USHA's +2 Chemistry (2nd Year) 49

VESVEV
CHEMICAL KINETICS
Chapter at aGlance
reaction :
Rate of H, + I, ’ 2HI( Bimolecular)
with which reactants are converted
It is the speed sec
into product. Its unit is mol lit 2SO, +O, ’ 2S0,(trimolecular)
o
measuredlover along time interval,
When the rate of reaction. Order of reaction :
is called average rate of powers of molar
It is defined as the sum of the
equation of the
Ax Concentration terms in the rate
= average rate of reaction Order
i.e.
At reaction. It is determined experiemnentally.
or zero. Its
number
Ax decrease in conc, of reactan t may be an integer, a fractional
value rarely exceeds three.
time taken
Suppose rate law for a reaction is
At

Ax increase in conc. of product

or t
At time taken Rate =k[A]'(B}'
When rate is measured over a small time interval. order of the reaction = 1 +2 =3
Acidic hydrolysis of ester is an example of pseudo
is called as instantaneous rate of reaction. So, rate hydrolysis of ester
first order reaction, while alkali
dx dx reaction. The
of reaction = or + is an example of 2nd order a
dt dt decompositon of NH, on Molybdenum surface is
hot quartz (Sio,),
dx change in conc, of reac tant zero order reaction. where as on
time int erval it is a 1st order reaction.
dt
Rate expression :
dx change in conc. of product For a reaction aA +bB’cC, the
rate of reaction
+
time int erval in
can be determined by studying the change
or dt

concentration of any one of the reactant or product.

Rate constant:
when concentation of So rate of reaction =
It is equal to rate of reaction called as specific
cach reactant is unity.It is also 1d[A]__1 dB]_1d[c]
reaction rate. c dt
dt b dt
Factors affecting rate of reactions
(i) Nature of reactant e.g. N, +3H, ’ 2NH,
Rate of reaction =
(ii) Concentation of reactant
(iii) Temperature d|N;]_1dH,] 1d[NH,]
dt 3 dt 2 dt
(iv) Catalyst
(V) Surface area of reactant Rate equation :
For zero order reaction,
(vi) Radiation
Molecularity of reaction: X

reactant molecules taking part k=*t

t 1s the number of reaction. It is a theoritical For lst order reactio,
n a single step of the an integer and never
COncept. Molecularity is always is very rare. 2.303
Zero. Molecularity higher than 3 k=
t log
e.g. PCI, ’ PCI, +CI, (unimolecular)
 50 +2 Sample Papers (2nd Year) USHAs
For 2nd order reaction, A = frequency factor or collision number
R&Thave their unsual notations.
X
k=-x The logarithimic form of the above equation can
t a(a-x) be written as
Where 'a' is the initial concentation of reactant and
'x' is the amount reacted after time 't'.
log
E¡ , -T
The unit of 'k' is k 2.303R| T,I,
mol--sec-! Where k, and k, are the rate constant at
where 'n' is the order of reaction. temperature T and T, respectively.
Half life period : Activation energy & Threshold energy:
The time required to reduce the concentration of The minimum amount of energy which the reactant
the reactant to one half of the initial concentration molecules must possess to make the collision
effective in order to give the product is konwn as
is called as half life period so% or t, threshold energy (E).
The energy required by the reactant molecules to
For a zero order reaction, cross the energy barrier or threshold energy in order
a to give the product is known as activation energy
t, =
2
2k (E,)
For a lst order reaction, E, =Eh-ER
0.693 & E, =E, -Ep
tË k
2 Where E,, and E. are the energy of reactant and
For a second order reaction,
product respectively. E, and E, are the activation
tË energy for forward and backward reaction
ka respectively.
2
Which means for zero order reaction half life period AH = E, -E,
is directly proportional to initial concentration and
Where AH = heat of reaction
for 2nd order reaction it is invesely proportional to
initial concentration of reactant. Half life period is If E, > E,, the reaction is endothermic.
independent of initial concentration of reactant for
first order reaction. If E, <E,, the reaction is exothermic.
A
Temperature co-efficient : The speed of a reaction For a lst order reaction when log (a - x) is plottea
Vs. time, a straight line is obtained whose slope
increases 2 - 3 times for each 10°C rise in
k
temperature. The ratio of the rate constants at two
(m) isequal to 2.303
different temperatures differing by 10°C is known
as temperature co-efficient. ie.e. Temperature co CH, -CHO ’ CO+CH,
efficient Kgsc =2 to 3. Rate =K[CH, -CHO}"
KzsC Order of this reaction is 3/2.
Arrhenius equation:The variation of rate constant This is a case of fractional order reaction. Otne
with tenmperature is represented by Arrhenius examples are
equation, K= Ae RT e=k[H,'(Br,
H, + Br, ’2HBr, Rate: order
Where K=rate constant of the reaction.
E, = energy of activation =l+
USHA's 2
Chemistry (2nd Year) 51
LIfetime : Where n no of half lives gone,
in which 98% of the renction is completed
The time A Initial amount
called life time of the renction, A, anount left after tíme 't'.
Timetaken for the completion of nth fraction of
reaction of Tst order is given by the expression. time taken
half life period
2.302 |og For a lst order reaction,
Amount of substance left after 'n' half lives ty9y% =0xts%

A, = tyg%, 3x tyo%

A
CHOOSE AND WRITE THE CORRECT ANSWER
x 10-5 sec.
The rate constant of areaction ís 2
The Arrhenius equation is 6.
the initial rate is
Ifthe initialconcentration is 0.1 M,
1.

(a) K AeRT (b) K=e RT (a) 2 x 104M sec (b) 2 x 10-ZM sec-!
RT (c) 2 x 106M sec-! (d) 2 x 10-"M sec-l
required for 99.9%
(c) K Ae RT (d) K Ae E 7. For a 1st order reaction, the time
activation completion is
Considering an exothermic rcaction, with competion
2 backward (a) ten times the time required for half
energy E, and E', for the forward and of reaction
reactions respectively, Now we can say (b) three times the tine
required for 90%
(a) E, = E, completion of reaction
required for 75%
(b) E, > E, (c) five times the time
completion of reaction
(c) E,<E,
more
(d) can't be predicted which is
(d) all are correct
reaction is 6.93
8 The half life period for a 1st order
3. When logK is plotted Vs for a 1st order reaction sec., its rate constant is
is equal to (a) 10 sec-! (b) 100 sec-l
we get a straight line.The slope of the line (d) 1sec-!
Ea (c) 0.1 sec-!
Ea example of
(a) 2.303R
(b) R Alkaline hydrolysis of ester is an
order reaction
2.303R Ea (a) 1st order reaction (b) 2nd
(C) (d) 2.303 zeroorder reactin
E, the (c)
2×10-2 mole lit-'sec. If (d) pseudo lst order
reaction
ror a reaction K= reactant is 1M, the half life
COncentration of the depends upon
10. The rate of a reaction
period of the reaction is (b) temperature
(a) concentration of reactant
(a) 20 sec (b) 25 sec
(c) 34.6 sec (d) 50 sec (d) all of these
product, increases by (c) catalyst
SThe rate of a reaction A-’ of'A' is increased 10 reaction depends upon
a factor of 100, when conc. 11. The rate constant of a
temperature (b) catalyst
fold, The order of the reaction is (a)
reactant (d) all of these
(a) 3 (b) 2 (c) nature of
(c) I (d) 0.5
 US
52 +2 Sample Papers (2nd Yea) USHA's
2N.0.
20. The rate constant for the reaction 2N,0,
12. For areaction, H0, ’ H0+0., +0. is 3x 105 sec-. If the rate is 2.4 x 10s M
sec-, the concentration of N,0, is
dH,0]K{[H,0.]
dt

dH,o] -K,[H,0,].
(a) 1.4 M (b) 0.04M
(d) 0.8 M
dt doK/H,0,]
The relation between K,, K, and K is
(c) 1.2 M
21. Which of the following curves represents Ist order
reaction ? 28.
(a) K -K, - K, (b) K,=K -2K,
(c) 2K,-4K - K, (d) 2K,-2K, =K,
th
13. The rate constant of a reaction is independent of (b)
(a)
(a) temperature (b) catalyst
(c) conc. of reactant (d) none of these
14. The unit of rate constant for 2nd order reaction is
(a) mole lit' sec (b) mole- lit sec-! 29.
(c) mole- lit' sec (d) molelit² sec (c) (d) t
15. Ifthe rate of formation of NH, for the reaction
N, + 3H, ’ 2NH, is 2 x 104 Msec-, the rate of
disappearance of hydrogen is 30.
(a) 1x 104M sec-! (b) 2x 10*M sec 22. Which equation gives relationship between rate
(c) 3x10+ M sec- (d) 6x 10M sec-! constant and tempeature ?
16. The half lifeperiod for a zero order reaction is equal (a) Ostwald's equation (b) Kirchoff's equation
to (c) Arrhenius equation (d) Nernst equation
0.693 23. At 25°C the half life of decomposition of H,0, is
(a) (b)
K 2K 50min. If initially 4M H0, is present, amount of 31
a H,0, left after 200 min is
(c) Ka
(d) K
1 (a) 2M (b) 0.5 M
17. For a lst order reaction log Kis plotted against T (c) 0.2SM (d) IM
and, the slope of the line is - 1.5x 10'K. The 24. The rate constant is numerically same for three
activation energy for the reaction would be reactions of lst, 2nd and 3rd order respectively. If
(a) 2872 J molei (b) 28.72 J mole conc. of the reactant is more than IM, which one is
(d) 1200 J mole-! 3
(c) 1914 J mole! true for the rates of the three reactions ?
18. Which of the following statements regarding (a) r, =, =I;
molecularity is wrong ?
(b) r,<I, <I,
(a) it is the number ofreactant molecules colliding (c) I,>, >I; (d) none of these
in asingle step of chemical reaction. 25. In the above question if conc. of the reactant is less 3
(b) it refers to individual step of the reaction. than 1 M, then
(c) it may be whole number or fractional (a) r=,=I, (b) r,<r, <I;
(d) the rate of reaction is independent of (c) r,>I,>, (d) none of these
molecularity. 26. A reaction X ’ product, completed s0% in 25
19. For a chemical change 2A+ 3B’ Product's the
rates w.r.t. A is r, and w.r.t. "B' is r,. The rates, r, min. If concentration of X is doubled, 50%
and r, are related as completed in 50 min, the order of the reaction is
(a) r, =I, (b) 2r, - 3r, (a) 0 (b) 1
(c) 3r, =2r, (d) r,-3r, (c) 2 (d) 3
USHA's 2 Chemistry (2nd 53
Year)
reaction involving two different reactants can 35. A catalyst has no effect on
A
27. never energy
be
(a) rate of forward reaction(b) activation
first order reaction (c) thershold energy (d) heat of reaction
(a)
6) unimolecular reaction
36. For the reaction, A+2B >C, the relative rate of
second order eaction
(c) reaction can be represented by
(d) bimolecular reaction
substance with half life period 4 days is taken to (a) =+ 1dB] dc]
A dt 2 dt dt
28. 12 days. The amount of substance
another placein
left now is
(b)
d[A]__dB]
=-2
1 dt dt dt
1
(b)
(a) 4 (c)
1 dt 2 dt dt
(d)
(C) 16 32
(d) +
1dB]
2 dt dt
29. For
every 10°C rise in temperature the rate of dt
times are as follows :
reaction increases nearly 37. The rate of reaction at different
(b) 2times 10 20 30
(a) 10 times time (sec)
1.51 x1021.49x10
(c) 5 times (d) 8 times rate(Msec)1.5x102 1.48x 10-2
H, The reaction is
30. The reaction CH,COOC,H, + H,0of (b) lst order
(a) zero prder
CH,COOH + C,H,-OH is an example (c) 2nd order (d) 3rd order
reaction
(a) zero order ’B, it is found that
38. For a chemical reaction A
(b) 1st order reaction the rate of reaction doubles
the conc. of A' is
when
(c) 2nd order reaction increased four times. The order of reaction is
(d) fractional order reaction (a) 0
(b) 0.5
log (a - x) is plotted Vs
31. For a lst order reaction (c) 1 (d) 2
line is obtained with slope
time, a straight zero order reaction is
39. The unit of rate constant for
K 2.303 (b) mole lit'sec-!
(a) sec-!
(a) (b) K
2.303
(c) mole-'lit sec-! (d) mole-'lit'sec-!
the rate = K[AJ/B]. The
K (d) -2.303 K 40. For a gaseous reaction suddenly
(c) 2.303 volume of the vessel containing the gas is
reaction is 2.5 x 10mole
J2. The rate constant ofa 1
lit sec-!. The order of the reaction is reduced to th of the initial volume. The rate of
4
(a zero (b) 1st rate would be
reaction relative to initial
(c) 2nd (d) 3rd
energy is
33. For a reaction, A ’B+ C, activation (b) 16
reaction is +5kJ/mole. (a)
1 kJ/mole and enthalpy of B+C
16
The activation energy for the reaction (c) 8
(d) same
1O
A is for a lst order reaction is
(b) 20 kJ/mole 41. The half life period 0.08 M
(a) 10 kJ/mole min. The initial amount of
the reactant was
15 kJ/mole instant is 0.01 M.The time
(c) 30 kJ/mole (d)
kJ mole and concentration at any
+25 taken for the reaction is
34, For the reaction A ’ B+ C.AH =
(b) 20 min
The activation energy for the reaction is (a)
10 min
(a) 25 kJ/mole (b) less than 25 kJ/mole (c) 30 min
(d) 40 min
of these
(c) more than 25 kJ/mole (d) none
 4. 3. 2. 1. 42.
(12.b) 11. (10.d) 9. 8 7. 6. (b)5. 54
41. 36. 31. 26. 21. 16. 11. 6. 1.
(c) (d) (b) (a)
(c) tempeature A
(d) (b) (K=
c) (d) (c) (b) (a) E,=AHE,-(c)
(c) (c) (c) (a) (b) (c) (d) (c) (c) 2. large
’ SoFor K= decrease
lowering increase
increase
allthesealof
l correctaralel Rate R,R_ It log
7.
Rate 10®= 2x2x10 2K
½ is E, EXPLANATORY
HINTS 42. 37. 32. 27. 22. 17. 12. increase
d[H,0]_,d[O,]
d[H,0,]_ of a K exothermic Ae
dt 0-693 = - is
these =K K[A]" zero (b) (a) (c) (b) (c) (a) (b) (d) (c)3.
K[A]=2 = 10 RTEa of in in indue
K[A" 2-303RT E,
[CH,COOC,H,] order =- 38. 33. 28. 23. 18. 13.
ANSWERS activation number
8. threshold number to in
’n=2 E, rate
6.93 0-693 x
10
dt x 1
reaction. reaction,
ve (39.b) 34.(ca) (29.b) 24.(bc) (19.c) (bc1)4. (C)9. (a)4.
105 = logA + or, of of of
=0-1sec 100 energyenergy
activated
molecular reaction
x +2
=25sec E AH
<
[NaOH] 0-1 (10.bd) (b) 5.
dt B, =- Sample
=2x106 for
40.(b) 35.(d) 30.(b) 25.(c) 20.(d) 15.(c) molecules.
collisions.
ve a
rise
of
Papers
27. I,>,>,
26.(a) (25.c) r,(24.=b) 23. 22.(C) 21.(b) t% 20. (19.c) 18.(c) (17.a) (16.b) (15.c) 14.(b) 13.(c)
(b) (a) (d) (2nd
a=
a,
unimolecular So
initial
conc.
Lya 200K=Ae Rate
Molecularity 2K a KA?Ratreactant
e conc.
= of
it
2-303R mole-l.lit.Sec-! = ’K=.
d[N,]
dt
is K[A],
,-3r,=2r,= 2 2 ’E,=2.303 1 E, -d[H;]_ 3
min=4 d[A] =2872
mole-! J dt Year)
zero K 3 dt
N,0,] -=1-5x
8.314
10x (Mol[AgT
order
r, Rate 3
reaction = half K is x 2
K dt3alvways d[H,] 1
[AJ', lives d[B] 1 1-5 10*=3x10Msec-!
x2x dt
reaction.
x
K[A} r,= 3x10-5 2-4x10-s a 102
whole d[NH,]
dt sec
=0-8M number. USHA's
 USHA's 2
Chemistry (2nd Year) 55

4,a ,
28. (b) 38, (b) R, K[4AJ" =2
2 timeg R, K[AJ"
29.(b)
b) Rate =K[CH,CO0C,H] ’4"=2’2= 2
Here, water is taken in large excess. n=0.5
Kt 39. (b) mole lit-'sec-!
-x)* + log a
31. (c) log(a 2-303 40. (b) Conc. of both Aand B is increased four times.
order reaction, unit of K= molel-n lit-
32 (c) For nth Since it is a 2nd order reaction, The rate of
Isec-'. reaction is increased to 42 = 16 times.
For endothermic reaction,
33. (a) 41. (c)
E, =E, -AH= 15-5=10k
kJ/mole
4. (c) more than 25 ’0-01=0-08x
heat of reaction
35. (d)
Or, n =3.
36. (c)
dA]1B_dg
dt 2 dt dt time taken=3 x t,=3x 10=30 min.
27 (a) Since rate of reaction is constant through out 42. (b) increase in number of activated molecules.
the reaction, it is a zero order reaction.

B VERY SHORT- TYPE QUESTIONS WITH ANSWERS

reaction.
rate of reaction 7. Give an example of zero order
1. According to Arrherius equation, Give reasons. Ans. Decomposition of ammonia giving nitrogen
increases with increase in temp. an
800° is
of and hydrogen in presence of Pt - catalyst at
Ans. With increase in temp. the kinetic energy example of zero order reaction.
number of effective
the molecules increases. So that
Hence rate of P
collision increases giving more product. 2NH, 300p N,+ 3H,
reaction increases. Rate = K[NHJ
to conc. of the
2. How is rate constant related 8. Express the rate of reaction for the reaction A, t
of reactants and
reactant ?
independent of conc. of 3B, ’ 2AB, in terms
Ans. Rate constant is products.
reactant. Ans. Rate of reaction

3. For areaction logK is plotted

Vs.,
T'
the slope dA,]_ 1dB,]_1dAB,]
dt 3 dt 2 dt
of the staright line is Define rate of reaction.
9.
amount of reactant
Ans. It is defined as the
Ans. Slope formed per unit time.
2.303R consumed or amount of product
influence the rate of dx
Write two factors which Rateof reaction =
(w.r.t. reactant)
reaction. dt
reactant and tempeature.
Ans. Concentration of order =+ dx
(w.r.t. product)
5. rate constant for 2nd
relationship between activation
What is the unit of dt
reaction ? 10. What is the
and threshold energy ?
energy
Ans. Mole- lit sec-. having rate
6. Calculate order of the reaction Ans. E, = E, - E, of reactant
Where E = activation energy
expression, rate = K[AB: E
= threshold energy
energy of reactant.
3 E, = average kinetic
Ans. Order =
2 2
 56 +2 Sample Papers (2nd Year) USHA's
11. Write the unit of rate of reaction. 20. Decomposition of H,0, takes place in the
Ans. mole lit-! sec-! following way
12. A subs tance with initial concentration 2M [H,0, ’ H,0 + O] x 2 (slow)
follows zero order kinetics with rate constant 2 0+0 ’0, (fast)
x 10Msec-'. How long will this reaction take to 2H,0, ’ 2H,0 +0,
go to completion ? What is the order of overall reaction ?
Ans. We know K=* Ans. Order is determined from the slowest step. So
t
order of the reaction is 1.
Here x =2M, K=2 x 10- M
sec-!
21. Write the integrated rate equation for a 2nd
X 2M order reaction of the type, 2A ’ product.
= 100 sec
k 2x 10Msec-!
1 X
Hence it will take 100 sec for completion of the
reaction. Ans. K= t'ala- x)
13. The rate of reaction is doubled for every 10°C where K= rate constant.
rise in temperature. If the temp is raised from a = initial amount
30°C to 70°C the rate of reaction will be
X= amount reacted at time t'
increased by how many times ?
Ans. Rise in temperature = 40°C
22. What is the effect of temperature on activation
energy ?
Rate of reaction will be, 24=16 times the initial rate.
14. Inyersion of Cane Sugar is an example of Ans. There is no effect of temperature on activation
energy.
order reaction.
23. Define rate constant of a reaction
Ans. Pseudofirst
Ans. It is a constant and equal to the rate of reaction
15. What is the relationship between rate constant when concentration of the reactants is unity (l mole/litre).
and half life period of a lst order reaction ? 24. Hydrolysis of ester in presence of mineral acid
0.693 is an example of order reaction.
Ans, 'i
2 K Ans. Pseudo first order
K=rate constant of the reaction. 25. Alkaline hydrolysis of ester is an example of
order reaction.
2
l = half life period of the reaction. Ans. 2nd
16. Activation energy for a chemical reaction 26. If unit of rate constant is mole lit-! sec! order of
the reaction is
depends upon
Ans. Nature of reactant. Ans. zero
17. For a lst order reaction the time required for 27. If for a reaction, the half life period is directty
75% completion is - -times, the time required proportional initial concentration of reactant,
for 50% completion. what is the order of the reaction
Ans. 2 Ans. Zero order
18. In all reactions increase in concentation of 28. Write the Arrhenius equation
Fa
reactants increases rate of reaction. Yes or No.
Ans. K= Ae RT
Ans. No, in zero order reactions rate of reaction is
independent of concentration of reactant. Where K= rate constnat
19. The unstable intermediate compound formed by A = Collision number
reactants after absorption of activation energy Ea = activation energy
is called as R= 8.314 JK-' mole!
Ans. Activated complex T= absolute temperature
USHA'S +2 Chemistry(2nd Year) 57

of reaction vary with activation reaction

How does rate So. Give an example of fractional order
29. energy?
Ans. CH,CHO’ CH, + CO
Ans. The reactions with smaller activation energy
proceedfaster
and Vice versa. Rate = K<CH,CHOJ:
How is
heat of reaction related to activation order of the above reaction = 1.5
30. energy ? independent of
39. For a reaction half life period is What is the
Ans. AH=E, - E!, initial concentration of reactant.
reaçtion. order of reaction ?
Where AH= heat of Ans. First order reaction
activation energy for forward reaction.
40. Rate constant of a reaction depends upon
E'=activation energy for backward reaction. Ans. temperature
order
What is the unit of rate constant for first
31. reaction ? 41. The reaction A + 2B
-’ 2C obeys the rate
What is the
Ans. Sec-l or
minute-l equation : Rate = KA"B}"
complex ? order of the reaction ?
32. What is activated
state of thereactant
Ans. It is the unstable transition Ans. Order =+3/2 =2
to threshold energy. 2
with highest energy equal 42. What is photochemical
reaction ?
reaction ? rate is influenced by light
33. What is zero order Ans. The reaction whose
in which rate of reaction is reaction.
Ans. The reaction
reactant is called as radiation is called as photochemical
independent of concentration of the decomposition of H,0,.
e.g. photosynthesis,
zero order reaction. reaction the
43. For a zero order of 2

light 2HC) concentration.

e.g. Ha0 +Ch below ?
of the reaction given Ans. Varies directly with
34. What is the order zero order reaction vary
with
44. How does rate of
2N,0, ’2N,0, +0, progress of time ? remaians
reaction. order reaction
Ans. It is a lst order Ans. Rate of a zero
of 1st order reaction unchanged with progress of time. tË
35. Give an example C

PCL, +Cl; reaction,

Ans. PC1, 45. For n' th order 2

Experimentally found, Rate =K (PCI,] Ans.

cal-n

So order of reaction = 1 reaction, the molecularity

is
order
directly proportional to lst power 46. For a zero
Rate of reactionis zero. Yes or no be
of the concentration of reactant. of a reaction can never
equation for 1st order Ans. No, moleculararity
36. Write the integrated rate
zero.
Ae-what is A?
reaction.
RT
47. In the equation K= collision number or
2.303 called as
Ans, k= -log Ans. A is a constant is sec-!.
a-X unit
frequency factor and its
t
reaction. vary with activation
Where K=rate consant
of the
How does the value of K'
48.
a= initial amount of reactant. energy activation energy increases
X= amount decomposed in time the Ans. As the value ofdecreases.
is samne as (K) value
a reaction the rate constant
37. If the rate constant of concentration of reactant, Arrhenius equation)
rate of reaction at any (As given in
what is the roder of reaction ?
Ans. Zero order reaction
 58 +2 Sample Papers (2nd Year USHA's
49. Can all molecular collisions yield the product ? S2. Write two factors which intluence rate constant
Ans. No, only the effective collisions yield the of a reaction ?
product. Ans. Temperature and catalyst.
50. What is the condition when all collisions between 53. The ratio between the rate constants at two
the molecules can be effective collision?
different temperature differing by 10°C is called
Ans. When activation energy of the reactant is zero,
then K=A. Where K =rate constant Ans. Temperature co-efficient
A = collision number.
Under such conditions all collisions can be effective 54. For a1st order reaction when rate of reaction is
collision to form the product, But this concept is plotted vs. conc. of reactant a straight line is
theoritical. obtained whose slope is 2.5. What is its rate
S1. What is the unit of rate constant for zero order constant.
reaction ? Ans. Rate constant = slope = 2.5 Sec-!.
Ans. Mol lit' sec.

C SHORT -TYPE QUESTIONS WITH ANSWERS

l.ExpBain why H, and 0, do not combine with the rate of reaction decreases. So in presence of -ve
each other at room temperture. catalyst the reactant follows a path of higher activation
Ans. Át room temperature the energy of H, and O, energy.
is not sufficient to cross the threshold energy. Therefore
they do not react with each other at room temperature.
But on giving an electric spark to the mixture, a vigorous
reactieh occurs giving water. (Evecatalyst)
2./ Define catalyst. Give an example.
Ans. The substance which may increase or decrease (without catalyst),
E
the rate of a chemical reaction but its concentration E
remains unchanged when the reaction is over is called as
catalyst. The action of catalyst is specific. Normally it
lowers the activation energy of the reactant.
e.g. N, +3H, , 2NH,
In this reaction iron is used as catalyst to increase Progress of reaction
the rate of synthesis of ammonia. What do you mean by autocatalyst ?
3. What is temperature co-effiient ? Ans. When one of the product of the reaction acts
Ans. It is defned as- the ratio of the rate constants as catalyst, that is called as autocatalyst. In such reactions,
of a reaction at two different temperatures differing by the rate of reaction is slow in the beginning but after
10°C. This value is found to be between 2 and 3. some time the rate of reaction increases, as one of the
So, =temperature co-efficient. product acts as catalyst.
e.g. In the reaction between KMnO, and oxalic acid
K{t +10}° C the Mn ion formed in solution acts as
Kc autocatalyst.
Why in most of the cases the rate of reaction
=2 to 3
decreases with progress of reaction ?
4/ Explain, how a -ve catalyst decreases the rate of Ans. Rate of reaction varies directly with
reaction, giving the reaction path way ? concentration of the reactant, except in zero order
Ans. -ve catalyst increases the
so that less number of molecules are activation energy,
able to cross the
reactions. As concentration of reactant decreases with
progress of reaction, so rate of reaction decreases with
threshold energy giving less product molecules. Hence progress of reaction (except in zero order reaction).
 59
USHA's) +2 Chemistry (2nd Year)
basis of activation energy hoW can you rate of reaction
Onthe Since water is taken in large Cxcess, order
slow and fast reaction ? ethylacetate. So
explain depends only on concentration of
Ans. Ifthe
activation energy for areaction is low. of reaction is 1 although molecularity is two.
number of
effective collisions will be more and the 13. Match the following :
the fast. On the other hand if the activation B
reaction will be A
reaction is high the number of effective
for a
energy will be less and the reaction will be slow. (a) half life of zero ) Ku-10
K¹c
=2
collisions
Write the
integrated rate equation for 1st order (b) unit of rate of
reaction and also the unit of rate constant for
such reaction. reaction ii) 2 2k
is
Ans. The equation
0.693

2.303 a (c) Arrhenius equation in) 2 k

K= log a-X Ea
t
of the reaction. \iv) k= Ae RT
Where K= rate constant (d) Temperature
amount of reactant
a = initial t co-efficient
reactant consumed in time (v) Mol lit' see-1
X= amount of
constant is sec-!. (ii)
The unit of rate example. Ans. (a)
Give an
Deife 1st order reaction. (b) (v)
9 which rate of reaction is
Ans. The reaction in ration (c) (iv)
Propertional to lst power of the concent (i)
directly () molecularity and
called lst order reach. comparison between
of thereactant is 14. Give a
+O, reaction.
e.g. 2H,0, ’ 2H,0 order of a
Order
Rate = K [H,0,]' Ans. Molecularity
So order of reaction
= 1 ’ It is the sum of the
reaction. It is the number of molar
two characteristics of zero order ’
molecules/atoms/ions powers of the
10,Give of
reaction is independent
reactants
conc. of the
Rate of of the reactant species
Ans. -’ in the rate of equation
concentration of the reactant. to the initial taking part in a single of the reaction
half life is directly proportional step of the reaction. may be a whole
’ a
always a whole|-’ Itnumber,
ty,= It is fraction or
concentration of the reactant. 1.e. 2K number and its value is
generally not exceeding zero, and its value may
constant is Msec-'. exceed three.
’ The unit of rate sugar dissolves faster
in reaction
powdered three.
step of ’ Itrefers to the
Il, Explain whycrystalline sugar. It refers to single as a whole.
water than surface area than a reaction. determined
Powdered sugar has more in obtained from ’ It is
Ans. molecules will come It is balanced experimentally
crystalline sugar. Thus sugar and dissolve
faster simple
water chemical equation.
contant with more amount of -’ Rate of reaction
reaction is depends on order.
than crystalline sugar. Rate of
of
order reaction. independent
12, Define pseudofirst molecularity of a reaction is molecularity.
Ans. In certain cases depends only on 1.
one reaction.
reaction is half life of a which the
two but rate of
Which means order of reaction 1 5 Define
defined as the tÉme during itsinitial
Concentration term. reaction. Ans. It is half of
pseudofirst order the
of reactant is reduced to
Such reaction is called as concentration or
denoted by t,
H’ amount. It is
eg. CH,C00C,H,+ H,0CH,COOH
reaction,
+ C,H, OH
order
For a first

Here Rate = K[CH,C00C,H,

 60 +2 Sample Papers (2nd Year) USHAS
0.693 e.g. No reaction takes place between H, and O. at
K room temperature, but on giving an electric spark to the
where K= rate constant. míxture a vigorous reaction occurs giving water.
16. Explain, how a catalyst increases the rate of 21. Differentiate between rate of reaction and
reaction, giving the reaction path way. specific reaction rate.
Ans. Acatalyst lowers the activation energy, so that Ans. Rate of reaction : It is the speed at which
larger number of molecules are able to cross the threshold reactants are converted to products.
energy giving more product molecules. Hence the rate It depends upon concentration of the reactant.
of reaction increases.
It decreases with progress of reaction.
Specific reaction rate : It is a constant in the rate
without catalyst equation of the reaction.
It refers to rate of reaction at a secific condition
L -inpresence of catalyst when concentration of reactants is unity.
E, E, It is constant through out the progress of reaction.
22. Define zero order reaction. Give an example.
Ans. The reaction in which the rate of reaction is
E, independent of conc. of reactant is called as zero order
reaction.
water
Progress of reaction ’ e.g. Hap tC ’ 2HCs)
In presence of catalyst the reactant follows a path surface
of lower activation energy. Rate = K [H' [CIJ', so order of reaction -0+0-0
17. Define threshold energy. 23. Write two characteristics of lst order reaction.
Ans. Tbe reactant molecules must possess a certain
Ans. ’ Rate of reaction is directBy proportional to
amout of energy before they can react upon collisions to Ist power of molar conc. of the reactant.
yield the product. This energy barrier is called as
threshold energy. So each reactant molecule must over ’ Unit of K is time (sec, min', etc.)
cone this energy barrier (E,) before converted to product. ’ Half life is independent of initial concentration
18. What is life time ofa reaction ? of the reactant.
Ans. The time required for 98% completion of the ’When log(a-x) is plotted Vs, t',a straight line
reaction is called as life time of the reaction. The shorter K
the life time the faster is the reaction. is obtained whose slope = Hence from the graph
2.303
19. Why does Zn' dust react faster with dil. HCI we can calculate the value of 'K'.
than Zn' granules ? 24. Why is the rate symbol w.r.t., the reactant taken
Ans. Zn' dust has more surface area than as -ve and w.r.t. product taken as +ve?
Zn
granules. Therefore 'Zn' dust comes in contact with more Ans. The cncentration change w.r.t. reacctant is -
hydrochloric acid than Zn' granules. So 'Zn' dust ve as reactant conc. decreases. But rate of reaction is
dissolves faster than Zn' granules in dil. HCI. always positive. Therefore minus sign is always wrten
20. What is the effect of before the rate symbol w.r.t. reactants.
reaction?
temperature on rate of a
On the other hand the concentration change w.r.L.
Ans. In most of the cases the rate of product is tve, as product conc. increases. Therefore ve
increases with increase in temperature of the reaction sign is written before the rate symbol w.r.t products.
it is due to increase in reactants,
kinetic energy of the reactant e.g. N, + 3H,’ 2NH,
molecules, which ltimagely increases the number of The rate of reaction
effective collisions. Hence the rate of reaction increases.
It has been found that the rate of
3 times for each 10°Crise reaction
in temperature.
increases2 to dN,]1dH,).
dt 3 dt
1d[NH,]
dt
 USHA's +2 Chemistry(2nd Year) 61

of coal burns at moderate rate in air 30. What is difference between average rate and
25. Alump
while coal dust burns explosively, explain. instantneous rate of a chemical reaction.
Ans. Alump of
coal has less surface area then Ans. When change in concentration is measured
powderedcoal, So it comes in contant with less amount Over longer interval of time it is called average rate of
oxygen and burns at moderate rate. While coal dust
reaction.
over
of surface area and comes in contant with more When change in concentration is measured
has more so burns violently. Small interval of time, it is called as instantneous
rate of
amount of OXYgen,
activation energy. reaction.
26. Define
Ans. The extra amount of energy required by the PROBLEMS
cross the energy barrier in order to
reactant molecules to 31. For the reaction, 2S0, + 0,
’2S0, the rate
product is called as activation energy. Msec. Find the rate
yieldthe of reaction w.r.t 0, is 0.48
Thus E, = E -ER of reaction w.r.t. SO, and SO,.
Where E, = activation energy Ans. For this reaction,
= threshold energy Rate of reaction =
reactant.
E, = energy of
the reaction. 1d(so,]_ do,] 1d[so,]
Lower the activation energy, faster is dt dt
+ dt
takes place in two steps as
2
27. Suppose a reaction djo,] =0.48 Msec
follows Given
dt
A 10 sec B+C d(so,]dso,] =2x d(o,]
C+D 2sec ’ dt
dt
dt
SO,
A +D’B+ E Hence the rate of reaction w.r.t.
overall reaction ?
What is the order of rate rate of reaction w.r.t. SO,
slower step, so it is the 2x 0.48M Sec-l= 0.96 M
sec-.
Ans. The Ist step is ’ Product, the rate
of
determining step. 3 For the reactionA increased
overall order of the reaction of A is
reaction doubles, when conc. of the reaction ?
Hence rate = KIA] and order
four times. What is the
is one. zero order the reaction is n'.
What is the rate equation for a constant Ans. Suppose order of
28. the unit of rate.
reaction ? Also write Rate, = K [A]P
for such reaction. Rate, = K{4A}
= 4" x K[AJ
Ans. The rate equation is 4" x K{A" =2
X Rate2 2’
K=
t of the reaction
As given, Rate K[A]"
Where K=rate constantdecomposed in time "t'. 2 ’ n=%
reactant ’ 4n =2’ 2n
X=amount of 8o order of the
reaction is ½. 0.5M
unit of K=mole lit-! sec zero order initial concerntration of arectant is half
equation for half life of a 33/ The 1.5 x10-² M
see-'. Find
29, Derive an with rate constant
reaction. reaction is K life of the
reaction.
zero order order seaction.
Ans, The rate equation for Ans. Since it is a
zero

When t t,x =amount of reactant. ty2K 0.5 M

Where a = initial sec-!
reaction. 2x 1.5x 10M
K=rate constant of the = 16.6 sec.

’K=
2k
ty
 +2 Sample Papers (2nd Year)
62

34. For a forward reaction activation energy is 55

Given =0.18 M sec-l
USHA'S
kJ/mole and for backward reaction is 70 kJ/ dt
mole. Find heat of the reaction. -d[N,] 0.18
Ans.We know, AH =E - E 0.06 M sec-!
dt 3
- 55- 70 =-15 kJmole.
Hence heat of reaction is - 15 kJ/mole.
S+QNH,) 2
-x 0.18 = 0.12 M sec-l
Where, E, = energy of activation for forward dt 3
reaction. Hence rate of disappearance of N, 0.06M sec- and
rate of formation of NH, is 0.12 M sec-!
E,= energy of activation for backward reaction.
139, Calculate half life of a lst order reaction, whera
35./The half life of a 1st order reaction is 200 sec. the rate constant of the reaction is 6,93 x 10:
Calculate the rate constant of the reaction. sec'.
Ans. t,, = 200 sec Ans. K=6.93 x 10 sec-, t, =?
0.693 0.693 We know for a lst order reaction,
K=
200
=3.46 x 10- sec-l
ty 0.693
36./ For the reactionA ’B +C, the activation t,= K
energy is 15 K cal/mole and enthalpy of reaction
0.693
is +5 Kcal/mole. Find activation energy for the 100 sec.
reaction B+CA 6.93 x 103
Ans. We know AH =E-E! 40. Fora reaction X ’ product, it was found the
Where AH=enthalpy of reaction. order of reaction is 2. How would the rate change
1
E,= energy of activation for forward reaction. if the conc. of X is reduced to 3d ofthe
E energy of activation for backward reaction.
original value ?
NowE=E,-AH=15 - 5= 10 Kcal/mole.
Hence activation energy for the reaction, Ans. Rate, = K[X]'
B+ C’A is 10 Kcalmole
37. Fora 1st order reaction t, =2 min. How long Again Rate, =
willit take to reach 25% of the initial conc. of
the reactant ?
Ans. a = 100, a, = 25
Rate, 1KX1
Rate, 9K{X 9

Now, a,= a ’ Rate, = x Rate,

’ 25 = 100 x The rate of the reaction will be 9 th of the initial
rate.
41. ^how that for alst order reaction the time taken
for 99.9% completion is 10 times the time
’n=2 required for half completion of the reaction.
’ Number of half lives gone =2
Total time taken =2 x 2=4 min. Ans. tg99% 230 10g
K
100
100-99.9
38. For the reaction N, +3H, ’2NH,, the rate of 2.303 2.303
disappearance of H, is 0.18 Msec-. Find the rate K
-log 1000 = x3
K
of disappearance of N, and rate of formation of
NH, 2.303 100
Ans. Rate of reaction Againt% K -log 100-50
1dNH,] 2.303 2.303
3 dt 2 dt K
log2 K
x 0.301
 2
USHA's Chemistry (2nd Year) 63
2.303 x3 2.303 2.303 x 3
K = 10 K
-log1000 = K
2.303
x 0.301
ts0% K 2.303 100
x 10 (proved) Again, t0% K
log
100 90
Ky9.9% of 1st order was completed in 2.303
75% of a reaction
2.303
completed -log 10 =
42. minutes. wnen was It half K K
2.303 2.303 x3
Ans. K = t -log (a-x) t99% K =3
2.303 2.303
2.303 100 tgo%
-log 100-75 log4 K
32
32
=3 Xtg0%
2.303 x2x 0.3010
0.693
plotted Vs time
16 46. When for a reaction log (a-x) is slope -0.03s-'.
32 with
astraight line is obtained, reaction.
0.693
0.693
= 16 min. Find the rate constant of the
Again ty, K
A2 For a reaction the initial
0.69%6
conc. of the reactant is
Ans slope =
K
2.303
reaction is 2.5
0.25 M. If the rate constant of the
K
’-0.03 = =
the reaction.
x10- sec-, find the initial rate of 2.303
0.03 =6.909 x 102 sec-!
2.303 x
Ans. For a lst order reaction,
’K=
time of a 1st order reaction,
Rate = K [A]' 47. Calculate natural life sec,
whose rate constant is 0.25
[A]= 0.25 M 1
= 4sec
K=2.5x10-² sec-l ==
Ans. Natural life time (T) k 0.25
102 = 6.25 x 103M sec!,
’ Rate=0.25 x 2.5 x constant of a 1st order
reaction
reaction is increased by a 48. Calculate rate
44. The rate constant of a from 290 K to which is 90% completed in 10
min.
changed
factor of2, when temp isenergy of the reaction. 2.303 100
300 K. Find activation Ans, K= log 100- 90
10
Ans. T, - 290 K, T, = 300K,
From Arrhenius equation,
K2=2,E,=?
K 2.303
10
log 10 = 0.2303
min-!
min-!
the reaction is 0.2303
So rate constant of reduced to
K E,_I-I rection asubstance is
49. For a lst order
2.303R T,T 1 what time will it be reduced
Ea 300-290 rdin 100 sec. In
’ log2 2.303R300 x 290,
E, x 10
to th? 2.303
0301= 2.303 x log3
2.303 x 8.314 x 300 × 290 Ans. K= -log 100
>E -3.01x3x290×2.303x 8.314 100

=55.14 kJ/mole 99.9% 2.303

45. required for Again t = -log
Show that the time
order reaction is 3 times the K %
completion of a 1st
completion of the 2.303
time required for 90% x log9
’t= 2.303 x log3
reaction.
100 100
2.303
Ans. ty g K
log 100-99.9
 64 +2 Sample Papers(2nd Year)
2.303 x 100 x 2log3
=200 sec 2.303
(log10-log 2)
USHA's
2.303 x log3 0.082
1 2.303
Therefore the substance will be reduced to th in -x0.699 =19.6 min.
0.082
200 sec. 53. A 1st order reaction is 20>
50. Decomposition of Afollows two parallel 1st order completed in 10 min
Calculate the time taken for the reaction to
reactions with K,= 1.3 x 104 sec- and K, = 3.9
75% completion.
x10-5 sec'. Find % distribution of the products. Ans. Let initial conc. of reactant = 100 mo/
K After 10 min the amount reacted = 20 mo/l
’K=503,
Ans. Suppose, A -log a-x
K 2.303 100 2.303
K,=1.3x 104 sec- & K, =3.9 x 105 sec!. log (log10-log8)
10 100-20 10
Over all rate constant of the reaction is
=0.2303(1-0.9031)
K=K, +K=(1.3x104+3.9 x 105) sec-l
=1.69 x 10 sec-! -0.2303x0.0969 =0.0223 min.
2.303 100 2.303 100
Now t=
Now %yield of 'B' = K x 100 K \og 100-75 0,0223
-log 25
K
2.303 2.303
1.3 x 10-4 -log 4 = -x0.6021 =62.15 min
x 100 =76.92 0.0223 0.0223
1.69 x 104 54. The half life period of a lst order reaction is
and % yield of 'C' = 23.08
100sec. Caleulate the time required for 80%
51. Fora reactionA’product, it was found that completion.
the rate of reaction is increased by afactor of 8
Ans. 0.693 0.693
when conc. of 'A' is increased 4 times. Find the -’K= =6.93 x 10' sec-!
order of the reaction. K 100
Ans. Suppose order of the reaction is 'n'. Now time required for 80% completion is given by
Rate, = K{AJ. t=
2.303 2.303 100
Rate, = K{4AJ = 4° K[AJP K -log 6.93 x 10 -log100-80
2.303 x 10
As given Ratez
Rate, 8
6.93 -(log10 -log 2)
2.303 x 10 x0.699
4° K[Ab" -84h =8 ’22n =2’n= 1.5 6.93
- 232 sec

K[Ab 55. For a zero order reaction, show that t

52. The rate constant of a lst order =1.5 x t0%*
reaction was
found to be 0.082 min'. When the initial
of the reactant is 0.15 mo/lit, how
conc. Ans. K
long will it for zero order reaction.
take for the concentration to drop to 0.03
lit ?
mol 50a
Ans. K=0.082 min!., 100K (where a = initial reactant)
2.303 75a
K= log (for lst order reaction) and s% =
100K

2.303 0.15 2.303 75a 100K

log =1.5
0.082 0.03 0.082
log 5 100K 50a

=1.5xtso%
 +2
USHA's Chemistry (2nd Year) 65

D
-TYPE
LONG. QUESTIONS WITH ANSWERS
Define rate of a reaction. Discuss any four factors (ii) NO+½0, ’ NO, (faster)
Q.1. influencingthe rate of reaction.
of reaction is defined as the number of CO+ 2 0, ’ CO, (slower)
Ans. Rate consumed or number of moles Inthis case NO bond is weaker than 'C0* bond
moles of reactant species
hence broken easily and reacts faster.
productformedin unit tíme. Mathematically
of
dx
number of moles of reac tan t consumed (d) Catalyst - A positive catalyst decreases the
time taken activation energy of the reactant, so that rate of reaction
dt increases. In presence of a +ve catalyst larger numbers
number of moles of product formed of rectant molecules cross the energy barrier giving more
dx
+
time taken product.
dt
Ni
heat CHo
The variousfactors influencing rate of reaction are e.g. C,Hug t H
Niis the +ve catalyst in the above reaction.
(a)Concentration of reactant -According to law energy
action- the rate of: a chemical reaction is dirctly Further a -ve catalyst increases the activation
of mass decreases.
of the reactant, therefore rate of rection
proportional to the molar conc. of the reactants.
when the number of reactant molecules increases. e.g. 2H,0, H,PO 2H0+O,
well as the number decomposition of
the collision frequency increases as that rate of reaction H,PO, acts as -ve catalyst in the
of effecitve collisions increases. So hydrogen peroxide.
Surface area affects
increases. (e) Surface area of reactant-
introduced in to a jar the reaction is
e.g. A burning splinter when increase in conc. of the rate of reaction only when react faster
solids
of oxygen it gives a flash due to heterogeneous in nature. Finely devided
expoOsed for contant
oxygen, which is a reactant
for combustion. because of their more surface area
only the effective with other reactant molecules.
(b) Temperature - We know orientation) result the hydrochloric acid than
collisions (collision in proper e.g. Zn dust reacts faster with
increases the kinetic energy comes in contact with more
Zn granules because the dust
product. As the tempeature
This will increase the collision HCI molecules.
of the molecules increases. of reaction will be () Radiation The rate of certain
reactions
frequency and ultimately the rate every 10°C rise in specific wave length,
increased. It has been found that
for increases with light radiation of
doubled or tripled. substance. Such rections are
temperature the rate of rection is when falls on the reacting
reaction.
between copper turning called as photochemical
e.g. No reaction takes place but on slight heating Cl, in dark is
e.g. Reaction between H, andreaction is explosive.
very
tempeature,
and nitric acid at room giving Cu(NO,) NO, slow, while in presence of
light the
a vigorous reaction takes place 0.2. Write short notes on:
and O, gas.
-During a chemical reaction (a) Half life period
(c) Nature of reactant bonds are formed with (b) Activation energy
new
Old bonds are broken and nature of the Arrhenius equation
of atoms. Consequently the (c) Order and Molecularity
rearrangement bonds of the reactant
eaciant and strength of the of reaction. 1he
(d)
hOlecules greatly influence the rateinvolves less bond Ans. (a)
Half life period:
time
eaction will be faster if it fasterif involves more reaction is defned as the
Half life period of a Again it is
of the reaction.half
rearrangement, otherwise it will be
bond rearrangement. Again
gaseous state
the reactants in
required for half completion
conc.
which the initial
becomes
solid state. the time in
eact faster thar the reactants in tso%
(very fast) It is denoted by t, Or
e.g (i) Na + H,O ’ NaOH + %H, (Moderate)
Ca +2H,O ’Ca(OH), + H,
 66
+2 Sample Papers (2nd Year)
When t t,X=
The activation energy depends upon
reactant and strength of the bonds
USHAS
nature of t%.
Where a - initial concentration of the reactant Again for the backward reaction, undergoing rapture,
X= amount reacted in tìme t'. E, - E-E
Considering a lst order reaction. Where E = activation energy for the backwava
rection.
K- 2.303 -log
t a-x E, = potential energy of the product.
During progress of reaction an activated
energy, whichcompl
can ebex
2.303 is formed with maximum potential
-log a changed to product as well as rectant. The activation
2 energy for a reaction can be decreased or increased in
2.303 2.303 x 0.301 0.693 presence of a catalyst.
-log 2 = (activated
t
0.693 AB*C complex)
’
K |E, E.
Hence half life period for a Ist order reaction is A+BC
independent of concentration of reactant. JAB+C E,
But for a zero order reaction,
X En
K= t

a
Progress of reaction
’K= Significance :
ty 2K If the activation energy for a reaction is low, the
Which means for a zero order reaction half life reaction will be fast. On the other hand the
period is directly proportional to initial conc. of the activation energy is high, the reaction will be slow.
reactnat.
Heat of reaction = E,- E,
In general for 'n'th order reaction, t,, a a ln
For an endothermic reaction , E > E,
It may be noted that, shorter the half life period,
faster is the reaction. ’ AH=E,- E, tve
(b) Activation energy : For an exothermic reaction, E< E,
Ans. The reactant molecules must acquire a certain ’ AH=E,- E, =-ve
amount of energy before they can react upon collisions
to yield the products. Which means there is an (c) Arrhenius equation :
energy
barrier for each reaction which is called as threshold Ans. Arrhenius equation gives a relationship
energy. Therefore the reacting species must be provided between rate constant of a reaction with temperatu°t.
with sufficient amount of energy so as to cross the The equation is
energy
barrier in order to yield the product. K- Ae kT
This extra energy required by the reactant molecules Where, K=rate constant
to overcome the energy barrier or threshold energy is
A= Arrhenius constant or collision number
called as activation energy.
E- activation energy of the reactant
So E, =E-Eg R=8.314 JK- mole-!
Where E, = activation energy of the reactant. T=Absolute temperature
E, = threshold energy
E, = potential energy of the reactant. ’ In K=n A- E,
RT
 + 2
USHA's
Chemistry (2nd Year) 67

2.303 log A- Order of a reaction may be whole number, fraction

2.303 log K = RT
’ or zero. However its value does not exceed three. It
E, is always determined experimentally and refers to
> logK= 2.303RT + log A the reaction as a whole. It has no meaning for
individual steps of the reaction. Rate of a reaction
the form y = mx t c, an equation of a depends on its order but not on molecularity.
This is in
1
Q.3. Derive an expression for rate constant of 1st
plotting a graph between log KVs order reaction. Write the unit of K.
straightline. So Show that for a 1st order reaction the time
Ea required for 99.9% completion is 3 times the time
obtained with slope = 2.303R required for 90% completion.
straight lineis
Ans. Consdering a lst order reaction.
Again attwo different tempeatures, T, and T, if the A’product
e constants are K and K, respectively, we can write
Ea
+ log A Now dA] - K[A]
log K, = 2.303RT
dt
reactant is 'a' moles
Suppose the initial conc. of the
Ea time t is x' mnoles/
+ logA "litre and amount decomposed after is (a - x)
& log K,= 2.303RT, concentration
litre. Now the instantanceous of reaction is
moles/litre. Hence the instantaneous rate
Ea
dx
log K, -log K,= 2.303R T dfa-dt x]-K(a-x)’ dt - K(a-x)
Ea dx
Kz -= Kdt
log a-x
K 2.303R TT, Integrating both sides,
of Arrhenius equation.
This is also another form number
Molecularity of a reaction is defined as the
(d)
reactant molecules colliding in a single step to - In (a - x)= Kt tc
eq(1)
of
chemical reaction. Where, C= integration constant
bring about the ofreactant molecules that reaction
Depending on the number classified K=rate constant of the
the reactions are When t =0, then x=0
collide in a single step,
bimnolecular or trimolecular. x0+C
as unimolecular, ’-h(a -0)= K
PCle -’ PCla t Clhio (unimilecular) ’C=-In a
e.g. ’ 2HI, (Bimolecular) in eq (1) we can get,
(Trimolecular) Putting the value of "C
In a
Z SO(e +O0) 2S0
It refers -In (a - x) = Kt
always a wbole number and never zero. for ’ Kt= In a - ln
(a -x)
lt is
a reaction and no meaning
of
0 Single step = ]In
overall reaction. sum of the a-X
is defined as the 2.303
Order of a reaction concentration of the reactants -log a-X order
powers of the molar t equation for Ist
integrated rate
of the reaction. This is the
n the rate equation reaction is time-!
reaction. order
e.g. 2A+B ’ product The unit of
'K' for first
equation is -
Suppose the rate (sec-, min' etc)
Rate = K [AJ [B]' |=3
of the reaction =2+
Now order
 68 +2 Sanple Papers (2nd Year)
Problem:
For a lst order reaction,
Integrating both sides, USHAS
2.303 100
-log ’X= Kt +C .eq (1)
K 100- 99.9
Where, C= integration constant
2.303 2.303
log 1000 = x3 when t =0, then x=0
K K ’C= 0
2.303 100 2.303
Again 90%
t, log 10 Putting the value of "C° in eq (1) we can get
K 10800 -90 K x= Kt +0
2.303
x2 ’KX
K
t
2.303
x3 This is the integrated rate equation for zero
Now, tg9.9% k -=3 reaction.
order
2.303
tgo% The unit of 'K is mole lit sec!.
k
’tg =3x ty (proved) Problems -Suppose order of the reaction w..t NO
Q.4. Derive an expression for rate constant of zero is x' and w.r.t. CL is 'y'. So the rate equation is
order reaction.
Rate, K[NOJHCL
For the reaction, 2NO + CL, ’ 2NOCI, the Again Rate, = K[2NO} (2CL,]
rate of reaction is increased by a factor of 8, by = 2x*y x K[NOHCL'
doubling the conc. of both. Again doubling the
conc. of CL only doubles the rate. Find order of
the reaction w.r.t NOand CL.
Ans. Considering a zero order reaction,
(4+3
As given, RateRate28
AProduct
2 xK[NOl'[,f' =8

Now
K[NO]'[CI,)'
dt ’2xty =2 ’x+y=3
Suppose the initial conc. of the reactant is 'a' moles/ Again Rate, = K[NOJ [2CL,}
litre and after tine t the amount = 2 x K[NO]
moles/litre. Then conc. of the reactantdecomposed is x [CL,'
at any instant =
(a - x) moles/litre Given Rate,-=2
Now the instantaneous rate of reaction is Rate,
dËa-x] =K[a-x]
dt
Where K is the rate constant of the ’=2!
K{NO]|C,]
dx
reaction
=K ’y=1
dt
’ dx = Kdt
Hence x =3-1 =2
Therefore order of reaction w.r.t. NO'is 2 and W.I
Cl, is 1.