cbse.12.che.student material.chemical kinetics-1.0

8/7/2019 CBSE.12.Che.student Material.chemical Kinetics-1.0

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Chemical Kinetics

Chemical Kinetics It is the branch of

chemistry which deals with the rates of

chemical reactions and the mechanism by

which they occur.

Rate of a chemical reaction It can be

defined as the speed with which the reactants

are converted into products.

It may be expressed either as the rate of

decrease in concentration of reactants or the

rate of increase in concentration of products.

For a reaction

A B

Rate of reaction=[ ]

=

t

A [ ]t

B

Where , concentrations of A and

B respectively

[ ]A [ ]B

t Change in time

Average and Instantaneous rate of a

reaction:-

Average Rate of Reaction

The average rate of a reaction is defined as therate of change of concentration of a reactant ora product over a specified measurable periodof time. This can be calculated by dividing theconcentration difference by the given timeinterval. Considering the above

reaction , if [A] 2 is theconcentration of reactant A at time t2 while [A]1 is the concentration reactant A at a time t1then average rate (r) is

The square brackets are used to express molarconcentration.

Equation 1 can be written as,

[] signifies the change in concentration of A,while 't' is the time interval.Similar to the above, with [B]2 as theconcentration of product B at time t2 and [B]1as the concentration product B at a time t1,

then the average rate in terms of B is,

Equation 3 can be written as,

Equations (2) and equation (4) represent theaverage rate of a reaction. For the hypothetical

reaction , the rate of the reaction inthe terms of appearance and disappearance ofthe product and reactant is given as,

Instantaneous Rate of Reaction

Instantaneous rate of reaction is defined as therate of change of concentration of any one ofthe reactants or products at a given time. Tomeasure the instantaneous rate the timeinterval ' t' should be made as small aspossible so that there is the least possiblechange in rate over that interval. Such ratesmay be represented in terms of infinitesimallysmall change in concentration of reactant or

product (written as d[x]) in infinitesimallysmall interval of time, 'dt'. The rate of thereaction may be expressed as:

If the rate is expressed in terms ofconcentration of any one of the reactants,which keeps on decreasing, the negative signis used. On the other hand, if the rate of thereaction is expressed in terms of theconcentration of any one of the products whichgoes on increasing, it is a positive value.Mathematically, instantaneous rate (rinst) for

the reaction is given by,

Instantaneous rate is the value of for thetangent at a given time 't'. In terms of theconcentration versus time curves of the


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reactants and the products shown earlier, it isactually the slope of the tangent.rinst = -slope for the reactant = + slope for theproduct

Example: Dehalogenation of trimethyl bromide(CH3)3 CBr is given by the reaction.

The following data were obtained.

Time (hr)[(CH3)3 CBr] x

10-2 M

0 10.39

3.15 8.96

6.20 7.76

10.00 6.39

18.30 3.53

30.80 2.07

Calculate the instantaneous rate by plottingthe data as concentration versus time andtaking the slope of the tangent drawn to thecurve at some point of time 't'.Solution:The plot of concentration versus time is shownin figure below. The rate of the reaction at aparticular time is determined by drawing atangent to curve at a point corresponding tothat time. Then the slope of the tangent givesthe rate of the reaction at that time.

The instantaneous rates were calculated attimes 6.5 hours and 16.2 hours. The rates are,At time 6.5 hours = 0.39 M / hrAt time 16.2 hours = 0.23 M / hrFrom the above data it is observed that theinstantaneous rate appear to change with time.

Factors Affecting Rate of Reaction

1.Concentration of the reactants: In mostcases, the rate of a reaction is accelerated withincrease in concentration of a reactant. A pieceof wood burns faster in oxygen than in air.2.Temperature at w hich the reactionoccurs: A rise in temperature increases therate of a reaction. Cooking at sea level takesless time than on the mountain top becausewater boils at lower temperature at sea levelthan at the mountain top.3.Concentration of catalyst (inhomogenous reactions): A catalyst usuallyspeeds up the rate of reaction although it isnot consumed in the reaction. Oxidation ofsulphur dioxide (SO2) to sulphur trioxide (SO3)is a very slow reaction. However, this reactionaccelerates in the presence of nitric oxide(NO).4.Surface area: In a heterogeneous reactionan increase in surface area of a solid reactantor catalyst leads to an increase in the rate of areaction. A reaction between a solid phase and

a gas or between a solid and a liquid occurs onthe surface area of the solid. For example,when charcoal is crushed to powder it igniteseasily to produce a flame; solid charcoal hasbeen subdivided into many smaller particleswith larger surface area per volume andtherefore burns rapidly.Rate Law

The representation of rate of reaction in termsof concentration of the reactants is known asrate law. It is also called the rate equation orrate expression.

Rate Expression and Rate Constant

Let us consider a reaction of a simple type.

In this reaction, only a single substanceundergoes the reaction and, thus, the rate ofthe reaction will depend only on theconcentration of A. Mathematically, it may beexpressed as:

Rate = k [A]Where [A] represents the molar concentrationof A while k is a constant of proportionalityfor this reaction and is known as rate constant.The rate constant is also called velocityconstant or specific reaction rate.If the concentration of the reactants involvedin the reaction is unity i.e., [A] = 1,we get:Rate of reaction = k x 1 = kThus, the rate constant of a reaction at a giventemperature may be defined as the rate of the


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reaction when the molar concentration of eachof the reactants is unity.For another hypothetical reaction,

The rate of reaction can depend on theconcentrations of A and B in the followingmanners.

i)

ii)The expressions, k[A][B] and k'[A]2[B] are therate law expressions for the rate of thereaction and k is the rate coefficient or specificrate constant of the reaction. There can beother rate law expression for the samehypothetical reaction given above such as,Rate = k''[A][B]o

Rate = k'''[A]1/2[B]1

Rate Law

In general, for any hypothetical reaction,

The rate law expression can be written as,Rate (r) = k [A]a[B]b.It is an equation that relates the true rate ofreaction to the concentrations of the reactantsraised to some power.

Rate Constant

For the equation: a A + b B c C + d D,

Rate = k [A]a [B ]b

Rate constant is defined as the rate of the

reaction when the concentration of each

reactant is taken as unity.

Characteristics of Rate Constant

The value of rate constant

Gives an idea about speed of the reaction Is fixed for a reaction at a particular

temperature. Changes with temperature. Is independent of the concentration of the

reacting species Has units depending on the order of the

reaction

Order of a Reaction

The order of a reaction is the sum of thepowers to which the concentration terms areraised in a rate law expression. The order ofreaction is determined with respect to eachreactant in the reaction. For the reaction,

Where there are more than one reactants, theorder of the reaction is determined with A andthen with B.For a general reaction,

The reaction rate is described by theexpression, Rate= k [A]p [B]q [C]rWhere, k is the rate constant of the reaction.[A], [B] and [C] are the molar concentrationsof the reactants A, B and C.Then,Order of the reaction with respect to A = pOrder of the reaction with respect to B = qOrder of the reaction with respect to C = r

And,Overall order of the reaction = p + q + r.The total number of concentration variableswhich determine the rate of any reaction, iscalled the overall order of the reaction.

Characteristics of Order of Reaction The order of a reaction is generally a small

integer, half-integer or zero. It may haveany value such as, 1, 2, 3, 1/2, 3/2 or 0.

Order of reaction is obtained from theexperimentally obtained rate concentrationdata. So, order of reaction is anexperimental parameter.

Generally, reaction order cannot bededuced from the stoichiometry of thereaction.

Order of the reaction depends on the way areaction goes through to completion. Thiscould be either in one elementary step or aseries of complex steps. If the reactiontakes place in a single step then thestoichiometric coefficient(s) of thereactant(s) in the balanced chemicalequation gives the order of the reactionwith respect to the respective reactant.The overall order then is given by the sumof all the stoichiometric coefficients.

In complex reactions the reaction order isto be determined experimentally.

Zero Order ReactionsThe reaction whose rate does not depend uponthe concentration of the reactant is called azero order reaction. Thus, for a zero orderreaction


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Units of Rate Constant for Reactions ofDifferent Orders:

Reaction

OrderRate Law

0 Rate = -k [A]

= k

1 Rate = -k [A]

2 Rate= -k [A]2

3 Rate= -k [A]3

Rate Constant (k)Unit of Rate

Constant ( k)

mol L-1-s-1

mol L-1 min-1

= time-1

s-1

min-1

= concentration-1 time-1

Mol-1 L s-1

mol-1 L min-1

= concentration-2 time-1

mol-2 L2 s-1

mol-2 L2min-1

Molecularity of a ReactionElementary reactions are classified accordingto their molecularity. The number of reactingspecies, which are involved in simultaneouscollision to bring about a chemical reaction, iscalled the molecularity of the reaction.1. Unimolecular reaction-- decomposition ofNH4NO2 to N2 and 2H2O,The molecularity is 1

2. Bimolecular reaction ---

The molecularity is 2

Characteristics of Molecularity

The molecularity of any process can onlybe a small positive integer and cannot bezero, fractional or negative.

Molecularity of a reaction depends uponthe mechanism postulated for the reactionand is not an experimental parameter.

The molecularity of a reaction is not thesame as the order of reaction. However,for an isolated, single step reaction, themolecularity and the order of the reactionare equal to each other.

When a reaction proceeds through two or moreelementary reactions, each elementaryreaction has its own rate. Some elementaryreactions may be fast, while others may beslow, the rate of formation of a product cannotbe faster than the rate of the slowestelementary reaction.The slowest elementary reaction in anymechanism is called the rate-determiningreaction or rate determining step. The rate ofthe overall reaction, i.e., the rate of formation

of the final products, is governed by the rate ofthe slowest elementary reaction. For example,in a reaction,

The overall rate of reaction is governed by therate of the slowest step,

as its half-life is the longest (1s) in thissequence of reactions.The rate of formation of G and H will be

governed by the slowest step.

Comparison of Order and Molecularity of a

Reaction

Molecularity Order

Number of reacting

species undergoing

simultaneous

collision

Sum of the powers to

which the

concentration terms

are raised in a rate

law expressionTheoretical concept Experimentally

determined

Has integral values Can have fractional

values also

Cannot be zero Can be zero

Provides no Helps in judging the


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information on

reaction mechanism

slowest step, hence

gives further

information about

the mechanism

Example:Express the relationship between

the rate of production of iodine and the rate of

disappearance of hydrogen iodide in the

following reaction:

Solution:Rate of production of iodine = 1/2 x Rate ofdisappearance of HI

Example: The rate of formation of a dimer in asecond order dimerisation reaction is 9.1 x 10-6mol L-1 s-1 at 0.01 mol L-1 monomerconcentrations. Calculate the rate constant.Solution: Let the second order dimerisationreaction be, 2A A2Rate of formation of dimmer (r) = k[Reactant]2 = k[A]2r = 9.1x10-6 mol L-1 s-1= k (0.01 mol L-1) 2or,

Example:With the help of the following rateexpressions of the reactions, find out theoverall order of the reactions and the orderwith respect to the following reactant:(a) For reaction:

(b) For reaction:

(c) For reaction:

Solution: The order with respect to eachreactant and the overall order of the reaction

are tabulated below:Reaction Rate Order Overall

Order

(i) K

[NO]2[O2]

wrt

NO2=2,wrt

O2=1

3

(ii) K[N2O] wrt N2O=1 1

(iii) K[SO2Cl2] Wrt SO2Cl2

= 1

1

Integrated Rate equation

The rate of reaction in the differential form

cannot be used to determine rate law and

order of the reaction.

So the differential equations are integrated

over a meaningful range of limits to give the

integrated rate equation:

Zero Order ReactionsWhen a reaction has a rate which isindependent of the concentration of thereactant(s) it is called a zero-order reaction.

In the above reaction increasing theconcentration of the reacting species A will notspeed up the rate of the reaction.

d[A] = k dtIf this differential equation is integrated bothsides[A] = - kt + IWhere, I is the integration constant.At t= 0, the concentration of the reactant A =

[A]0, where [A]0 is initial concentration of thereactant. Substituting in above equation[A]0 = -k x 0 + I [A]0 = ISubstituting the value of I, gives an equationwhich is often called the integrated zero-orderrate law.[A] = - kt + [A]0Where [A] represents the concentration of thechemical of interest at a particular time and[A]0 represents the initial concentration. Zeroorder rate constant is given as,

The reaction is zero-order if it occurs in aclosed system when there is no net build-up ofintermediates and there are no other reactionsoccurring. For a zero order reaction theconcentration versus time profile is linear andthe rate of reaction versus time has the profileas shown in the graph. The slope of thisresulting line is the zero order rate constant - kand intercept [A]0.


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First Order ReactionsFor a first order reaction with rate constant

(k), at time (t) the initial concentration [A]0will change to the new concentration at time t[A]t.The rate of formation of X from the chemicalreaction:

Where the initial concentration of A is [A]o.And the initial concentration of X is 0. Theconcentration of X at time t is [X]t. Theconcentration of A at time t is [A]t.The rate of a reaction is:

The rate for a first order reaction is:Rate = k[A]tThese two may be combined as:

The concentration of A at time t may also bewritten in terms of X (the amount that hasreacted) since the area under a plot of [A] vstime is the amount that has reacted.

In terms of X the concentration of A at time tin the rate law equation is given as:

The above equation can also be written as

This equation rearranges it to

Integrating this function with very smallchanges in X and t, we have

(i)

Where C is constant of integration which can

be evaluated as follows;

Substituting this equation in equation (i)

This rearranges to giveln [A]o - ln ([A]o - [X]) = kt


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Since [A]o - [X] at time t is also [A]t, this maybe rewritten as follows:

This is the integrated first order rate equation,which rearranges in different ways for differentapplications:

When the concentration of the reactant are[A]1 and [A]2 at time t1 and t2 respectivelythen the above equation can be written as,

Taking antilog on both sides, the equation

arranges to,

In the log form the first order rate equation iswritten as,

A plot of ln [A]t against t gives a straight linewith slope = -kand intercept equal to ln [A]0.

If a graph is plotted between

Half Life of a Reaction

The half-time (or half-life period) of a reactionmay be defined as the time period duringwhich the concentration of a reactant getsreduced to one-half (50%) of its initial value or

the time required for the completion of 50% ofthe reaction. Half-life time is denoted by t1/2and its value depends upon the speed of thereaction. Fast reactions have short half-lifetime, while slow reactions have long half-lifetime.For a zero-order reaction the rate constant is

Substituting this in the above equation we

have,

Half-life is given as,

It is clear that t1/2 is directly proportional to theinitial concentration of the reactants andinversely proportional to the rate constant for azero order reaction.The half life (t1/2) of the first order reaction can

be derived from the rate constant as follows:

When the reaction has proceeded half waythen [A]=[A]o/2. On substitution of this valuein the integrated equation the expression of


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t1/2 becomes,

or

Only for the first order reaction t1/2 isindependent of the initial concentration of thereactant. This relation can be used todetermine the order of a reaction.In general, for a reaction of order n, t1/2 isproportional to initial concentration of A raisedto power n - 1, that is,

Pseudo F irst Order Reaction

In some acid catalyzed reactions like theinversion of cane sugar and hydrolysis of ethylacetate, the stoichiometric equations showthem to be bimolecular but they are found tobe first order by experiment.

For the inversion of cane sugar reaction therate of reaction is proportional to theconcentration of sucrose only.So, in the rate equation,Rate = k' [C12H22O11] [H2O]The term [H2O] is constant. The equation,thus, becomesRate = k[C12H22O11]Where k = k' [H2O]As the reaction behaves as first order reaction,such reactions are called pseudo first orderreactions.

Temperature Dependence of Reaction

Rate and Arrhenius Equation

The temperature coefficient of a reaction,defined as a ratio of the rate constants at twotemperatures of a particular reaction differingby 10 C (usually measured from 25 C to 35C), gives the dependence of reaction rates ontemperature It is given by,

Temperature coefficients for most of thereactions lie between 2 and 3, i.e., the rateconstant can double (or even triple) when thetemperature is raised by ten degrees near thenormal room temperature.The effect of temperature on the rate constant

is mathematically expressed by the Arrheniusequation. Arrhenius studied gas phasereactions and in 1897 arrived at an empiricalequation that described the temperaturedependence of reaction rate constant 'k' by theequation,

The equation called Arrhenius equationindicates exponential dependency of the rateconstant on temperature. Here 'A' is theArrhenius factor or the frequency factor alsocalled the pre exponential factor. It is a

constant specific to a particular reaction. Ea isthe energy of activation for the reactionmeasured in joules/mole (Jmol-1), R is the gasconstant, T the temperature, and theexponential factor (-Ea/RT) is a measure of theprobability for the occurrence of a molecule atthe top of the energy-barrier.

Threshold energy is the energy required by

the reacting molecules to overcome the

activation barrier.

Activation energy is the difference between the

threshold energy & the average energy of the

reacting molecules.

Ea = ET - ERWhere, Ea is the activation energy of thereaction; ET is the threshold energy; ER is theaverage energy of the reactant molecules.Each reaction also has a typical energy ofactivation value Ea. The concept of activationcan be easily visualized from the below figure.


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So, it is seen that, When the activation energy is small, then

larger number of the reactant moleculeswill be able to cross over the top of theenergy-barrier, and the reaction will befaster. Thus, if the activation energy is low,then the reaction is fast.

When the activation energy is high, thenonly a few molecules would be able tocross the top of the energy barrier, and thereaction will be slow. Thus, if the activationenergy of a reaction is high, then thereaction is slow.

When the activation energy is zero,then each molecule will be able to cross thetop of the energy barrier, and the reaction willbe instantaneous, and almost explosive. Thus,if the activation energy of a reaction is zero,then the reaction is instantaneous and very,fast.

Arrhenius explanation of how temperature

increases the reaction rate

At any temperature, the number of molecules

possessing energies equal to or greater than a

certain energy (say, 'E') is proportional to the

area under the curve beyond that energy (the

shaded area shown in the Figure (a). When the

temperature is increased, the distribution gets

broadened and the area under them curve

beyond 'E' increases, shown in Figure (b).

Thus, at higher temperature, more molecules

would possess energies equal to or greater

than certain energy i.e., threshold energy.

Therefore with a rise in temperature, more

molecules are able to take part in chemical

reaction. As a result, the reaction rate

increases with an increase in temperature.

According to Arrhenius, a rise in temperature,

increases in the rate of reaction mainly due tothe increase in the number of molecules

possessing energies equal to or greater than

the threshold energy for the reaction.

Graphical Method for Determination of

Activation Energy

Arrhenius equation for the rate constant of a

reaction is

Where, is the activation energy of the

reaction

Rewriting Arrhenius equation by taking

logarithm on both the sides,


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Or,

Subtracting one equation from the other one

gets

Knowing k1, k2, T1,T2, Ea can be calculated from

the equation .

Effect of Catalyst on Reaction Rates

Catalyst provides an alternative pathway of

lower activation energy so the reacting

molecules can cross the energy barrier easily.

Two types of catalytic reactions are usuallydistinguished according to the number ofphases of a system. Homogenous catalysis and Heterogenous catalysisHomogenous catalysts are of the same phase

of the reactants. Oxidation of sulphur dioxide(SO2) to sulphur trioxide (SO3) in the presenceof nitric oxide (NO) is an example ofhomogenous catalytic reaction.In heterogenous reaction, the catalyst exists ina different phase from the reactants. Usually asolid catalyst is used and the reactants can beeither in the liquid or gaseous phase. Nitricoxide can be replaced by platinum in the abovereaction to demonstrate heterogenouscatalysis.

Here, the surface area of the catalyst affects

the rate of the reaction, especially under lowreactant concentrations. Another example ofheterogenous catalytic reaction ishydrogenation of unsaturated hydrocarbon.

AutocatalysisThe phenomenon where the reaction rateincreases as a product is formed is calledautocatalysis. An example of autocatalyticreaction is the Belousov-Zhabotinskii (BZ)reaction.

The product HBrO2 is the reactant in step I.


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The effect of temperature on the rateconstant can be explained by CollisionTheory, especially for gas phase reactions.

A reaction can take place only when thereacting molecules collide with energygreater than the threshold energy and withproper orientation.

In collision theory, the rate constant isrelated to three factors Z, f and p by theequation k = Zfp

The fraction of collisions that have energygreater than the threshold value increaserapidly with temperature and this explainsthe exponential temperature dependenceof rate constant.

Transition state theory explains the rate ofreaction in terms of formation of a'transition state' of reacting molecules. Theformation of transition state requiresenergy of activation.

The activated complex is an unstablehigher energy transition state soon breaks

and decomposes to transform intoproducts. The high and low activation energy values

explain the stability and reactivity ofreactants and products.

Reversible reactions have different forwardactivation energies and backwardactivation energies. The overall activationenergy of a reaction in any directiondetermines the rate of reaction in thatdirection.

Review Questions

1. For the reaction 3H2(g)+N2(g) 2 NH3(g),

how are the rate of reaction expression

dt

]H[d 2 anddt

]NH[d 3 interrelated? (Delhi

2006)

Answer:

dt

]NH[d

2

1

dt

]H[d

3

1 32 +=

2. Identify the reaction order if the unit of the

rate constant is sec-1. (Delhi 2006)

Answer: First order.

3. Define average rate and Instantaneous rate.

(Outside Delhi 2003)

Answer: Average rate: It is defined as the

average charge in the concentration of

reactants or product during a definite time

interval

ervalinttime

nncentratiochangeincoeAveragerat =

t

x

=

Average rate can be determined by taking the

change in concentration during a time interval.

Instantaneous rate: When the rate of

reaction is determined at a particular time, it is

called instantaneous rate.

Instantaneous rate = Slope of the tangent at a

particular time

dt

dx=

Instantaneous rate can be determined by

drawing a tangent and determine the slope of

it at particular time.


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4. Distinguish between reaction rate and

reaction rate constant (Specific reaction rate)

of a reaction. (Delhi 2004)

Answer:

Reaction rateReaction rate

constant

1. The rate of reaction

is the rate of

disappearance of

reactant or rate of the

appearance of

product.

1. The rate constant

or specific reaction

rate is equal to the

rate of reaction

when the

concentration of the

reactant is unity.

2. The rate of reaction

can be calculated by

calculating the

decrease in

concentration of the

reactant in unit time.

For reaction A B

rate of reaction

dt

]B[d

dt

]A[d+==

2. Rate constant

can be calculated

with the help of rate

law.

rate = k [A]

where k = rate

constant

[A] = concentration

of reactant

The value of k

depends upon the

order of reactionand temperature.

5. For a certain chemical reaction variation in

the concentration in [R] vs. time (s) plot is

given below.

For this reaction write/draw

(i) what is the order of the reactions?(ii) What are the units of rate constant k?(iii)Give the relationship between k and t1/2

(half life period)

(iv)What does the slope of the above lineindicate?

(v) Draw the plot log [R]0/ [R] vs time t (s)Answer: (i) First order reaction

(ii) Per sec.

(iii) k =

(iv) rate constant (k)

(v)

6. State the role of activated complex in a

reaction and state its relation with activation

energy. (Outside Delhi 2001)

Answer: Activated complex: In order that the

reactants many change into products, they

have to cross an energy barrier. When the

reactant molecules absorb energy, their bonds

are loosened and new bonds start forming

between them. This highly unstable transition

state between reactants and products is called

activated complex. It immediately dissociatesto form the stable products.

Activation energy = energy of activated

complex Average energy of reactants.

7. The rate of a reaction is given by

Rate=k [N2O5] In this equation what does k

stand for? (Outside Delhi 2000, 2002)

Answer: Here k is the rate constant for the

reaction and is equal to the rate of the reaction

when the concentration of the reactant is

unity.


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8. Define activation energy of a reaction.

(Outside Delhi 2000, 2002)

Answer: the minimum extra energy over and

above the average potential energy of the

reactants which must be supplied to the

reactants to enable them to cross over the

energy barrier between reactants and products

is called activation energy.

9. A first order reaction is 20% complete in 10

minutes. Calculate the time for 75%

completion of the reaction. (Outside Delhi

2000, 2002)

Answer: Let a be the initial concentration of

the reactant.

Thus At t= 10 min, a x = a -10020 a =

5a4

t = ?, a x = a - a100

75=

4

a

for a first order reaction

4

5log

t

303.2

5/a4

alog

min10

303.2k ==

and 4logt

303.2

4/a

alog

min10

303.2k ==

4logt303.2

45log

min10303.2 =

or 0.0223 min-1=t

3865.1

t = 62.1749 mins

10 . Rate constant k of a reaction varies with

temperature according to the equation:

log k = constant -R303.2

Ea xT

1

where Ea is the energy of activation for the

reaction. When a graph is plotted for log K

versusT

1,a straight line with a slope

-6670K is obtained? Calculate energy of

activation for this reaction. State the units.

(R=8.314 JK-1mol-1). (Outside Delhi 2000,

2002)

Answer: Slope of line = -R303.2

Ea

=

-6670K

Ea =2.303 R x 6670 = 2.303 x 8.314 x 6670

=127711.43 J mol-1

11 . The following experimental data was

collected for the reaction:

Cl2(g) + 2NO (g) 2NOCl (g)

Trial

Initial

cone.

[Cl2]

mol L-1

Initial

cone.

[No]

mol L-1

Initial rate

Mol L-1 s-1

1 0.010 0.010 1.20 x 10-4

2 0.010 0.030 10.8 x 10-4

3 0.020 0.030 21.6 x 10-4

Construct the rate equation for the reaction.


Answer: The rate law is

r = K [Cl2]x [NO]y

From trial 1, 1.20 x 10-4 = K [0.010]x [0.010]y

From trial 2, 10.8 x 10-4 = K [0.010]x [0.030]y

From trial 3, 21.6 x 10-4 = K [0.020]x [0.030]y

Dividing (2) by (1), 9=3y 2y =

Dividing (3) by (2), 2=2x 1x =

12 . The decomposition of a compound is found

to follow a first-order rate law. If it takes 15

minutes for 20 per cent of original material to

react, calculate (i) the specific rate constant,

(ii) the time at which 10 per cent of the

original material remains unreacted, (iii) the

time it takes for the next 20 per cent of the

reactant left to react after the first 15 minutes.

(Delhi 2002)

Answer: (i) For a first order reaction


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K=A

]A[log

t

303.2 o

or K=]A8.0[

]A[log

15

303.2

o

o

or K= 8

10log15

303.2

or K=0.015 min-1

(ii) K= 10logt

303.2

]A1.0[

]A[log

t

303.2

1o

o

1

=

From (1) and (2)

11 t

10log

15

25.1log10log

t

303.2

8

10log

15

303.2==

25.1log

10log15=t1

min78.154t1 =

After 154.78 min., 10% of the original

material remains unreacted.

(iii) Also, k =

]A8.0[2.0]A8.0[

]A8.0[log

t

303.2

oo

o

2

k =8

10log

t

303.2

]A64.0[

]A8.0[log

t

303.2

2o

o

2

=

From (1) and (3)

8

10log

t

303.2

8

10log

15

303.2

2

=

t2 = 15 min.

13 . Mention the factors that affect the rate of

a chemical reaction. (Delhi 2002)

Answer: Factors that affect the rate of a

chemical reaction: Following factor affect the

rate of reaction.

(i) Nature of reactants: Different reactantsrequire different amount of energies forbreaking the old bonds and different amount ofenergies for the formation of new bonds.

2No (g) + O2 (g) 2NO2 (g)

[Fast]

2CO (g) + O2 (g) CO2 (g)

[Slow]

(ii) Concentration of reactants: Higher theconcentration of reactant, faster would be the

rate of reaction.(iii)Temperature: The rate of reactionincreases with increase in temperature.(iv)Surface area of reactant: Greater is thesurface area of reactant, faster will be the rateof reaction.(v) Presence of catalyst: The presence ofcatalyst increases the rate of reaction.

14 . For the reaction 2A+B+C A2 B+C, or the

rate law has been determined to be rate = k

[A] [B]2.If the value of the k is 2.0 x 10-6 mol-2

L2

s-1

for the reaction, determine to be rate of

the reaction with [A]=0.2 molL-1; [B] = 0.1

mol L-1; [C] = 0.5 mol L-1. (Outside Delhi

2002)

Answer: The rate law of the reaction:

2A + B + C A2B + C is

rate = k [A] [B]2

obviously the rate of the reaction does not

depend upon the concentration of C

So, Rate = k [A] [B]2

= (2.0 x 10-6 mol-2 L2 s-1) (0.2 mol L-1) (0.1

mol L-1)

= 9.0 x 10-9 mol L-1 s-1.

15 . The rate constant of a reaction is 3 x 10-4

L mol-1. what is the order of the reaction?

(Delhi 2003)

Answer: Second order. Hint: Decide the

order based on the unit of rate constant .

16 . The rate constant of a reaction is 1.5 x 107

s-1 at 500C and 4.5 x 107 s-1 at 1000C.

Calculate the value of activation energy. Ea for

the reaction. [R = 8.314 J K -1 mol-1] (Delhi

2003)


15/19

STUDENT MATERIAL


Answer:

=

21

22a

1

2

TT

TT

R303.2

E

k

klog

=

373x323

323373

314.8x303.2

E

10x5.1

10x5.4log a

7

7

373x323

50x

314.8x303.2

E3log a=

Ea =50

373x323x314.8x303.2x4771.0

= 22011.76 J mol-1 = 220.12 kJ mol-1.

17 . What is known as activation energy? How

is the activation energy affected by (i) the use

of a catalyst and (ii) a rise in temperature?


Answer: Activation energy: The minimumextra energy over and above the average

potential energy of the reactants which must

be supplied to the reactants to enable them to

cross over the energy barrier between

reactants and products is called activation

energy.

Activation energy = Threshold energy

Average energy of reactants.

(i) Activation energy of the reactantsdecreases by the use of a catalyst.

(ii) Activation energy of the reactantsdecreased by a rise in temperature.

18 . The following rate data were obtained at

300 K for the reaction 2 A + B C+D

Experiment

No.

[A]

mol L-1

[B]

mol L-1

Rate of

formation of

D

mol L-1 min-1

1. 0.1 0.1 7.5 x 10-3

2. 0.3 0.2 9.0 x 10-2

3 0.3 0.4 3.6 x 10-1

4. 0.4 0.1 3.0 x 10-2

Calculate the rate of formation of D when [A]

= 0.8 mol L-1 and [B] = 0.5 mol L-1 (Outside

Delhi 2003)

Answer: In experiment 2 and 3 the

concentration of A in same. Therefore,

From the exp. 2,

Rate of formation of D [B]a

9 x 10-2 mol L-1 min-1 [0.2]a

From the exp. 3,

3.6 x 10-1 mol L-1 min-1 [0.4]a

a

2

1

2.0

4.0

10x9

10x6.3

=

(2)2 = (2)a

a = 2

Similarly from the experiment 1 and 4.

b

3

2

2.0

4.0

10x5.7

10x3

=

Or, 4 = (4)b

Or, (4)1 = (b)b

b = 1

So, the rate law for the reaction is.

Rate of formation of D = k [A]2 [B]1

Substituting the value of experiment 1, we get,

7.5 x10-3 mol L-1 min-1

= k [0.1]2.[0] mol2 L-2 x mol L-1

k=33

113

Lmol001.0

minLmol10x5.7

1223-3

minLmol1

10x7.5x10=k

So, the required rate of formation of D,

= 7.5 mol-2 x L2 x min-1 [0.8 mol L-1]2 x [0.5

mol L-1]

= 7.5 x 0.64 x 0.5 mol L-1 min-1 = 2.4 mol L-1

min-1.

19 . Define the order of a reaction. (Delhi

2004)

Answer: The order of a reaction is equal to

the sum of the powers (exponents) to which

the various concentration terms are raised in

the rate law expression of the reaction.


16/19

STUDENT MATERIAL


20 . What is meant by an elementary reaction?


Answer: A reaction which takes place in one

step is called elementary reaction. For example

reaction between H2 and I2 to form 2HI is an

elementary reaction.

21 . Give one example of pseudo first order

reaction. (Outside Delhi 2004)

Answer: CH3COOC2H5 + H2O CH3COOH +

C2H5OH

rate = k [CH2 COOC2H5]1 [H2O]

0

22 . A reaction:

Reactant Product is represented by

Predict (i) the order of the reactions in this

case.

(ii) What does the slope of the graph

represent? (Delhi 2005)

Answer: (i) the reaction is of zero order.

(ii) Slope of the straight line graph =

- k =dt

]R[d

23 . Express the relation between the half-life

period of a reactant and its initial concentration

for a reaction of nth order. (Outside Delhi

2005)

Answer: t1/2

24 . Show that in a first order reaction, time

required for completion of 99.9% is 10 times of

half-life (t1/2) of the reaction. (Delhi 2005)

Answer: When reaction is completed 99.9%

ooo ]R[001.0]R[999.0]R[ =

n

o]R[ ]R[logt303.2K =

K =o

o

]R[001.0

]R[log

tl

303.2

K =310log

t

303.2

K = 10log3.t

303.2

K =t

909.6

t

909.6t =

For half-life of the reaction

t21

=K

693.0

Dividing (1) by (2), we get

K

693.0K

909.6

t

t

2

1

=

693.0

Kx

K

909.6

t

t

21

=

21

21

t10t10t

t==

25 . a) The following initial rate data were

obtained at 300 K for the reactions:

2A + B C + D[A] mol L-1 [B] mol L-1 Rate mol L-1 S-1

I 0.2 0.1 6.0 x 10-2

II 0.4 0.1 2.4 x 10-1

III 0.2 0.2 1.2 x 10-1

Deduce the rate law.


17/19

STUDENT MATERIAL


(b) If half-life of a reaction is inversely

proportional to initial concentration of the

reactant, what is the order of the reaction?

(Delhi 2005)

Answer: (a) Let the rate law for the reaction

be

rate = k [A]x [B]y

Then

or 4 = 2x

x = 2

Again,y]1.0[x]2.0[k

]2.0[x]2.0[k

10x0.6

10x2.1

r

r

x

yx

2

1

I

III ==

or 2 = 2y

y = 1

Hence the rate law is rate = k [A]2 [B].

26 . A substance with initial concentration a

follows zero order kinetics. In how much time

will the reaction go to completion? (Delhi

2005)

Answer: If k is the rate constant of the

reaction, then the time for the completion of

the reaction will be a/k units of time.

27 . The reaction A + B C has zero order.

What is the rate equation? (Outside Delhi

2005)

Answer: Rate = k [A]0 [B]0 = k.

28 . The rate of a particular reaction doubles

when temperature changes from 270C to 370C.

Calculate the activation energy of such


Answer: log

=

21

12a

1

2

TT

TT

R303.2

E

k

k

log 2 =

310x300

300310

314.8x303.2

Ea

Ea = 2log10

310x300x314.8x303.2

= 2.303 x 8.314 x 30 + 310 x 0.3010

= 53598.6 J mol-1

= 53.6 kJ mol-1

29 . For the reaction A B, the rate of

reaction becomes twenty seven times when

the concentration of A is increased three times.

What is the order of the reaction?

Answer: Let r= k [A]n

Then 27 r = k [3A]n [According to question]

n

n

]A[k

]A3[k

r

r27= or 33 = 3n

Order of reaction, n = 3.

(Delhi 2006)

30 . (a) What is rate constant.

(b) On what factors it depend. (Delhi 2006)

Answer: (a) Rate constant or specific reaction

rate: Suppose A and B are two reactants in a

reaction. The rate depends on concentration of

[A]x and [B]y. Then rate equations is

Rate yx ]B[]A[

Rate=k [A]x [B]y

Where k is called the rate constant or specific

reaction rate.

(b) The value of rate constant k is independent

of the concentration of the reactants but

depends upon

(i) the temperature of the reaction

(ii) the particular reaction considered.

31 . Nitric oxide reacts with hydrogen to give

nitrogen and water

2NO + 2H2 N2 + 2H2O

The kinetics of this reaction is explained by the

following steps:


18/19

STUDENT MATERIAL


(i) 2NO + H2 N2 + H2O2 (slow)(ii) H2O2 + H2 2H2O (fast)

What is the predicted rate law? (Delhi 2007)

Answer: 2NO + 2H2 N2 + 2H2O

Slow step of the reaction mechanism is

2NO + H2 N2 + H2O2

The rate law, therefore, is

Rate = k [NO]2 [H2]

32 . The rate constant for a first order reaction

is 60 s-1. How much time will it take to reduce

the concentration of the reactant to 1/10th of

its initial value? (Delhi 2007)

Answer: t =]R[

]R[log

K

303.2 o

Here k = 60 S-1. [R] = ]R[10]R[]R[101 oo =

t =]R[

]R[10log

60

303.2

t = .S0384.060

1x303.2=

Additional Questions

1. How is rate of reaction experimentally

determined?

2. For a reaction A + H2O B

Rate [A] What is its (i) molecularity (ii)

Order of reaction (AI 1997)

3. A first order reaction is 30% completed in

50 minutes.Calculate the value of rate constant

(Foreign 1998)

4. Calculate the activation energy of a reaction

nwhose reaction rate at 310K gets doubled for

10K rise in temperature. (AI 1999c)

5. Show graphically, how the rate of reaction

depends on the concentration of reactant when

there is only reactant and the reaction is of

first order? (AI 1997C)

6. A reaction is 50% complete in 2 hours and

75% complete in a4 hours. What is the order

of the reaction? (Outside Delhi 2006)

7. A first order reaction is 15% complete in 20

minutes. How long will it take to be 60%

complete? (Delhi 2007)

8. The first order rate constant for the

decomposition of ethyl iodide by the reaction

C2H5 I (g) C2 H4 (g) + HI (g)

At 600K is 1.60 x 10-5 S-1. Its energy of

activation is 209 kJ/mol. Calculate the rate

constant of the reaction at 700 k.

(Delhi 2007)

9. A first order decomposition reaction takes

40 minutes for 30% decomposition. Calculate

its t21

value. (Delhi 2008)

10 . A reaction is believed to be either first or

second order, and has a half-life of 10 seconds

at the beginning of an experiment but a half-

life of 20 seconds some time later. What is the

order of the reaction?

11 . A hydrogenation reaction is carried out at

500 K. If the same reaction is carried out in

the presence of a catalyst at the same rate,

the temperature required is 400K. Calculate

the activation energy of the uncatalyzed

reaction if the catalyst lowers the activation

energy by 20 KJ / mol.

12 . From collision theory, what is the factor

that is responsible for increasing the rate of a

reaction with temperature? Does the factor Z


19/19

STUDENT MATERIAL


R = 8.314 JK-1 mol-1] (Delhi 2006)increase with temperature?

13 . The rate constant for the first order

decomposition of certain reaction is described

by the equation.

T1025.134.14)k(log

4

=

What is the activation energy?

14 . What is the activation energy of a reactionwhose rate quadruples when the temperatureis raised from 293 K to 313 K.?

Homework Questions:

1. Define rate law. Give example.


2. What is a first order reaction?

Give two examples of first order reaction.

3. Write units of rate constant K for zero order,

first order, second order and nth order


4. Define the zero order reaction. Give is unit.


5. N2O5 decomposes according to the equation,

2252 ONO4ON2 +

The reaction follows first order kinetics. After

30 minutes from the start of decomposition in

a closed vessel, the total pressure developed is

found to be 284.5 mm Hg and on complete

decomposition, the total pressure is 584.5 mm

Hg. What is the rate constant of the reaction?

6. The rate of a particular reaction triples when

temperature changes from 50oC to 100oC.

Calculate the activation energy of the reaction.

[Given log 3 = 0.4771;

cbse.12.che.student material.chemical kinetics-1.0

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