Chapter five rates of chemical reaction
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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

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Chapter Five Rates of Chemical Reaction

Weather can occur ?

---chemical thermodynamics

How fast (reaction rate)?

---chemical kinetics



1. 2/





Chapter FiveRates of Chemical Reaction

5-1 Rates and Mechanisms of Chemical


5-2 Theories of Reaction Rate

5-3 Reaction Rates and Concentrations

5-4 Effect of Temperature on Reaction


5-5 Effect of Catalyst on Reaction Rates

5-1 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 molL-1S-1,


or molL-1h-1 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) = 15.8810-3 mol/L

5 : c2(H2O2) = 12.810-3 mol/L


Reaction Rates and Stoichiometry

H2O2 = H2O + 1/2 O2

aA + bB

cC + dD

  • To generalize, for the reaction

This equation can be used to establish the relationship between rate of change of one reactant or product to another reactant or product.

  • You have to be able to do this on the test, too!

- c


V = lim = -




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.






5-1.2 The Mechanisms of Chemical Reactions

  • A reaction mechanism is a description of the path that a reaction takes.

  • elementary reaction

  • overall reaction

  • types of elementary reactions

5-1.2 The Mechanisms of Chemical Reactions

elementary reaction: is one that the reactants can convert directly into the products in a single step when they act each other. (one-step reaction)

overall reaction:Many reactions are actually made up ofseveral elementary steps,which are combined to yield the overall 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 rate-determining step.

H2(g) + I2(g) 2 HI(g)

I2(g) 2I (fast)

H2+ 2I 2HI (slow)

rate-determining step.

Types of Elementary Reactions

  • molecularity --for Elementary Reactions:

  • unimolecular reaction: an elementary reaction in which the rearrangement of a single molecule produces one or more molecules of product. I2(g) 2I(g)

  • bimolecular reaction: the collision and combination

    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

5-2 Theories of Reaction Rate

  • One is the collision theory :

    The collision theory is based on the kinetic theory and assumes a collision between reactants before a reaction can take place.

    1918 Lewis

  • Another is the transition state theory:

    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.

5-2.1 Collision Theory and Activation Energy

Contents of Collision Theory:

reacting molecules must come so close that they


"effective" collisions : not every collision

between molecules creates products,

only few collisions between reactant

molecules will react.

Contents of Collision Theory:

  • According to this theory,

    product formation can only take place when there are "effective" collisions between reactant molecules involved in the rate determining step of the process.

Br(g) + HI(g) HBr(g) + I(g)

  • Straight on collision, hydrogen facing incoming bromine. Reaction occurs.

  • Straight on collision, hydrogen facing away from incoming bromine. Reaction does not occur.

  • Straight on collision, bromine at 90 degrees. Reaction does not occur.

What constitutes an effective collision?


enough energy

proper orientation


Activation molecule:

is the molecule have enough energy and can produce effective collision

  • the average molecules must absorb some energyto become activation molecules

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


2SO2(g) + O2(g) = 2SO3(g), Ea=251 kJmol-1

N2(g) + 3H2(g) = 2NH3(g), Ea=175.5 kJmol-1

HCl + NaOH NaCl+H2O, Ea20 kJmol-1


Ea63 kJmol-1

40 kJmol-1400 kJmol-1


5-2.2 The Transition State Theory

Transition state theory (TST) is also called

activated complex theory.

reactants pass through high-energy 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 kJmol-1 -132 kJmol-1

H = 226kJmol-1.

  • E + S = E-S P + E

  • ES

Factors That Affect Reaction Rates

  • Concentration of Reactants

  • Temperature

  • Catalysts ___Speed by changing mechanism

5-3 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.

Concentration and Rate

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.

5-3.1 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 = k[A]m[B]n


v = k[A]m[B]n

  • kis a rate constant that has a specific value

  • for each reaction.Thevalue of k is

  • determined experimentally.

  • Constant is relative here-

  • k changes with T

  • the unit() depend on m + n

  • when [A]=[B]=1molL-1, v =k

  • the greater the k , the faster the rate

law of mass action

2N2O5g4NO2g O2 (g)




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

5-3.2 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 5-1:

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.L-1) [OH-] (mol.L-1) Rate (mol.L-1 s-1)

0.010 0.030 6.0010-4 v1

0.010 0.075 1.5010-3 v2

0.055 0.030 1.8210-2 v3


v = k[ClO2]m[OH-]n


By inspection, m = 2. The reaction is 2nd order in ClO2

v = k[ClO2]m[OH-]n


By inspection, n = 1

  • The overall rate expression is therefore

  • v = k[ClO2]2[OH-]

First-order reactions

A first-order reactionis a reaction whose rate depends on the reactant concentration raised to the first power.


the rate equation is

Differential form:


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.


The characteristics of first-order reactions

  • A plot of lgcversus t(time) gives a straight line with a slope of -k1/2.303.

    2. The rate constant, k, has units of [time]-1.

3. half-life (t1/2)

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




  • t1/2h





11gct k1/2.303k1




Example 5-2(a) What is the rate constant k for the first-orderdecomposition of N2O5(g) at 25 if the half-life 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


Therefore, 22.6% of the N2O5 molecules will not have reacted after one day at 25.

Example 5-3SO2Cl2 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 half-life of SO2Cl2 decomposition?


K = 0.0554 h-1

  • [5-2]0.5g

t/h 4 6 8 10 12 14 16

c/mgL-1 4.6 3.9 3.2 2.8 2.5 2.0 1.6

3. 7mgL-1

k1log ct


5-6t0lgc00.81c3.7mgL-1 lgc0.57, 5-8



6h 4/




2040h 48120h

Second - order reactions

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

The characteristics of second- order reactions

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 half-life of 2th-order reactions

t1/2=1 / kc0.

(c = 2/c0)

Note that the half-life of a second-order reaction is notindependent of the initial concentration, as in the case of a first-order reaction. This is one way to distinguish a first-order reaction from a second-order reaction.






Example 5-4Butadiene(C4H6) dimerizes() to form C8H12. This reaction is 2nd order in butadiene. If the rate constant for the reaction is 0.84 Lmol-1min-1, 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?



t = 3.6 (min)


0.0100molL20min 0.00566molL

Zero - order reactions

is one where the rate does not depend on the concentration of the species.

v = k0 [A]0


c = - k0 t + c0

The characteristics of zero-order reactions

c = - k0 t + c0

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 half-life of a zero-order reaction is






Example 5-5

The decomposition of HI into hydrogen and iodine on a gold surface is 0th order in HI. The rate constant for the reaction is 0.050molL-1s-1. If you begin with a 0.500mol/L concentration of HI, what is the concentration of HI after 5 seconds?


c0= 0.500molL-1k =0.050molL-1 s-1

t =5s

[HI] = 0.5000.0505

= 0.250(molL-1)

5-4 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


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 dependence of reaction rate on temperature has led to a common 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.

5-4.1 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

5-4.2 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

  • kT:

The Arrhenius Equation:

Ea is the activation energy of the reaction (in kJ/mol)

R is the gas constant (8.314 JK-1mol-1)

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 ().



1Ea k




Taking the natural logarithm of both sides, the equation becomes

or in terms of common logarithms :

Example 5-6

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) 1.4310-3 1.3710-3 1.3210-3 1.2710-3 1.2310-3

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


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

5-4.3 Application of Arrhenius Equation

According to this equation, we can calculate E aand k

T1 k1

T2 k2

(5-14) - (5-13)

Example 5-7

The rate constant of a first-order reaction is 3.4610-2 /s at 298 K. What is the rate constant at 350 K if the activation energy for the reaction is 50.2 KJ/mol?


5-5 Effect of Catalyst on Reaction Rates

  • Catalyst: a substance that increase the rate of a chemical reaction , but is itself

    neither consumed nor produced in the reaction


  • Catalysts increase the rate of a reaction by

  • decreasing the activation energy of the reaction.

  • Catalysts change the mechanism by which the

  • process occurs.

Reaction O3 + O = O2

Catalysis can be classified into

homogeneous() catalysis,

heterogeneous () catalysis

enzyme catalysis.

three types

Homogeneous catalysis

  • In homogeneous catalysis, the catalyst is present in the same phase as the reactants,

  • as when a gas-phase catalyst speeds up a gas-phase reaction, or a species dissolved in solution speeds up a reaction in solution

The rate is very Slow,

but it can be catalyzed by Ag+ or Mn2+:

Heterogeneous catalysis

  • In heterogeneous catalysis, the catalyst is present as a distinct phase. The most important case is the catalytic action of certain solid surfaces on gas-phase and solution-phase reactions.


e.g., H2 + CH2=CH2

no reaction (k very small)



CH3CH3 rapid (k larger)

Ea (uncatalyzed)

Ea (catalyzed)








Enzyme Catalysis

  • Enzymes are biological catalysts.

    An average living cell may contain some 3000 different enzymes

E + S = E-S P + E

activated complex






P+ E



  • (1) (lock and key hypothesis)

  • .

(2) inducedfit hypothesis):



Tyr 248

Arg 145

Glu 270

1. (proximity effect)

(orientation arrange )

2. (multielement catalysis)

  • -,


Asp102 His57

His57 Ser195





a:His-57 C-N

, R1NH21






His57 H2O



, X


3. (surface effect)



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