reaction and what is the halflife of SO2Cl2 decomposition?
Solution:
t/h 4 6 8 10 12 14 16
c/mgL1 4.6 3.9 3.2 2.8 2.5 2.0 1.6
3. 7mgL1
k1log ct
56:
56t0lgc00.81c3.7mgL1 lgc0.57, 58
3.7mgL1
6.3h
6h 4/
10t0.9t0.9
12
12
2040h 48120h
v = k2[A]2 , v = k2 [A][B] [A]=[B]
The integrated rate law for a 2nd order reaction can be easily shown to be
1. A graph of 1/c against time is a straight line ,
the slope of which gives the rate constant for the reaction
2. The rate constant, k, has units of[c]1[t]1
3. The halflife of 2thorder reactions
t1/2=1 / kc0.
(c = 2/c0)
Note that the halflife of a secondorder reaction is notindependent of the initial concentration, as in the case of a firstorder reaction. This is one way to distinguish a firstorder reaction from a secondorder reaction.
11/ct
k2
2k2[]1[]1
k2
3
Example 54Butadiene(C4H6) dimerizes() to form C8H12. This reaction is 2nd order in butadiene. If the rate constant for the reaction is 0.84 Lmol1min1, how long will it take for a 0.500 mol/L sample of butadiene to dimerize until the butadiene concentration is 0.200 mol /L?
Solution:
511
t = 3.6 (min)
5325 CHCOOCHNaOHCHCOONaCHOH
0.0100molL20min 0.00566molL
is one where the rate does not depend on the concentration of the species.
v = k0 [A]0
integrated
c =  k0 t + c0
The characteristics of zeroorder reactions
1. A graph of c against tis a straight line with a slope of k0.
2. The rate constant, k, has units of [c][ t ]1
3. The halflife of a zeroorder reaction is
1ctk0
2k0
k0
3
1830g5
Example 55
The decomposition of HI into hydrogen and iodine on a gold surface is 0th order in HI. The rate constant for the reaction is 0.050molL1s1. If you begin with a 0.500mol/L concentration of HI, what is the concentration of HI after 5 seconds?
Solution:
c0= 0.500molL1k =0.050molL1 s1
t =5s
[HI] = 0.5000.0505
= 0.250(molL1)
54 Effect of Temperature on Reaction Rates
Chemical reactions are faster when the
temperature is increased. Why?
Figure: At a higher temperature,T2, more molecules have an energy greater than E a , as shown by the yellow shaded area.
When we increase the temperature, kinetic
energies and speeds will increase and so
the average energy of a collision will also
increase.
As a result, the energy of any particular
collision will be more likely to exceed the
activation energy.
Thus, chemical reactions are faster at higher
temperatures than at lower temperatures.
Rule of thumb
the rate of a chemical reaction will double for each 10 increase in the temperature.
The rate of a chemical reaction will double for
each 10 increase in the temperature.
54.1 Rule of Thumb(Vant Hoff Law)
T : vT = k T[A]a [B]b
(T + 10) : v(T+10) = k T+10[A]a [B]b
a A + b B = c C + d D
v(T+10) k (T+10)
=  =  = 24
v T k T
54.2 The Arrhenius Equation
In 1889 Svante Arrhenius showed that the dependence of the constant of a reaction on temperature can be expressed by the following equation, now known as the Arrhenius equation
The Arrhenius Equation:
Ea is the activation energy of the reaction (in kJ/mol)
R is the gas constant (8.314 JK1mol1)
T is the absolute temperature
e is the base of the natural logarithm scale
A represents the collision frequency, and is called
the frequency factor ().
AEa
kEaT
1Ea k
2Ea
k
Ea
Taking the natural logarithm of both sides, the equation becomes
or in terms of common logarithms :
The rate constants for the decomposition of acetaldehyde
CH3CHO(g) CH4(g) + CO(g)
were measured at five different temperatures. The data are show below. Plot lgk versus 1/Tand determine the activation energy (in KJ/mol) for the reaction.
T(K) 700 730 760 790 810
k [1/(mol/L)1/2s] 0.011 0.035 0.105 0.343 0.789
Answer:We need to plot lg k versus 1/T . From the given data we obtain
1/T(1/K) 1.43103 1.37103 1.32103 1.27103 1.23103
log k 1.96 1.46 0.979 0.465 0.103
The slope of the line is calculated from two pairs of coordinates:
lg k
1/T
Thus, a plot of lg k versus 1/T gives a straight line
whose slope is equal to E a / 2.303R and whose
interceptwith the ordinate() is log A.
Ea = 2.303(8.314J/Kmol) (9.38103K)
= 1.80105J/mol
= 1.80102KJ/mol
According to this equation, we can calculate E aand k
T1 k1
T2 k2
(514)  (513)
The rate constant of a firstorder reaction is 3.46102 /s at 298 K. What is the rate constant at 350 K if the activation energy for the reaction is 50.2 KJ/mol?
Answer:
neither consumed nor produced in the reaction
MnO2
Catalysis can be classified into
homogeneous() catalysis,
heterogeneous () catalysis
enzyme catalysis.
three types
The rate is very Slow,
but it can be catalyzed by Ag+ or Mn2+:
25C
e.g., H2 + CH2=CH2
no reaction (k very small)
25C
Pd
CH3CH3 rapid (k larger)
Ea (uncatalyzed)
Ea (catalyzed)
PE
C2H4
+
H2
C2H6
RC
catalysis
An average living cell may contain some 3000 different enzymes
E + S = ES P + E
activated complex
E1
ES
E2
E+S
G
P+ E
ESESP
ES
(2) inducedfit hypothesis):
Zn
Zn
Tyr 248
Arg 145
Glu 270
1. (proximity effect)
(orientation arrange )
2. (multielement catalysis)
,
Asp102 His57
His57 Ser195
Ser195
(2)
Ser195,
His57
a:His57 CN
, R1NH21
b:
1
a
b
His57
His57 H2O
Ser195

, X
2
+
