IIT JEE Main Advanced Physical Chemistry 12th Chemical Kinetics

8/16/2019 IIT JEE Main Advanced Physical Chemistry 12th Chemical Kinetics

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Topic Page No.

Theory 01 - 06

Exercise - 1 07 - 24




Answer Key 42 - 43

Contents

hemical Kinetics

SyllabusChemical Kinetics :

Rates of chemical reactions; Order of reactions; Rate constant; First order reactions; Temperature

dependence of rate constant (Arrhenius equation).

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CHEMICAL KINETICS # 1

CHEMICAL KINETICS

Rate/Velocity of chemical reaction :

The rate of change of concentration with time of different chemical species taking part in a chemical reaction is

known as rate of reaction of that species.

Rate =t

c

!

! =

sec

.lit / mol = mol lit –1 time –1 = mol dm –3 time –1

Rate is always defined in such a manner so that it is always a positive quantity.

Types of Rates of chemical reaction :

For a reaction R "# " P

Average rate =takentimeTotal

ionconcentratinchangeTotal =

t

c

!

! = –

t

]R[

!

! =

t

]P[

!

!

Instantaneous rate : rate of reaction at a particular instant.

Rinstantaneous

=0t

lim# $%

&'()!!

tc =

dtdc = –

dt]R[d =

dt]P[d

Relation between reaction rates of different species involved in a reaction :

For the reaction : N2 + 3H

2 "# " 2NH3

Rate of reaction =dt

]N[d 2* =dt3

]H[d1 2* =dt

]NH[d

2

1 3

Order of reaction :Let there be a reaction m

1A + m

2B "# products.

Now, if on the basis of experiment, we find thatR + [A]P [B]q Where p may or may not be equal to m

1 and similarly q may or may not be equal to m

2.

p is order of reaction with respect to reactant A and q is order of reaction with respect to reactant B and(p + q) is overall order of the reaction.

Integrated rate laws :

Zero order reactions :

For a zero order reaction

General rate law is, Rate = k [conc.]º = constant

If C0 is the initial concentration of a reactant and C

t is the

concentration at time ‘t’ then

Rate = k ='t'

CC t0 *or kt = C

0 – C

tor C

t = C

0 – kt

Unit of K is same as that of Rate = mol lit –1 sec –1.

First Order Reactions :

k =t

303.2 log

t

0

C

C

Half life time (t1/2

)

t1/2 = k2log303.2 =

kln2 =

0.693

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Second order reaction :

tC

1 –

0C

1 = kt

Pseudo first order reaction :A second order (or of higher order) reactions can be converted into a first order reaction if the other reactant istaken in large excess. Such first order reactions are known as pseudo first order reactions.

, For A + B "# Products [Rate = K [A]1

[B]1

k = )ba(t

303.2

* log )xb(a

)xa(b

*

*

Table : Characteristics of Zero, First, Second and n th Order Reactions of the Type A "# " Products

Zero Order First-Order Second-Order nth order

Differential Rate lawt Ä

]A[ Ä* = k[A]°

t

]A[

!

!* = k[A]

t

]A[

!

!* = k[A]2

n]A[kt Ä

]A[ Ä.*

(Integrated Rate law) [A]t = [A]

0 – kt In [A]

t = –kt + In [A]

0t]A[

1= kt +

0]A[

1

kt)1n(

)A(

1

)A(

11n

01n

t

*.

***

Linear graph [A]t v/s t In [A] v/s t

]A[

1 v/s t 1n

t )A(

1* v/s t

Half-life t1/2

=k2

]A[ 0t1/2

=k

693.0t1/2

=0]A[k

11n

0

2 / 1)A(

1t

*+

(depends on [A]0) (independent of [A]0) (depends on [A]0)

Methods to determine order of a reaction :

By comparison of different initial rates of a reaction by varying the concentration

of one of the reactants while others are kept constant

r = k [A]a [B]b [C]c if [B] = constant

[C] = constant

then for two different initial concentrations of A we have

10r = k [A

0]1a

20r = k [A

0]2

a

/

a

20

10

0

0

]A[

]A[

r

r

2

100 1

2334

5 .

Method of half lives :

The half lives of each order is unique so by comparing half lives we can determine order

for nth order reaction t1/2

+1n

0 ]R[

1

*

1n0

1n'0

'2 / 1

2 / 1

)R(

)R(

t

t*

*

.

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Methods to monitor the progress of the reaction :Pressure measurement :

Progress of gaseous reaction can be monitored by measuring total pressure at a fixed volume & temperature.

Let there is a 1st order reaction

A(g) "# nB(g)

, k = t

2.303

log t0

0

PnP

1)(nP

*

*

Final total pressure after infinite time = Pf = nP

0

Formula is not applicable when n = 1, the value of n can be fractional also.

Do not remember the formula but derive it for each question.

By titration method :By measuring the volume of titrating agent we can monitor amount of reactant remaining or amount of product

formed at any time. It is the titre value . Here the milliequivalent or millimoles are calculated using valence

factors.

V0 = vol. of titrant used at t = 0 [this is exclusively for HCl.]

Vt = vol. of titrant used at ‘t’

V6 = vol. of titrant used at t = 6

k =t

303.2 log

t

0

VV

VV

*

*

6

6

Optical rotation measurement :It is used for optically active sample. It is applicable if there is at least one optically active species involved

in chemical reaction.

where are r0, r

t, r

6 are angle of optical rotation at time t = 0, t = t and t = 6

K =0

t

Y Y2.303log

t r r6

6

*

*

Effect of temperature on rate of reaction :

In early days the effect of temperature on reaction rate was expressed in terms of temperature coefficient

which was defined as the ratio of rate of reaction at two different temperature differing by 10ºC (usually these

temperatures were taken as 25ºC and 35ºC)

T.C. =t

t

K

10K 7 8 2 to 3 ( for most of the reactions)

Arrhenius theory of reaction rate :

Products

Reactants9HR

9HP

Ea1 Ea2Threshold enthalpyor energy

! 9 9H = H – H = Ea – Eap R 1 2

Enthalpy (H)

Progress of reaction (or reaction coordinate)

9

9

!

H = Summation of enthalpies of reactants

H = Summation of enthalpies of reactants

H = Enthalpy change during the reactionEa = Energy of activation of the forward reactionEa = Energy of activation of the backward reaction

R

P

1

2

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T1

T2Fraction ofmolecule

Ea

T2

> T1

RT / Eae* # represents fraction of molecules K.E. having energy greater Ea

rate + RT / Eae*

dependence of rate on temperature is due to dependence of k on temperature.

RT / E

RT / E

a

a

Aek

ek*

*

.

+[Arrhenius equation]

General characteristics of catalyst :P.E. Ea

E'a

HR

HP Products

Reaction Coordinate

A catalyst drives the reaction through a low energy path and

hence Ea is less. That is, the function of the catalyst is to

lower down the activation energy.

Ea = Energy of activation in absence of catalyst.

E’a = Energy of activation in presence of catalyst.

Ea – E’

a = lowering of activation energy by catalyst.

Molecularity and Order :

The number of molecules that react in an elementary step is the molecularity of the elementary reaction.

Molecularity is defined only for the elementary reactions and not for complex reactions. No elementary reactions

involving more than three molecules are known, because of very low probability of near-simultaneous collision ofmore than three molecules.

The rate law for the elementary reaction

aA + bB "# " products rate = k[A]a[B]b, where a + b = 1, 2 or 3.

For an elementary reaction, the orders in the rate law equal the coefficients of the reactants.

Mechanism of a reaction :

Reactions can be divided intoElementary / simple / single stepComplex / multi-step

ELEMENTARY REACTION :

These reaction take place in single step without formation of any intermediate

T.S.

Ep

Er

P.E.

Reaction coordinates

For elementary reaction we can define molecularity of the reaction which is equal to no of molecules whichmake transition state or activated complex because of collisions in proper orientation and with sufficient energy

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COMPLEX REACTION :Reaction which proceed in more than two steps. or having some mechanism. ( sequence of elementary reactionin which any complex reaction procceds)

T.S.

intermediateE

Reaction coordinates

For complex reaction each step of mechanism will be having its own molecularity but molecularity of netcomplex reaction will not be defined.

CALCULATION OF RATE LAW/ ORDER

MECHANISM IN WHICH R.D.S. GIVENIf R.D.S. involves only reactant, product or catalyst on reactant siderate law of R.D.S. = rate law of reaction

RDS is having intermediate on reactant sideTo calculate order, we have to specify [ intermediate] in expression of rate law in terms of conc. of [R], [P] orcatalyst with the help of same equilibrium step given in mechanism.

MECHANISMS IN WHICH RDS NOT SPECIFIED :

STEADY STATE APPROXIMATION :

At steady statedt

]ermediate[intd = 0

COMPLICATIONS IN 1st ORDER REACTION

PARALLEL 1st ORDER REACTION OR COMPETING FIRST-ORDER REACTIONS

effT

1=

1T

1+

2T

1(remember)

]C[

]B[ =

2

1

k

k(remember)

21

2a1a

akk

kEkEE 21

7

7.

REVERSIBLE 1ST ORDER REACTION ( both forward and backward )

A B

t = 0 a 0t = t a –x xt = t

eq.a – x

eq.x

eq.

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x =bf

f

kk

ak

7 : ;t)kk( bfe1 7** (remember)

kf + k

b =

t

1!n 0

0

1

2

33

4

5

* xx

x

.eq

.eq

(remember)

SEQUENTIAL 1ST ORDER REACTION OR CONSECUTIVE FIRST-ORDER REACTIONS

A "# " 1k

B " "# " 2k

C all first order equation

t = 0 a 0 0t a – x y z

y =12

1

kk

ak

* {tk1

e* – tk2

e* } (remember)

tmax.

= : ;21 kk1

* !n 2

1

k

k(remember)

CASE- k1>> k

2

A "# " 1k

B " "# " 2k

C

CASE : k2 >> k

1

a

t

[C]

[A][B]

Conc

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PART - I : OBJECTIVE QUESTIONS

*Marked Questions are having more than one correct option.

Section (A) : Rate of Reaction

A-1. For a hypothetical reaction A ! L, the rate expression is -

rate = – dt

dC A

(A) Negative sign represent that rate is negative

(B) Negative sign indicates to the decrease in the concentrations of reactant

(C) Negative sign indicates the attractive forces between reactants

(D) None of the above is correct

A-2. xA + yB ! zC. Ifdt

]A[d" =

dt

]B[d" = 1.5

dt

]C[d = then x,y and z are :

(A) 1,1, 1 (B) 3, 2, 3 (C) 3, 3, 2 (D) 2, 2, 3

A-3. In the following reaction : xA # # ! # yB

log $%

&'(

)"

dt

]A[d = log $

%

&'(

)dt

]B[d + 0.3

where –ve sign indicates rate of disappearance of the reactant. Thus, x : y is :(A) 1 : 2 (B) 2 : 1 (C) 3 : 1 (D) 3 : 10

A-4. In the formation of sulphur trioxide by the contact process,

2SO2 (g) + O2 (g) ##! 2SO3 (g)

The rate of reaction is expressed as –d O

dt( )2

= 2.5 x 104 mol L-1 sec-1

The rate of disappearance of (SO2) will be -

(A) 5.0 x 10—4 mol L –1 s –1 (B) 2.25 x 10—4 mol L –1 s –1

(C) 3.75 x 10—4 mol L –1 s –1 (D) 50.0 x 10—4 mol L –1 s –1

A-5. Rate of formation of SO3 in the following reaction 2SO2 + O2 ! 2SO3 is 100 g min –1. Hence rate of disappearance

of O2 is :

(A) 50 g min-1 (B) 40 g min –1 (C) 200 g min –1 (D) 20 g min –1

A-6. A reaction follows the given concentration (M) –time graph. The rate for this reaction at 20 seconds will be:

0.5

0.4

0.3

0.2

0.1

0 20 40 6 0 8 0 1 0 0

Time/second

(A) 4 × 10 –3 M s –1 (B) 8 × 10 –2 M s –1 (C) 2 × 10 –2 M s –1 (D) 7 × 10 –3 M s –1

A-7. For the reaction : N2 + 3H2 ! 2NH3. If the rate of disappearance of hydrogen is 1.8 × 103. What is the

rate of formation of ammonia. (mole per litre per sec.)(A) 1.8 × 103 (B) 1.2 × 103 (C) 2.7 × 103 (D) 0.9 × 103

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A-8. The rate of a reaction is expressed in different ways as follows ;

+ 1/2(d[C]/dt) = – 1/3 (d[D]/dt) = + 1/4 (d[A]/dt) = – (d[B]/dt) The reaction is :

(A) 4 A + B #! # 2C + 3D (B) B + 3D #! # 4A + 2C

(C) 4A + 2B #! # 2C + 3D (D) B + (1/2) D #! # 4A + 3

A-9. ln the reaction; A + 2B #! # 3C + D, which of the following expression does not describe changes in the

concentration of various species as a function of time :(A) {d [C] / dt} = – {3d [A] / dt} (B) {3d [D] / dt} = {d [C] / dt}(C) {3d [B] / dt} = – {2d [C] / dt} (D) {2d [B] / dt} = {d [A] / dt}

A-10. For a chemical reaction 2X + Y ! Z, the rate of appearance of Z is 0.05 mol L –1 per min. The rate ofdisappearance of X will be -

(A) 0.05 mol L—1 per hour (B) 0.05 mol L—1 per min

(C) 0.1 mol L—1 per min (D) 0.25 mol L—1 per min

Section (B) : Rate Law

B-1. What is the order of a reaction whose

rate = KCA3/2 CB –1/2 ?(A) 2 (B) 1 (C) – 1/2 (D) 3/2

B-2. The rate of certain hypothetical reaction A + B + C ! products, is given, by r = – dA

dt = K [A]½ [B]1/3

[C]1/4. The order of reaction is given by :

(A) 1 (B) 1/2 (C) 2 (D) 13/12

B-3. The rate constant of nth order has units :

(A) Litre1 –n mol1-n sec –1 (B) Mol1 –n litre1-n sec

(C) Mol n12"

litre n2 sec –1 (D) Mole1 –n litren-1 sec –1

B-4. The rate constant of reaction changes when :

(A) Volume is changed (B) Concentrations of the reactants are changed

(C) Temperature is changed (D) Pressure is changed

B-5. For which of the following, the units of rate constant and rate of the reaction are same -

(A) First order reaction (B) Second order reaction

(C) Third order reaction (D) Zero order reaction

B-6. For a chemical reaction, 2A + 2B #! # C + D, the order of reaction is one with respect to A and one with

respect to B. The initial rate of the reaction is 4 × 10 –2 mol L –1 s –1. When 50% of the reactants are converted

into products, the rate of the reaction would become-(A) 2 × 10 –2 mol L –1s –1 (B) 1 × 10 –2 mol L –1s –1

(C) 4 × 10 –2 mol L –1 s –1 (D) 2 × 10 –1 mol L –1 s –1

B-7. For a gaseous reaction the rate equation is v = k[A][B]. If the volume of the gaseous system is suddenly

reduced to 1/3 of initial volume. The rate would become –

(A) 1/9 times (B) 9 times (C) 1/6 times (D) 6 times

B-8. aA + bB #! # Product, dx/dt = k [A]a [B]b . If concentration of A is doubled, rate is four times. If concentration

of B is made four times, rate is doubled. What is relation between rate of disappearance of A and that of B ?

(A) – {d [A] / dt} = – {d [B] / dt} (B) – {d [A] / dt} = – {4 d [B] / dt}(C) – {4 d [A] / dt} = – {d [B]/ dt} (D) None of these

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B-9. For the reaction, 2NO(g) + 2H2(g) #! # N2(g) + 2H2O(g) the rate expression can be written in the following

ways :

{d [N2] / dt} = k1 [NO][H2] ; {d[H2O] / dt} = k[NO][H2] ; { – d[NO] / dt} = k+1 [NO] [H2] ; { –d[H2] / dt} = k++1 [NO][H2]The relationship between k, k1 , k+1 and k++1. is :(A) k = k1 = k+1 = k++1 (B) k = 2k1 = k+1 = k++1(C) k = 2k+1 = k1 = k ++1 (D) k = k1 = k +1 = 2 k++1

B-10. For rate constant is numerically the same for three reactions of first, second and third order respectively.Which of the following is correct :

(A) if [A] = 1 then r1 = r2 = r3 (B) if [A] < 1 then r1 > r2 > r3(C) if [A] > 1 then r3 > r2 > r1 (D) All

B-11. In acidic medium the rate of reaction between (BrO3) ¯ and Br¯ ions is given by the expression. – [d (BrO3

–) /dt] = K [BrO3 – ] [Br ¯] [H+]2 It means :

(A) Rate constant of overall reaction is 4 sec –1

(B) Rate of reaction is independent of the concentration of acid

(C) The changes in pH of the solution will not affect the rate

(D) Doubling the concentration of H+ ions will increase the reaction rate by 4 times.

B-12. For the irreversible process, A + B #! # products, the rate is first –order w.r.t. A and second –order w.r.t. B. If 1.0mol each of A and B introduced into a 1.0 L vessel, and the initial rate was 1.0 × 10 –2 mol L –1 s –1 , rate when halfreactants have been turned into products is :

(A) 1.25 × 10 –3 mol L –1 s –1 (B) 1.0 × 10 –2 mol L –1 s –1

(C) 2.50 × 10 –3 mol L –1 s –1 (D) 2.0 × 10 –2 mol L –1 s –1

Section (C) : The integrated rate laws

C-1. A first order reaction follows the expressions

(A) Cttk1e = C0 (B) Ct = C0

tk1e (C) lnt

0

C

C= –k1t (D) ln

0

t

C

C = k1t

C-2. Which of following statement is false

(A) A fast reaction has a larger rate constant and short half-life

(B) For a first order reaction, successive half lives are equal

(C) For a first order reaction, the half-life is independent of concentration

(D) The half life of a reaction is half the time required for the reaction to go to completion

C-3. Half life period of a zero order reaction is –

(A) Independent of concentration

(B) Directly proportional to initial concentration

(C) Inversely proportional to concentration

(D) Directly proportional to the square of the concentration

C-4. Wrong data for the first order reaction is –

(A) t0.5 =100s, t0.75 = 200s (B) t0.75 = 32 min t0.5 = 16min

(C) Both the above (D) t0.5 = 100s, t0.75 = 150s

C-5. What is the half life of a radioactive substance if 75% of any given amount of the substance disintegrates

in 60 minutes –

(A) 2 Hours (B) 30 Minutes (C) 45 Minutes (D) 20 Minutes

C-6. For an elementary reaction X (g) ! Y (g) + Z (g) the half life periods is 10 min. In what period of timewould the concentration of X be reduced to 10% of original concentration -

(A) 20 Min. (B) 33 Min (C) 15 Min (D) 25 Min

C-7. 99% of a first order reaction was completed in 32 min. When will 99.9% of the reaction complete –

(A) 50 Min (B) 46 Min (C) 49 Min (D) 48 Min

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C-8. In the presence of an acid, the initial concentration of cane sugar was reduced from 0.20 to 0.10 molar

in 5 hours and from 0.2 to 0.05 molar in 10 hours. The reaction is of –

(A) Zero order (B) First order (C) Second order (D) Third order

C-9. For a second order reaction, if the conc. of a reactant decreases from 0.08M to 0.04M in ten minutes,

what would be the time taken for the conc. to decreases to 0.01M –

(A) 20 minutes (B) 30 minutes (C) 50 minutes (D) 70 minutes

C-10. The rate constant for a second order reaction 8.0 × 10 –4 litre mol –1min –1. How long will it take a 0.5Msolution to be reduced to 0.25M in reactant –

(A) 8.665 × 102 min (B) 8.0 × 10 –4 min (C) 2.50 × 103 min (D) 4.0 × 10 –4 min

C-11. A radioactive isotope decomposes according to the first order with half life period of 15 hrs. 80% of the

sample will decompose in -

(A) 15 × 0.8 hr. (B) 15 × (log 8) hr.(C) 15 × (log5 / log2) hr. (or 34.83) hr. (D) 15 × 10/ 8 hr.

C-12. Radioactive decay follows -

(A) Zero order kinetics (B) Second order kinetics

(C) First order kinetics (D) Pseudo first order kinetics

C-13. The t0.5 for the first order reaction,

PCI5(g) #! # PCI3(g) + Cl2(g)is 20 min. The time in which the conc. of PCI5 reduces to 25% of the initial conc. is close to-

(A) 22 min (B) 40 min (C) 90 min (D) 50 min

C-14. The rate constant of reaction 2 A + B #! # C is 2.57 × 10 –5 It mole –1 sec –1 after 10 sec. 2.65 × 10 –5 It.

mole –1 sec –1 after 20 sec. and 2.55 × 10 –5 It. mole –1 sec –1 after 30 sec. The order of the reaction is:(A) 0 (B) 1 (C) 2 (D) 3

C-15. For a first order reaction, the plot of log C against ‘t’ (logC vs 't') gives a straight tine with slope equal to :

(A) (k / 2.303) (B) ( – k / 2.303) (C) (ln k / 2.303) (D) – k.

C-16. In a certain reaction, 10% of the reactant decomposes in one hour, 20 % in two hours, 30% in three hours and

so on the dimensions of the rate constant is :

(A) hour –1 (B) mole litre –1 sec –1 (C) litre mole –1 sec –1 (D) mole sec –1

C-17. In presence of HCl, sucrose gets hydrolysed into glucose and fructose. The concentration of sucrose was found

to reduce from 0.4 M to 0.2 M in 1 hour and to 0.1 M in total of 2 hours. The order of the reaction is :

(A) zero (B) one (C) two (D) None of these

C-18. In a first order reaction the reacting substance has half-life period of ten minutes. What fraction of the substance

will be left after an hour the reaction has occurred ?

(A) 1/6 of initial concentration (B) 1/64 of initial concentration(C) 1/12 of initial concentration (D) 1/32 of initial concentration

C-19. In the following first order reactions (A) # # ! # 1K

Product, (B) # # ! # 2K

Product, the ratio k1 /k2 if 90% of (A) has

been reacted in time 't' while 99% of(B) has been reacted in time 2t is :

(A) 1 (B) 2 (C) 1/2 (D) None of these

C-20. Two substances A (t1/2 = 5 min) and B (t1/2 = 15 min) are taken in such a way that initially [A] = 4[B]. The time

after which both the concentration will be equal is : (Assume that reaction is first order)

(A) 5 min (B) 15 min

(C) 20 min (D) concentration can never be equal

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C-21. If a I-order reaction is completed to the extent of 60% and 20% in time intervals, t 1 and t2, what is the ratio,

t1 : t2 ?

(A) 6.32 (B) 5.58 (C) 4.11 (D) 8.33

C-22. For a reaction A ! Products, the concentration of reactant are C0 , aC0 , a2C0, a

3C0 ........... after time interval

0, t, 2t ........where 'a' is constant. Then :

(A) reaction is of 1st order and K = (1/1) ln a (B) reaction is of 2nd order and K = (1/tC0)(1 –a)/a

(C) reaction is of 1st order and K =t1 ln ,

- ./

0 1

a1 (D) reaction is of zero order and K = ,

- ./

0 1

a1ln

t1

C-23. The rate constant for the reaction A ! B is 2 × 10 –4 It. mol –1 min –1. The concentration of A at which rate of thereaction is (1/12) × 10 –5 M sec –1 is :

(A) 0.25 M (B) (1/20) 3 / 5 M (C) 0.5 M (D) None of these

C-24. Graph between concentration of the product and time of the reaction A! B is of the type Hence graph

between –

d[A]/dt and time will be of the type :

(A)

( –d[A]/dt)

Time

(B) (C) (D)

C-25. A graph plotted between log t50% vs. log concentration is a straight line. What conclusion can you draw from this

graph.

(A) n = 1 ; t1/2 2 a (B) n = 2, t1/2 2 1/a(C) n = 1 ; t1/2 = (0.693 / k) (D) None of these

C-26. What will be the order of reaction and rate constant for a chemical change having log t50% vs log concentration

of (A) curves as :

(A) 0, 1/2 (B) 1, 1 (C) 2, 2 (D) 3, 1

C-27. A drop of solution (volume 0.05 mL) contains 3.0 × 10 –6 moles of H+. If the rate constant of disappearance of H+

is 1.0 × 107 mole litre –1 sec –1. How long would it take for H+ in drop to disappear :(A) 6 × 10 –8 sec (B) 6 × 10 –7 sec (C) 6 × 10 –9 sec (D) 6 × 10 –10 sec

Section (D) : Methods to determine The rate law

D-1. When concentration of reactant in reaction

A ! B is increased by 8 times, the rate increase only 2 times. The order of the reaction would be -(A) 2 (B) 1/3 (C) 4 (D) 1/2

D-2. The data for the reaction A + B ! C isExp. [A]0 [B]0 initial rate

1 0.012 0.035 0.10

2 0.024 0.035 0.80

3 0.012 0.070 0.10

4 0.024 0.070 0.80

(A) r = k [B]3 (B) r = k [A]3 (C) r = k [A] [B]4 (D) r = k [A]2 [B]2 .

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D-3. A + B #! # Product,dt

dx =k [A]a [B]b

If , -

./0

1 dt

dx = k, then order is :

(A) 4 (B) 2 (C) 1 (D) 0

D-4. One litre of 2M acetic acid and one litre of 3M ethyl alcohol were mixed. The esterification takes place

according to the reaction:

CH3COOH + C2H5OH ! CH3COOC2H5 + H2OIf each solution is diluted by one litre water the rate would become –

(A) 4 times (B) 2 times (C) 0.5 times (D) 0.25 times

D-5. In the reaction : A + 2B + C ! D + 2ETher rate of reaction remains unchanged if the conc. of B is doubled and that of A and C is kept constant.

What is the order with respect to B.

(A) 0 (B) 1/2 (C) 1 (D) 3

D-6. The following data pertain to reaction between A and B :

S.No. [A] [B] Rate

mol.l –1 mol.l –1 mol.l –1sec –1

I 1 × 10 –2 2 × 10 –2 2 × 10 –4

II 2 × 10 –2 2 × 10 –2 4 × 10 –4

III 2 × 10 –2 4 × 10 –2 8 × 10 –4

Which of the following inference(s) can be drawn from the above data –

(a) Rate constant of the reaction 10 –4

(b) Rate law of the reaction is k[A][B]

(c) Rate of reaction increases four times on doubling the concentration of both the reactant,

Select the correct answer –

codes : –

(A) a,b and c (B) a and b (C) b and c (D) c alone

D-7. Using the data given below the order and rate constant for the reaction : CH 3CHO(g) ! CH4(g) + CO(g) wouldbe –

Experiment no. Initial conc. Initial rate

[mol/ !] [mol.lit –1sec1]

I 0.10 0.020

II 0.20 0.080

III 0.30 0.180

IV 0.40 0.320

Answer is –

(A) 2,[k = 2.0 ! /mol sec] (B) 0,[k = 2.0 mol/ ! sec]

(C) 2,[k = 1.5 ! /mol sec] (D) 1,[k = 1.5 sec –1]

D-8. For the reaction 2A + 3B #! # products, A is in excess and on changing the concentration of B from 0.1 M to

0.4 M, rate becomes doubled, Thus, rate law is :

(A)dt

dx = k[A]2 [B]2 (B)

dt

dx = k[A] [B] (C)

dt

dx= k[A]0 [B]2 (D)

dt

dx = k[B]1/2

D-9. For the reaction A #! # Products, – dt

]A[d = k and at different time interval, [A] values are :

Time 0 5 min 10 min 15 min

[A] 20 mol 18 mol 16 mol 14 mol

At 20 minute, rate will be :

(A) 12 mol /min (B) 10 mol/min (C) 8 mol/min (D) 0.4 mol/min

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D-10. A ! Product and , -

./0

1 dt

dx = k[A]2 . If log ,

-

./0

1 dt

dx is plotted against log [A], then graph is of the type :

(A) (B) (C) (D)

D-11. If a is the initial concentration of reaction, then the half life period of a reaction of n th order is directly

propotional to -

(A) an (B) an –1 (C) a1 –n (D) an+1

D-12. The half-life period for a reaction at initial concentrations of 0.5 and 1.0 moles litre-1 are 200 sec and 100

sec respectively. The order of the reaction is -

(A) 0 (B) 1 (C) 2 (D) 3

D-13. Consider a reaction A #! # B + C. If the initial concentraton of A was reduced from

4 M to 2 M in 1 hour and from 2 M to 1 M in 0.5 hour, the order of the reaction is-(A) One (B) Zero (C) Two (D) Three

Section (E) : Methods to monitor the progress of reaction

E-1. Consider the reaction 2A(g) #! # 3B(g) + C(g). Starting with pure A initially, the total pressure doubled in 3 hrs.

The order of the reaction might possibly be

(A) zero (B) first (C) second (D) unpredictable from this data

E-2. Formation of NO2F from NO2 and F2 as per the reaction 2NO2(g) + F2(g) #! 2NO2F(g) is a second orderreaction, first order with respect to NO2 and first order with respect to F2. If NO2 and F2 are present in a closed

vessel in ratio 2 :1 maintained at a constant temperature with an initial total pressure of 3 atm, what will be the

total pressure in the vessel after the reaction is complete?

(A) 1atm (B) 2 atm (C) 2.5 atm (D) 3 atm

E-3. In a gaseous state reaction, A2 (g) #! # B(g) + (1/2)C (g), The increase in pressure from 100 mm to 120 mm

is notices in 5 minutes. The rate of disapearance of A2 in mm min –1 is :

(A) 4 (B) 8 (C) 16 (D) 2

E-4. The decomposition of a gaseous substance (A) to yield gaseous products (B), (C) follows First order kinetics.

If initially only (A) is present and 10 minutes after the start of the reaction the pressure of (A) is 200 mm Hg and

that of over all mixture is 300 mm Hg, then the rate constant for 2A ! B + 3 C is :(A) (1/1200) ln 1.25 sec –1 (B) (2.303 /10) log 1.5 min –1

(C) (1/10) ln 1.25 sec –1 (D) None of these

E-5. In the reaction NH4NO2 (aq.) ! N2 (g) + 2 H2O (l ) the volume of N2 after 20 min and after a long time is 40 ml and70 ml respectively. The value of rate constant is :

(A) (1/20) In (7/4) min –1 (B) (2.303 /1200) log (7/3) sec –1

(C) (1/20) log (7/3) min –1 (D) (2.303 / 20) log (11/7) min –1

E-6. –N2Cl #!3 Cu /

–Cl + N2 Half-life is independent of concentration of reactant. After 10 minutes

volume of N2 gas is 10 L and after complete reaction it is 50 L. Hence rate constant is:

(A) (2.303 /10) log 5 min –1 (B) (2.303 /10) log 1.25 min –1

(C) (2.303 /10) log 2 min –1 (D) (2.303 /10) log 4 min –1

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Section(F) : Effect of Temperature

F-1. The activation energies of the forward and backward reactions in the case of a chemical reaction are 30.5

and 45.4 KJ/mol respectively. The reaction is –

(A) Exothermic (B) Endothermic

(C) Neither exothermic nor endothermic (D) Independent of temperature

F-2. Chemical reaction occurs as a result of collisions between reacting molecules. Therefore, the reaction rate

is given by -(A) Total number of collisions occurring in a unit volume per second

(B) Fraction of molecules which possess energy less than the threshold energy

(C) Total number of effective collisions

(D) None of the above

F-3. The chemical reactions in which reactants require high amount of activation energy are generally -

(A) Slow (B) Fast (C) Instantaneous (D) Spontaneous

F-4. For a reaction for whi ch the activation energies of forward and reverse reactions are equal -

(A) 3H = 0 (B) 3S = 0 (C) The order is zero (D) There is no catalyst

F-5. The activation energy of reaction is equal to-

(A) Threshold energy for the reaction(B) Threshold energy + Energy of the reactants

(C) Threshold energy – Energy of the reactants(D) Threshold energy + Energy of the products

F-6. Which of the following explains the increase of the reaction rate by catalyst -

(A) Catalyst decreases the rate of backward reaction so that the rate of forward reaction increases

(B) Catalyst provides extra energy to reacting molecules so that they may reduce effective collisions

(C) Catalyst provides an alternative path of lower activation energy to the reactants

(D) Catalyst increases the number of collisions between the reacting molecules.

F-7. The activation energy of the reaction

A + B ! C + D + 38 k.cal is 20 k.cal, What would be the activation energy of the reaction,

C + D ! A + B(A) 20 k.cal (B) –20 k.cal (C) 18 k.cal (D) 58 k.cal

F-8. Rate of which reactions increases with temperature :

(A) of any (B) of exothermic reactions

(C) of endothermic (D) of none.

F-9. For a zero order reaction. Which of the following statement is false :

(A) the rate is independent of the temperature of the reaction.

(B) the rate is independent of the concentration of the reactants.

(C) the half life depends upon the concentration of the reactants.

(D) the rate constant has the unit mole It –1 sec –1.

F-10. A large increase in the rate of a reaction for a rise in temperature is due to

(A) increase in the number of collisions (B) the increase in the number of activated molecules

(C) The shortening of mean free path (D) the lowering of activation energy

F-11. The first order rate constant k is related to temp. as log k = 15.0 – (106 /T) Which of the following pair of value iscorrect ?

(A) A = 1015 and E = 1.9 × 104 KJ (B) A = 10 –15 and E = 40 KJ

(C) A = 1015 and E = 40 KJ (D) A = 10 –15 and E = 1.9 × 104 KJ.

F-12. The decomposition of N2O into N2 & O2 in presence of gaseous argon follow second order kinetics with

k = (5.0 × 1011 L mol"1 s! 1) TK41570

e"

(K stands for Kelvin units). The energy of activation of the reaction is :

(A) 5.0 x 1011 J (B) 41570 J (C) 5000 J (D) 345612.98 J

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F-13. How much faster would a reaction proceed at 25°C than at 0°C if the activation energy is 65 kJ?

(A) 2 times (B) 5 times (C) 11 times (D) 16 times

F-14. The rate constant, the activation energy and the frequency factor of a chemical reaction at 25 °C are

3.0 × 10 –4 s –1, 104.4 KJ mol –1 and 6.0 × 1014 s –1 respectively. The value of the rate constant as T ! 4 is :(A) 2.0 × 1018 s –1 (B) 6.0 × 1014 s –1 (C) infinite (D) 3.6 × 1030 s –1

F-15. For a given reaction, energy of activation for forward reaction (Eaf) is 80kJ.mol"1

. 3H = "40kJ.mol"1

for thereaction. A catalyst lowers Eaf to 20 kJ.mol

"1. The ratio of energy of activation for reverse reaction before and

after addition of catalyst is :

(A) 1.0 (B) 0.5 (C) 1.2 (D) 2.0

Section (G) : Mechanism of reactionsG-1. For the reaction H2 (g) + Br2 (g) ! 2HBr (g) the experiment data suggested that r = k[H2][Br2]

1/2

The molecularity and order of the reaction are respectively :

(A) 2, 3/ 2 (B) 3/2 , 3/2 (C) Not defined, 3/2 (D) 1,1/2

G-2. For the reaction NO2 + CO ! CO2 + NO the experimental rate expression is – dt

dc = k[NO2]

2 the number of

molecules of CO involves in the slowest step will be -

(A) 1 (B) 2 (C) 3 (D) depends on mechanism

G-3. The reaction of hydrogen, and iodine monochloride is represented by the equation :H2(g) + 25Cl(g) 2HCl(g) + 52(g)

This reaction is first –order in H2(g) and also first –order in 5Cl(g). Which of these proposed mechanismcan be consistent with the given information about this reaction ?

Mechanism 5 : H2(g) + 25Cl(g) 2HCl(g) + 52(g)

Mechanism 55 : H2(g) + 5Cl(g) # !Slow

HCl(g) + H5(g)

HI(g) + 5Cl(g) #!fast HCl(g) + I2(g)

(A) 5 only (B) 55 only (C) both 5 and 55 (D) neither 5 nor 55

G-4. The reaction, X + 2Y + Z ! N occurs by the following mechanism(i) X + Y M very rapid equilibrium

(ii) M + Z ! P slow(iii) O + Y ! N very fastWhat is the rate law for this reaction

(A) Rate = k[Z] (B) Rate = k[X] [Y]2 [Z] (C) Rate = [N] (D) Rate = k[X] [Y] [Z]

G-5. In the Lindemann theory of unimolecular reactions, it is shown that the apparent rate constant for such a

reaction is kapp = C1

Ck167

where C is the concentration of the reactant k1 and 6 are constants. Calculate the

value of C for which kapp has 90% of its limiting value at C tending to infinitely large values, given 6 = 9 x 105.(A) 10"6 mole/litre (B) 10"4 mol/litre (C) 10"5 mole/litre (D) 5 x 10"5 mol/litre

G-6. Trimolecular reactions are uncommon because(A) the probability of three molecules colliding at an instant is very low.(B) the probability of three molecules colliding at an instant is high.(C) the probability of three molecules colliding at an instant is zero.(D) the probability of many molecules colliding at an instant is high.

G-7. Select the correct statements :(A) the molecularity of an elementary reaction indicates how many reactant molecules take part in the step.(B) the rate law of an elementary reaction can be predicted by simply seeing the stoichiometry of reaction.

(C) the slowest elementary step in sequence of the reactions governs the overall rate of formation of product.(D) a rate law is often derived from a proposed mechanism by imposing the steady state approximation orassuming that there is a pre-equilibrium.

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Section (H) : Complications in first order reactions

H-1. For an elementary reaction, net rate is , -

./0

1 dt

dx = k[A]2 – k'[C] [B]2 then, select the correct statement :

(A) –dt

]A[d 2=

dt

]B[d 2=

dt

]C[d is the relation among (B) 2A 2B + C is the required reaction

(C) both are correct (D) none is correct

H-2. Consider the elementary reaction sequence shown in figure. Which of the following

equations are correct ?

(A)dt

]A[d= "k1[A] + k4[D] (B) dt

]C[d= k2[B] " k3[C]

(C)dt

]D[d = k4[D] + k3[D] (D) Nothing can be said about order of reactions in this problem

H-3. For an elementary reaction of reversible nature, net rate is :

, -

./0

1 dt

dx= k1 [A]

2 [B]1 – k2 [C], hence, given reaction is :

(A) 2A +B

1 C (B) 2A + B C (C) 2A C + B –1 (D) None of these

H-4. At a given temperature, k1 = k2 for the reaction

A + B C + D

If $%

&'(

)dt

dx= k1 [A] [B] – k2[C] [D] in which set of the concentration reaction ceases?

[A] [B] [C] [D] [A] [B] [C] [D]

(A) 0.1 M 0.2 M 0.3 M 0.4 M (B) 0.4 M 0.25 M 0.2 M 0.5 M

(C) 0.2 M 0.2 M 0.3 M 0.2 M (D) 0.2 M 0.2 M 0.4 M 0.2 M

H-5. The substance undergoes first order decomposition. The decomposition follows two parallel first order reactions

as :

K1 = 1.26 × 10 –4 sec –1 and K2 = 3.8 × 10

–5 sec –1

The percentage distribution of B and C

(A) 80% B and 20% C (B) 76.83% B and 23.17%C

(C) 90% B and 10% C (D) 60% B and 40% C

H-6. The rate constant for two parallel reactions were found reactions were found to be 1.0 × 10 –2dm3 mol-1 s –1 and

3.0 × 10 –2 dm3 mol –1 s –1. If the corresponding energies of activation of the parallel reactions are 60.0 kJ mol –1

and 70.0 kJ mol –1 respectively, what is the apparent overall energy of activation ?

(A) 130.0 kJ mol –1 (B) 67.5 kJ mol –1 (C) 100.0 kJ mol –1 (D) 65.0 kJ mol –1

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PART - II : MISCELLANEOUS QUESTIONS

COMPREHENSION

Comprehension # 1

A(g) #! # 2B(g) + C(g)

Initially at t = 0 gas A was present along with some amount of gas (C). At t = 0 mole fraction of gas C is

1/3. After some time t = t1, total pressure is half of the final total pressure at t = t

x (a very long time). Assume this

decomposition is a first order, at a constant temperature. It is also given at t = tx, final total pressure is 35 bar.

1. At t = t1 pressure of gas B is :

(A) 2.5 bar (B) 1.25 bar (C) 5.0 bar (D) data is insufficient

2. Rate constant (k) = (log 64 – log 49) s –1. Value of t1 in seconds is :

(A) 2.15 s (B) 1.5 s (C) 2.3 s (D) 1.15 s

3. Ratio of rate constant at t = 0 to t = t1 to t = t

x is :

(A) 2 : 3 : 4 (B) 1 : 1 : 1 (C) 1 : 3 : 5 (D) 1 : 3 : 5

Comprehension # 2

4. For the (Set-1) :

(A) if T1 > T

2, k

1 > k

2 always (B) if T

1 > T

2, k

1 > k

2 (for exothermic reaction)

(C) if T1 > T

2, k

1 < k

2 (for endothermic reaction) (D) Ea

1 8 Ea

2

5. For the (Set-1) :

(A) Ea1 > Ea

2if T

1 > T

2(B) Ea

1 < Ea

2if T

1 > T

2

(C) Ea1 = Ea2 (D) Ea1 = 0.5 Ea2

6. Comparing set-I and II :

(A) k4 > k

3& k

2 > k

1, if T

2 > T

1 (endothermic) (B) k

4 < k

3& k

2 > k

1, if T

2 < T

1 (endothermic)

(C) k4 > k

3& k

2 > k

1, if T

2 < T

1 (exothermic) (D) k

4 < k

3& k

2 < k

1, if T

2 > T

1 (exothermic)

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Comprehension # 3

A reaction is said to be first order if it's rate is proportional to the concentration of reactant. Let us consider a

reaction

A(g) #! B(g) + C(g)At t = 0 a 0 0

At time t a – x x x

The rate of reaction is given by the expression dt

dx

= k(a –

x) and integrated rate equation for a given reaction is

represented as k =t

1 l n ,

-

./0

1 " xaa

where a = initial concentration and (a – x) = concentration of A after time t.

7. Thermal decomposition of compound X is a first order reaction. If 75% of X is decomposed in 100 min. How long

will it take for 90% of the compound to decompose?

Given : log 2 = 0.30

(A) 190 min (B) 176.66 min (C) 166.66 min (D) 156.66 min

8. Consider a reaction A(g) #! 3B(g) + 2C(g) with rate constant 1.386 × 10 –2 min –1. Starting with2 moles of A in 12.5 litre vessel initially, if reaction is allowed to takes place at constant pressure & at 298K thenfind the concentration of B after 100 min.

(A) 0.04 M (B) 0.36 M (C) 0.09 M (D) None of these

Comprehension # 4

Competing First-Order Reactions

Frequently a species can react in different ways to give a variety of products. For example, toluene can be

nitrated at the ortho, meta, or para positions, We shall consider the simplest case, that of two competing

irreversible first-order reactions :

A # #! # 1k C and A # #! # 2k Dwhere the stoichiometric coefficients are taken as unity for simplicity. The rate law is

, -

./0

1 dt

]A[d= – k

1[A]

– k

2[A]

= – (k

1 + k

2) [A] 9 [A] = [A]

0t)kk( 21e 7" .

For C, we have , -

./0

1 dt

]C[d = k

1[A] = k

1[A]

0t)kk( 21e 7" . Multiplication by dt and integration from time 0

(where [C]0 = 0) to an arbitary time t gives [C] = )e1(

kk

]A[k t)kk(

21

01 217""7

Similarly, integration of , -

./0

1 dt

]D[d gives [D] =

21

02

kk

]A[k

7(1 – t)kk( 21e 7" )

The sum of the rate constants k1 + k2 appears in the exponentials for both [C] and [D].

At any time we also have]D[

]C[ =

2

1

k

k

9. A starting initially with only A Which of the following is correct at time t

(A) [A]0 = [A]

t +[B]

t + [C]

t(B) [A]

0 = [A]

t + 2 [B]

t + 3 [C]

t

(C) [A]0 = [A]

t +

2

]B[ t +

3

]C[ t(D) [A]

0 =

3

2[A]

t +[B]

t + [C]

t

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10. X starting with only 'X', ratiott

t

]Z[]Y[

]X[

7

(A) Independent of time (B))1e(

1kt "

(C) Depends upon initial concentration of X (D) [A]0 (ekt –1)

11. At high temperature acetic acid decomposes into CO2 & CH

4 and simultaneously into CH

2CO (ketene) and H

2O

(i) CH3COOH # # # ! #

": 11 s3k CH4 + CO

2(ii) CH

3COOH # # # ! #

": 12 s4k CH2CO + H

2O

What is the fraction of acetic acid reacting as per reaction (i) ?

(A)4

3(B)

7

3(C)

7

4(D) none of these

12. For A starting with pure A ratio of rate of production of B to C is

(A) Independent of time (B) Independent of temperature

(C) Depends upon initial concentration of A (D) Independent of mechanism of reaction

Comprehension # 5

For the given sequential reaction

A #! # 1k B #! # 2k Cthe concentration of A, B & C at any time 't' is given by

[A]t =

tk

01

e]A[ "

; [B]t = )k k (

]A[k

12

01

" ; <tk tk

21 ee ""

"[C]t = [A0] – ( [A]t + [B]t )

13. The time at which concentration of B is maximum is

(A)

12

1

k k

k

"(B)

2

1

12 k

k ln

k k

1

"(C)

2

1

21 k

k ln

k k

1

"(D)

12

2

k k

k

"

14. Select the correct option if k1 = 1000 s –1 and k2 = 20 s

–1.

(A)

[C]t

[B]t[A]t

c o n c .

time

(B)

[A]t[B]t

[C]t

C o n c .

time

(C)

[A]t[B]t

[C]t

C o n c .

time

(D)

[A]t

[B]t

[C]t

C o n c .

time

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18. Match the following :

Column-I Column-II

(A) If the activation energy is 65 kJ then how much time (p) 2

faster a reaction proceed at 25°C than at 0°C

(B) Rate constant of a first - order reaction is 0.0693 min –1. (q) Zero

If we start with 20 mol L

–1

, it is reduced to 2.5 mol L

–1

in how many minutes

(C) Half - lives of first - order and zero order reactions (r) 11

are same. Ratio of rates at the start of reaction is

how many times of 0.693 Assume initial concentration to

be same for the both.

(D) The half-life periods are given , (s) 30

[A]0

(M) 0.0677 0.136 0.272

t1/2

(sec) 240 480 960

order of the reaction is

ASSERTION / REASONDirections :

Each question has 5 choices (A), (B), (C), (D) and (E) out of which ONLY ONE is correct.

(A) Statement-1 is True, Statement-2 is True; Statement-2 is a correct explanation for Statement-1.

(B) Statement-1 is True, Statement-2 is True; Statement-2 is NOT a correct explanation for Statement-1.

(C) Statement-1 is True, Statement-2 is False.

(D) Statement-1 is False, Statement-2 is True.

(E) Statement-1 and Statement-2 both are False.

19. Statement-1 : A fractional order reaction must be a complex reaction.

Statement-2 : Fractional order of RDS equals to overall order of a complex reaction.

20. Statement-1 : The time of completion of reactions of type A ! product (order


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25. Statement-1 : In the reaction, 52 + 2S

2O

32 – ! S

4O

62 – + 25 – , the rate of disappearance of thiosulphate ions is

twice the rate of disappearance of 52.

Statement-2 : The rate of disappearance of 52is twice the rate of disappearance of S

2O

32 – ions.

26. Statement-1 : For A + 2B #! # C (rate= K[A]1[B]0), the half life time of reaction is only defined when conc.

of A and B are in stoichiometric ratio

Statement-2 : For above given order half life of reaction is directly proportional to conc. of A and not to conc. of B due to its zero order.

27. Statement-1 : Many reactions occurring on solid surface are zero order reactions.

Statement-2 : 22

Au2 O2 / 1)g(N)g(ON 7 # #! # ; rate = k[N2O]

0 = k = constant is a zero order reaction.

28. Statement-1 : Half life of a certain radioactive element is 100 days. After 200 days, fraction left undecaye

will be 25%.

Statement-2 :

n

0

t

2

1

C

C, -

./0

1 : , where symbols have standard meaning.

29. Statement-1 : Time taken for the completion of 75% of a 5st order reaction is double than its t½.

Statement-2 : Time taken for completion of any fraction of a 5st order reaction is a constant value.

30. Statement-1 : If the activation energy of reaction is zero temperature will have no effect on the rate constant

Statement-2 : Lower the activation energy faster is the reaction

TRUE / FALSE

31. Order of a reaction can be written from the balanced chemical equation.

32. In a complex reaction the rate of overall reaction is governed by the slowest step.

33. If t1/2

for a first order reaction is 6.93 s, the value of rate constant for the reaction would be 10s –1.

34. Molecularity of a reaction is always whole number.

35. Order and molecularity of a single step reaction may or may not be same.

36. The activation energy of a catalysed reaction is more than the activation energy of the uncatalysed reaction.

37. For a zero order reaction t3/4 is related to t1/2 as t3/4 = 1.5 t1/2

38. The rate of an exothermic reaction increases with the rise in temperature.

39. Partial orders are never negative.

40. Order of reaction may be change with change in practical conditions

41. The rate of reaction is uniform in zero order reaction.

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42. The rate law of the elementary reaction; 3A #! B must be r = k [A]3

43. If the partial orders are equal to corresponding coefficients in the balanced reaction, the reaction must be

elementary.

44. Every species that appears in the rate law of reaction must be a reactant or product in that reaction.

45. Molecularity defined only for RDS.

46. Product can form only when the required orientation and energy conditions are met.

47. Activated complex is an intermediate product.

48. The pre-exponential factor A has the same units for all reactions.

49. All collisions between reactants yield the desired product.

50. If the partial orders differ from the coefficients in the balanced reaction, the reaction must be complex.

51. The rate of the reaction A ! B having the rate law , -

./0

1 :" ]B[]A[k

dt

]A[d when plotted against time will exhibit a

maximum at some time.

52. For a first order reaction, the time required to reduce successively the concentration of reactant by a constant

fraction is always same.

53. As a first order reaction proceeds at a constant temperature, the rate remains constant.

54. If concentration of catalyst appear in rate law (rate = k [catalyst]1 [reactant]1) then it may becomes pseudo first

order reaction during the reaction.

55. Larger the value of Ea , greater is the effect on the value of k for a given temperature change.

56. A catalyst in a chemical reaction decreases the activation energy of the forward reaction and increases the

activation energy of the reverse reaction

57. A catalyst in a chemical reaction increases the forward Ea and decreases the backward E

a

58. A catalyst in a chemical reaction decreases both forward and backward Ea

59. At lower temperature, increase in temperature cause more change in the value of k than at higher temperature.

60. Molecularity of a reaction may includes the number of product molecules taking part in the reaction.

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FILL IN THE BLANKS

61. For collision to be effective the energy possessed by the colliding molecules should be equal to or greater than

the ____________.

62. In the reaction, H2 + I2 #! 2HI, the rate of disappearance of H2 is _______ the rate of appearance of HI.

63. For an endothermic process, the minimum value of activation energy can be _______.

64. The rate of a reaction is ________ to the collision frequency.

65. The rate constant for the zero order reaction has the dimensions___________.

66. The reactions with molecularity more than three are _________.

67. A catalyst increases the rate of the reaction by__________ activation energy.

68. If activation energy of reaction is low, it proceeds at _______ rate.

69. In a multistep reaction, the ________ step is rate determining.

70. Rate constant of a reaction __________ with increase in temperature.

71. The ratio t7/8 / t1/2 for a first order reaction would be equal to _________.

72. For a zero order reaction, the rate of the reaction is equal to the ______ of the reaction.

73. The value of temperature coefficient is generally between _________.

74. For a certain reaction, xM #! yL, the rate of reaction increases by 4 times when the concentration of M isdoubled. The rate law is _________.

75. The rate equation r = k [A][B]1/2 suggests that order of overall reaction is _______.

76. A plot of [A] vs t for a certain reaction A #! B with r = k [A]0 will be a straight line with slope equal to ________.

77. [Eactivated complex –

Ereactants] = ____________.

78. In the Arrhenius equation k = Aexp ( –E/RT), A may be termed as the rate constant at __________.

79. For a ______ order reaction the half-life (t1/2) is independent of the initial conc. of the reactants.

80. For a first order reaction A #! P, a graph of log [A] vs t has a slope equal to __________.

81. A catalyst is chemically ____________ at the end of a reaction

82. The order of a reaction is the ________ of the _________ of all the concentration terms in the rate equation.

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PART - I : MIXED OBJECTIVE

Single Choice Type

1. Consider the reaction :

A #! B + CInitial concentration of A is 1 M. 20 minutes time is required for completion of 20 % reaction.

Ifdt

]B[d = k[A], then half life (t

1/2) is

(A) 55.44 min. (B) 50 min (C) 62.13 min (D) None of these

2. If decomposition reaction A (g) #! B (g) follows first order kinetics then the graph of rate of formation (R) of B

against time t will be

(A) (B) (C) (D)

3. For the first order decomposition of SO2Cl2(g),

SO2Cl

2(g) ! SO

2(g) + Cl

2(g)

a graph of log (a0 – x) vs t is shown in figure. What is the rate constant (sec –1)?

-1 –

-2 –

-3 –

2 4 6 8 10| | | | |

l o g ( a – x )

0

Time (min) !

(0,0)

(A) 0.2 (B) 4.6 × 10 –1 (C) 7.7 × 10 –3 (D) 1.15 × 10 –2

4. The rate constant for the forward reaction A (g) + 2B(g) is 1.5 × 10 –3 s –1 at 100 K. If 10 –5 moles of A and 100moles of B are present in a 10 litre vessel at equilibrium then rate constant for the backward reaction at this

temperature is :

(A) 1.50× 104 L mol –1 s –1 (B) 1.5 × 1011 L mol –1 s –1

(C) 1.5 × 1010 L mol –

1 s –

1 (D) 1.5 × 10 –

11L mol –

1 s –

1

5. Reaction A + B #! C + D follows following rate law : rate = 21

2

1

]B[]A[k 7

. Starting with initial conc. of 1 M of

A and B each, what is the time taken for concentration of A of become 0.25 M.

Given : k = 2.303 × 10 –3 sec –1.(A) 300 sec. (B) 600 sec. (C) 900 sec. (D) 1200 sec.

6. The reaction A (g) #! B(g) + 2C (g) is a first order reaction with rate constant 3465 × 10 –6 s –1. Starting with0.1 mole of A in 2 litre vessel, find the concentration of A after 200 sec., when the reaction is allowed to take

place at constant pressure and temperature.

(A) 0.05 M (B) 0.025 M (C) 0.0125 M (D) None of these

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7. The variation of concentration of A with time in two experiments starting with two different initial concentration of

A is given in the following graph. The reaction is represented as A(aq) #! B(aq). What is the rate of reaction(M/min) when concentration of A in aqueous solution was 1.8 M?

0.6

0.8

11.2

1.5

5 10 15 20

Experiment-1

Experiment-2

time(min.)!

C o n c e n t r a t i o n ( M ) !

(A) 0.08 M min –1 (B) 0.036 M min –1 (C) 0.13 M min –1 (D) 1 M min –1

8. In respect of the equation k = A exp ( – Ea / RT), which one of the following statements is correct?(A) R is Rydberg's constant (B) k is equilibrium constant

(C) A is adsorption factor (D) Ea is the energy of activation

9. Rate of a reaction can be expressed by Arrhenius equation as :k = Ae –E/RT

In this equation, E represents

(A) The fraction of molecules with energy greater than the activation energy of the reaction

(B) The energy above which all the colliding molecules will react

(C) The energy below which colliding molecules will not react

(D) The total energy of the reacting molecules at a temperature, T

10. The rate constant, the activation energy and the Arrhenius parameter (A) of a chemical reaction at 25°C are

3.0 × 10 –4 s –1, 104.4 kJ mol –1 and 6.0 × 1014s –1 respectively. The value of the rate constant at T ! 4 is(A) 2.0 × 1018 s –1 (B) 6.0 × 1014 s –1 (C) infinity (D) 3.6 × 1030 s –1

11. A first order reaction is 50% completed in 20 minutes at 27°C and in 5 min at 47°C. The energy of activation of the reaction is

(A) 43.85 kJ/mol (B) 55.14 kJ/mol (C) 11.97 kJ/mol (D) 6.65 kJ/mol

12. For the first order reaction A —! B + C, carried out at 27 ºC if 3.8 × 10 –16 % of the reactant molecules existsin the activated state, the E

a (activation energy) of the reaction is [log 3.8 = 0.58]

(A) 12 kJ/mole (B) 831.4 kJ/mole (C) 100 kJ/mole (D) 88.57 kJ/mole

13. For a certain reaction of order n, the time for half change, t1/2, is given by t1/2 =2 / 1

0xC

k

)22( " where k is

constant and C0 is the initial concentration. What is n?(A) 1 (B) 2 (C) 0 (D) 0.5

14. Given that for a reaction of order n, the integrated form of the rate equation is k =$$

%

&

''

(

)"

" "" 1n0

1n C

1

C

1

)1n(t

1 where C0

and C are the values of the reactant concentration at the start and after time t. What is the relationship between

t3/4 and t1/2 where t3/4 is the time required for C to become 1/4 C0?

(A) t3/4 = t1/2 [2n"1 + 1] (B) t3/4 = t1/2 [2

n"1 " 1](C) t3/4 = t1/2 [2

n+1 " 1] (D) t3/4 = t1/2 [2n+1 + 1]

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15. In three different reactions, involving a single reactant in each case, a plot of rate of the reaction on the y"axis,versus concentration of the reactant on the x"axis, yields three different curves shown below.

(i) (ii) (iii)

What are the possible orders of the reactions (i), (ii), (iii).

(A) 1, 2, 3 (B) 2, 1, 1/2 (C) 0, 1, 2 (D) 0, 1, 1/2

16. The time elapsed of a certain between 33% and 67% completion of a first order reaction is 30 minutes. What is

the time needed for 25% completion?

(A) 150.5 minutes (B) 12.5 minutes (C) 180.5 minutes (D) 165.5 minutes

17. A reaction 2A + B #! # k

C + D is first order with respect to A and 2nd order with respect to B. Initial conc.

(t = 0) of A is C0 while B is 2C0. If at t as 30 minutes the conc. of C is C0 /4 then rate expression at t = 30 minutes is :

(A) R = 7 C03 k/16 (B) R = 27 C0

3 k / 32 (C) R = 247 C03 k / 64 (D) R = 49 k C0

3 / 32

18. For a certain reaction, a plot of {[C0 – C] / [C]} against the time t, yields a straight line. C0 = initial conc. of the

reactant and C is the reactant concentration after time t. What is the order of the reaction :

(A) 3 (B) zero (C) 1 (D) 2

19. In a I order reaction A #! products, the concentration of the reactant decrease to 6.25% of its initial value in 80minutes. What is (i) the rate constant and (ii) the rate of the reaction, 100 minutes after the start, if the initial

concentration is 0.2 mole/litre?

(A) 2.17 × 10"2 min"1, 3.47 × 10"4 mol.litre"1 min"1

(B) 3.465 × 10"2 min"1, 2.166 × 10"4 mol.litre"1 min"1

(C) 3.465 × 10"3 min"1, 2.17 × 10"3 mol.litre"1 min"1

(D) 2.166 × 10"3 min"1, 2.667 × 10"4 mol.litre"1 min"1

20. At 373 K, a gaseous reaction A ! 2B + C is found to be of first order. Starting with pure A, the total pressure atthe end of 10 min. was 176 mm and after a long time when A was completely dissociated, it was 270 mm. The

pressure of A at the end of 10 minutes was :

(A) 94 mm (B) 47 mm (C) 43 mm (D) 90 mm

21. The reaction A(s) ! 2 B(g) + C(g) is first order. The pressure after 20 min. and after very long time are 150 mmHg and 225 mm Hg. The value of rate constant and pressure after 40 min. are :

(A) 0.05 In 1.5 min –

1, 200 mm (B) 0.5 ln 2 min –

1 ,300 mm(C) 0.05 In 3 min –1, 300 mm (D) 0.05 In 3 min –1 , 200 mm

22. The reaction [Co (NH3)5Br]2> + H2O #! [Co(NH3)5(H2O)]

3+ + Br " is followed by measuring a property of the

solution known as the optical density of the solution which may be taken to be linearly related to the concentration

of the reactant. The values of optical density are 0.80, 0.35 and 0.20 at the end of 20 minutes, 40 minutes and

infinite time after the start of the reaction which is first order. Calculate the rate constant.

(A) 6.93 x 10"3 min"1 (B) 3.51 x 10"2 min"1 (C) 6.93 x 10"2 min"1 (D) 3.51 x 10"3 min"1

23. The inversion of cane sugar proceeds with half life of 50 minute at pH = 5 for any concentration of sugar. However

if pH = 6, the half life changes to 500 minute of any concentration of sugar . The law expression for sugar

inversion can be written as :(A) r = K [sugar]2 [H+]0 (B) r = K [sugar]1 [H+]0 (C) r = K [sugar]1 [H+]1 (D) r = K [sugar]0 [H+]0.

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24. The reaction A #! # k

Products, is zero order while the reaction B #! # k

Products, is 1st order. For what initial

concentration of A the half lives of the two reactions are equal.

(A) 2 M (B) ln 2 M (C) 2 log 2 M (D) 2 ln 2 M

25. For the reaction 3A ! Products the value of k = 1 × 10 –3 ! / (mol –min) the value of – d[A] / dt inmol/lt-sec when [A] = 2M is :

(A) 6.67 × 10 –3

(B) 1.2 × 10 –2

(C) 2 × 10 –4

(D) 4 × 10 –3

26. Two I-order reactions have half-lives in the ratio 3 : 2. Calculate the ratio of time intervals t1 : t2. Where t1 is the

time period for 25% completion of the first reaction and t2, for 75% completion of the second reaction.

(A) 0.311 : 1 (B) 0.420 : 1 (C) 0.273 : 1 (D) 0.199 : 1

27. The Arrhenius relationship of two different reactions is shown below. Which reaction is

faster at a lower temperature and which is more sensitive to changes of temperature ?

(A) B faster, A more sensitive (B) B in both cases

(C) A in both cases (D) A faster, B more sensitive

28. When a graph between log K and 1/T is drawn a straight line is obtained. The point at which line cuts y -axis and

x -axis respectively correspond to the temp :

(A) 0, Ea / 2.303 R log A (B) 4, Ea / (R ln A)(C) 0, log A (D) None of these

29. A ! B KA = 1015 e –2000/T ;

C ! D KC = 1014 e –1000/T

Temperature T K at-which (KA = KC) is :

(A) 1000K (B) 2000K (C) (2000 / 2.303) K (D) (1000 / 2.303) K.

30. The rate of a reaction gets doubled when the temperature changes from 7ºC to 17ºC. By what factor will itchange for the temperature change from 17ºC to 27ºC?

(A) 1.81 (B) 1.71 (C) 1.91 (D) 1.76

31. For the reaction A + 2B ! products(started with concentrations taken in stoichiometric proportion), the

experimentally determined rate law is – dt

]A[d = k ]A[ ]B[ . The half time of the reaction would be :

(A)k

693.0(B)

k / 1

693.0(C)

k2

693.0(D) not defined

32. For a reaction 2A + B ! product, rate law is –dt

]A[d = k[A]. At a time when t =

k

1, concentration of the reactant

is : (C0 = initial concentration)

(A)e

C0 (B) C0e (C) 20eC (D)

0C1

33. Concentration of the reactant in first-order is reduced to 2e

1after : (Natural life =

K

1)

(A) one natural life-time (B) two-natural life-time

(C) three natural life-time (D) four natural life-time

34. If for a reaction in which A(g) converts to B(g) the reaction carried out at const.

V & T results into the following graph.

(A) then the reaction must be A(g) ! 3B(g) and is a first order reaction.(B) then the reaction must be A(g) ! 3B(g) and is a second order reaction.(C) then the reaction must be A(g) ! 3B(g) and is a zero order reaction.(D) then the reaction must be A(g) ? 3B(g) and is a first order reaction.

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35. The instantaneous rate of disappearance of the MnO4 – ion in the following reaction is 4.56 × 10 –3 ms –1. Then the

rate of appearance of 52 is :2MnO4

– + 10 5 – + 16H+ ! 2Mn2+ + 552 + 8H2O2MnO4

– + 10 5 – + 16H+ ! 2Mn2+ + 552 + 8H2O(A) 1.14 × 10 –3 Ms –1 (B) 5.7 × 10 –3 Ms –1 (C) 4.56 × 10 –4 Ms –1 (D) 1.14 × 10 –2 Ms –1

36. Consider the following reactions at 300 K. A ! B (uncatalysed reaction). BA catalyst # # # ! # (catalyst reaction)

The activation energy is lowered by 8.314 KJ mol –1 for the catalysed reaction. How many times the rate of thiscatalysed reaction greater than that of uncatalysed reaction ? (Given e3.33 = 28)

(A) 15 times (B) 38 times (C) 22 times (D) 28 times

37. The conversion of vinyl allyl ether to pent-4-enol follows first-order kinetics.

The following plot is obtained for such a reaction. The rate constant for the

reaction is

(A) 4.6 × 10 –2 s –1

(B) 1.2 × 10 –2 s –1

(C) 2.3 × 10 –2 s –1

(D) 8.4 × 10 –2 s –1

38. A substance ‘ A' decomposes in solution following the first order kinetics. Flask 5 contains 1 L of 1 M solution ofA and flask 55 contains 100 ml of 0.6 M solution. After 8 hr, the conc. of A in flask 1 becomes 0.25 M. What willbe time for cone. of A in flask 55 to become 0.3 M ? :(A) 0.4 hr (B) 2.4 hr

(C) 4.0 hr (D) unpredictable as rate constant is not given

39. A simple mechanism for enzyme-catalyzed reaction is given by the following set of equations

E + S ES (enzyme) (reactant) (intermediate-1)

ES EP

(intermediate-1) (intermediate-2)

EP E + P (intermediate-2) (enzyme) (product)

This is known as the Michaelis –Menten mechanism. The potential energy diagram is shown in the fig. Whichof the following sets of identifications is correct ? (Assume that the temperature and pressure are constant).

(1) (2) (3) (4)

(A) E + P. EP ES E + S

(B) ES Activated complex EP Activated complex

(C) EP Activated complex ES Activated complex

(D) E + S ES EP E + P

More than one choice Type

40. For the reaction A ! B, the rate law expression istd

]A[d" = k [A]1/2. If initial concentration of [A] is [A]0, then

(A) The integerated rate expression is k = )AA(t

2 2 / 12 / 10

"

(B) The graph of A Vs t will be

(C) The half life period2 / 1

t =2 / 1

0]A[2

K

(D) The time taken for 75% completion of reaction4 / 3

t =k

]A[0

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41. Select incorrect statement(s):

(A) Unit of pre-exponential factor (A) for second order reaction is mol L –1 s –1.

(B) A zero order reaction must be a complex reaction.

(C) Molecularity is defined only for RDS in a complex reaction.

(D) Decay constant (@) of radioactive substance is affected by temperature.

42. In a consecutive reaction system A #! # 1E B !2E C when E1 is much greater than E2, the yield ofB increase with

(A) increase in temperature (B) decreases in temperature

(C) increase in initial concentration of A (D) decrease in initial concentration of A

43. Which of the following is/are correct statement?

(A) Stoichiometry of a reaction tells about the order of the elementary reactions.

(B) For a zero order reaction, rate and the rate constant are identical.

(C) A zero order reaction is controlled by factors other than concentration of reactants.

(D) A zero order reaction is always elementary reaction.

44. Which of the following statement is incorrect ?

(A) The order of reaction is the sum of powers of all the concentration terms in the rate equation.(B) The order of reaction with respect to one reactant is the ratio of the change of logarithm of the rate of the

reaction to the change in the logarithm of the concentration of the particular reactant, keeping the concentrations

of all other reactants constant.

(C) Orders of reactions can not be fractional.

(D) The order of a reaction can only be determined from the stoichiometric equation for the reaction.

45. Consider the decay of P to A and B by two parallel first order reactions as shown in Fig. Given

Reaction 3H Rate constant Energy of activation

P ! A 3HA kA EA

P ! B 3HB kB EB

Which of the following is(are) true?

(A) a = EB (B) b = EA (C) 3HA = b " d (D) 3HB = c " a

PART - II : SUBJECTIVE QUESTIONS

1. The oxidation of iodide ion by peroxy disulphate ion is described by the equation :

35 –

(aq) + S2O82 –

(aq)

#! # 53 –

(aq) + 2SO42 –

(aq)

(a) If –t

]OS[ 282

3

3 " = 1.5 × 10 –3 Ms –1 for a particular time interval, what is the value of –

t

][

3

53 " for the same time

interval ?

(b) What is the average rate of formation of SO42 – during that time interval ?

2. In the following reaction 2H2O2 (aq) #! # 2H2O (!) + O2 (g) rate of formation of O2 is 36 g min –1 ,

(a) What is rate of formation of H2O.

(b) What is rate of disappearance of H2O2.

3. The reaction 2NO(g) + Cl2(g) #! 2NOCl(g) is second order in NO and first order in Cl2. In a volume of2 dm3, 5 mole of nitric oxide and 2 mol of Cl2 were brought together, and the initial rate was 2.4 × 10

" 3 mole

dm"3 s"A. What will be the rate when half of the chlorine has reacted ?

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12. The decomposition of Cl2O7 at 400 K in gaseous phase to Cl2 and O2 is of 5 order reaction. After 55 sec at 400

K, the pressure of reaction mixture increases from 0.62 to 1.88 atm. Calculate the rate constant of given

reaction, also calculate the pressure of reaction mixture after 100 second.

[Given : !n13

31= 0.869, e1.58 = 4.858] CI

2O

7(g) # # ! # CI

2 (g) +

2

7O

2 (g)

13. For a homogeneous gaseous phase reaction 2A ! 3B + C the initial pressure was P0 while pressure after time

't' was P. Find the pressure after time '2t'.

IIT JEE Main Advanced Physical Chemistry 12th Chemical Kinetics

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Transcript of IIT JEE Main Advanced Physical Chemistry 12th Chemical Kinetics