C H A M PI O N S L E C T U R E SE RI ES
1
THEMODYNAMICS
Level-II
C-218 To C-223
L ecture Pla n ning & F lo w
N o.
H o m e w ork of this lecture
L ecture C o nte nts
Abhyaas – I ( R C Mukh erjee )
P-473 Q28-34
( N A vasthi ) P-182 Q1-3
Yes
No
Abhyaas – II ( R C M ukh erjee )
II
P-474 Q-35,39,40,44,45, P-464 Q1,2,5
( N A vasthi ) P182 Q4-7, Q10-50
Yes
No
Abhyaas – III ( R C Muk herjee )
P-429 Q 1-7,33,34,49,50
III Adiabatic E xpansion of an Ideal G as. Free expansion P-464 Q3,4,24,28-34
C alculation of H , U, Work, H eat etc.
N A vasthi
P-182 Q 8,9,51-61, P-199 Q1-18
IV
Yes
No
Abhyaas – IV ( R C Muk herjee )
P-433 Q 8-31,52-65
P-464 Q6-23,29,43-51
P-470 Q1-14,21-23,25,27,47-50,52-55
N A vasthi
P-193 Q 108-150, P-202 Q27-35
V
Yes
No
Abhyaas – V ( R C M uk herjee )
P-445Q 32,46,49-51, P-468 Q-36-38
VI
P-471 Q15-16,36,38,42,43,46
N A vasthi
P-188 Q 62-83, P-200 Q14-18
Yes
No
Abhyaas – VI ( R C Mukh erjee )
P-447Q 35-45, P-467 Q25-27, 39-42
P-472 Q17-20, 38,51,53,54,58
N A vasthi
Roll No.
STAMP
P-190 Q 84-107, P-201 Q19-26,40
Yes
No
Module Yes
No
I
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2
ABHYAAS - I
LEVEL - II
B asic terms of thermodynamics
Q-1
Categorize these property into state and path function.
(A) Internal energy
(B) Volume
(C) Heat
(E) Temperature
(F) Work
(G) Molar heat capacity
(D) Enthalpy
S ol n :
Q-2
Categorize these property into extensive and intensive property
(A) Temperature
(B) Internal energy
(C) Heat
(E) Molar volume
(F) molar enthalpy
(G) viscosity
S ol n :
Q-3
Classify the following physical properties as intensive or extensive
(A) free energy
(B) viscosity
(C) kinetic energy
(D) gas constant
(E) critical density
(F) specific heat capacity
(G) specific gravity
(H) dielectric constant
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(D) Density
THEMODYNAMICS
3
Q-4
Warming ammonium chloride with sodium hydroxide in a test tube is an example of :
(A) Closed system
(B) Isolated system
(C) Open system
(D) None of these
S ol n :
Q-5
Out of boiling point (I), entropy (II), pH (III) and e.m.f. of a cell (IV), intensive properties are :
(A) I, II
(B) I, II, III
(C) I, III, IV
(D) All of the above
S ol n :
Q-6
Classify the following as open, closed, or isolated system :
(i) A beaker containing as open, boiling water.
(ii) A chemical reaction taking place in an enclosed flask.
(iii) A cup of tea placed on a table.
(iv) Hot water placed in perfectly insulated closed container.
(v) A thermos flask containing hot coffee.
S ol n :
Q -7
Mechanical work is specially important in system that contain
(A) Solid-liquid
(B) Liquid-liquid
(C) Solid-solid
(D) G ases
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Q -8
4
Which of the following is a state variable property
(A) Number of moles (B) Boiling point
(C) Mass
(D) Density
(C) Both (a) and (b)
(D) None of these
S ol n :
Q -9
Internal energy is an example of
(A) Path function
(B) State function
S ol n :
Q -10
The intensive property among these quantities is
(A) Enthalpy
(B) Mass/Volume
(C) Mass
(D) Volume
S ol n :
Q -11
Which of the following is a extensive properties
(A) Specific heat
(B) Viscosity
(C) Enthalpy
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5
THEMODYNAMICS
Introduction of first L aw
Q-12
Which of the following statement correct (T / F)
(A) Thermodynamics is concerned with total energy of the system.
(B) 1st law of thermodynamics can be applied on the individual particle enclosed in vessel
(C) Many thermodynamic properties cannot be measured absolutely, so change in thermodynamic property is
required for calculation
(D) Feasibility of any chemical reaction cannot be explained by thermodynamics
(E) When surroundings are always in equilibrium with the system, the process is called reversible
(F) Work done in isothermal irreversible expansion is less than the work in isothermal reversible expansion.
S ol n :
Q-13
A system is provided 50 J of heat and work done on the system is 20 J. What is the change in the internal
energy ?
S ol n :
Q-14
The work done by a system is 10 J, when 40 J heat is supplied to it. Calculate the increase in the internal
energy of system.
S ol n :
Q-15
A gas occupies 2 L at STP. It is provided 300 J heat so that its volume becomes 2.5 L at 1 atm. Calculate the
change in its internal energy.
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6
ABHYAAS - II
LEVEL - II
C alculation of
Q-1
E, Q
What amount of ice will remain when 52 g ice is added to 100 g of water at 40°C?
Specific heat of water is 1 cal /g and latent heat of fusion of ice is 80 cal /g.
S ol n :
Q-2
What is heat absorbed by a system in going through a cyclic process showing in figure :
S ol n :
Q-3
A gas expands against a variable pressure given by P =
20 (L
atm)
V
. During expansion from volume of 1 litre to
o
10 litre, the gas undergoes a change in internal energy of 400 J. How much heat is absorbed by the gas during
expansion ?
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THEMODYNAMICS
7
Q-4
If 1.0 kcal of heat is added to 1.2 L of O 2 in a cylinder at constant pressure of 1 atm, the volume increases to 1.5
L. Calculate
E and
H of the process.
S ol n :
Q-5
Ice – Water mass ratio is mantained as 1 : 1 in a given system containing water in equilibrium with ice at constant
pressure. If C P (ice) = C P (water) = 4.18 J mol–1 K –1 molar heat capacity of such a system is
(A) Zero
(C) 4.182 JK –1 mol–1
(B) Infinity
(D) 75.48 JK –1 mol–1
S ol n :
Q-6
A piece of zinc at a temperature of 20° C weighing 65.38 g is dropped into 180 g of boiling water (T = 100° C).
The specific heat of zinc is 0.4 J g–1 C –1 and that of water is 4.2 J g–1° C –1 . What is the final common temperature
reached by both the zinc and water ?
(A) 97.3 ° C
(B) 33.4 ° C
(C) 80.1 ° C
(D) 60.0° C
S ol n :
Q-7
Two mole of an ideal gas is heated at constant pressure of one atomosphere from 27 º C to 127 º C .
If C v,m = 20 + 10–2 T JK –1 mol–1 , then q and U for the process are respectively :
(A) 6362.8 J, 4700 J
(B) 3037.2 J, 4700 J
(C) 7062.8, 5400 J
(D) 3181.4 J, 2350 J
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Q-8
8
A sample of liquid in a thermally insulated container (a calorimeter) is stirred for 2 hr. by a mechanical linkage to
a motor in the surrounding, for this process :
(A) w < 0; q = 0; U = 0
(B) w > 0; q > 0; U > 0
(C) w < 0; q > 0; U = 0
(D) w > 0; q = 0; U > 0
S ol n :
Q-9
Which has maximum internal energy at 290 K ?
(A) Neon gas
(B) Nitrogen gas
(C) Ozone gas
(D) Equal
S ol :
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C alculation of W ork
Q-10
A sample of an ideal gas is expanded from 1m3 to 3m3 in a reversible process for which P = KV 2 , with K = 6 bar/
m6 . What is work done by the gas ?
S ol n :
Q-11
Determine which of the following reactions at constant pressure represent surrounding that do work on the
system :
I. 4NH 3 (g) + 7O 2 (g)
4NO 2 (g) + 6H 2 O (g)
II. CO (g) + 2H 2 (g)
CH 3 O H ( )
III. C (s, graphite) + H 2 O (g)
IV. H 2 O (s)
(A) III, IV
C O (g) + H 2 (g)
H2O ( )
(B) II and III
(C) II, IV
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(D) I and II, IV
THEMODYNAMICS
9
Q-12
A given mass of gas expands from the state A to the state B by three paths 1, 2 and 3 as shown in the figure. If
w1 , w2 and w3 respectively be the work done by the gas along three paths then :
(A) w1 > w2 > w3
(B) w1 < w2 < w3
(C) w1 = w2 = w3
(D) w2 < w3 < w1
S ol n :
Q-13
In the cyclic process shown in P-V diagram, the magnitude of the work done is :
P2
(A)
(C)
P1
2
(B)
2
4
(P2 – P1) (V 2 – V 1)
(D)
V2
V1
2
2
(V 2 – V 1)2
S ol n :
Q-14
10 mole of ideal gas expand isothermally and reversibly from a pressure of 10 atm to 1 atm at 300 K. What is
the largest mass which can lifted through a height of 100 meter ?
(A) 31842 kg
(B) 58.55 kg
(C) 342.58 kg
(D) None of these
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Q-15
10
1 mole of NH 3 gas at 27° C is expanded in reversible adiabatic condition to make volume 8 times ( = 1.33). Final
temperature and work done respectively are :
(A) 150 K, 900 cal
(B) 150 K, 400 cal
(C) 250 K, 1000 cal
(D) 200 K, 800 cal
S ol n :
Q-16
An ideal gas is taken around the cycle ABCA as shown in P-V diagram. The net work done by the gas during the
cycle is equal to :
(A) 12P1 V 1
(B) 6P1 V 1
(C) 5P1 V 1
(D) P1 V 1
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THEMODYNAMICS
11
ABHYAAS - III
LEVEL - II
Adiabatic Process
Q-1
1 mole of CO 2 gas at 300 K is expanded under reversible adiabatic condition such that its volume becomes 27
times. (a) What is the final temperature ?
Given
(b) What is work done?
= 1.33 and C V = 25.08 Jmol–1 K –1 for CO 2 .
S ol n :
Q-2
One mole of an ideal monoatomic gas is put through rev path as shown in figure. Fill in the blanks in the table
given below :
S ta te
1
2
3
Path
1 2
2 3
3 1
P
V
N ame of process
T
q
w
E
H
cyclic
S ol n :
Q-3
One mole of monoatomic ideal gas was taken through process A B C D as shown in figure. Calculate.
(i) W AB , WBC , W CD , WDA
(ii) qAB , qBC , qDA
(iii)
H AB ,
H BC ,
H CD ,
H DA
[Use : n (3 / 2) = 0.40; n (4 / 3) = 0.29]
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Q-4
12
Two mole of ideal diatomic gas (C V,m = 5 / 2R) at 300 K and 5 atm, expanded irreversely & adiabatically to a final
pressure of 2 atm against a constant pressure of 1 atm. Calculate q, w
H &
U.
S ol n :
Q-5
A sample of 4 mol O 2 is originally confined in 20L at 270K and then undergoes adiabatic expansion against a
constant pressure of 600 Torr until the volume has increased by a factor of 3. Calculate q, w,
T, U and
H.
(The final pressure of the gas is not necessarily 600 Torr).
S ol n :
Q-6
What is
E when 2.0 mole of liquid water vaporises at 100º C ? The heat of vaporisation,
H
vap.
of water at
100º C is 40.66 KJmol .
–1
S ol n :
Q-7
The molar enthalpy of vaporization of benzene at its boiling point (353 K) is 30.84 kJmol–1 What is the molar
internal energy change? For how long would a 12 V source need to supply a 0.5 A current in order to vaporise
7.8 g of the sample at its boiling point ?
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13
Q-8
THEMODYNAMICS
The valve on a cylinder containing initially 10 liters of an ideal gas at 25 atm and 25 0 C is opened to the
atmosphere, where the pressure is 760 torr and the temperature is 25 0 C. Assuming that the process is
isothermal, how much work (in L.atm) is done on the atmosphere by the action of expansion?
S ol n :
Q-9
200 L of a certain liquid is confined in a adiabatic system at the initial pressure of 100 atm. This pressure is
suddenly released and external pressure is made to 5 atm, the liquid expanded by 1% against this external
pressure. Then, find U, w and
H.
S ol n :
Q-10
(a) A certain mass of a gas initially at (1L, 5 atm, 300 K) is expanded reversibly and isothermally to a final volume
of 5L, calculate work done by the gas and heat supplied in this process to the gas.
(b) Now,if the gas is restored to initial position by compressing it using an external constant pressure of 5 atm.
Find work done on the gas in this process and heat rejected by gas
(c) In the above two processes, what is the net heat gained by surroundings?
[ N ote : From above question see that surroundings has done extra work on the system but system has returned
that work in the form of heat to surroundings and work is considered on organized form of energy while heat as
an unorganised form hence in the above process, there must be net increment in randomness of universe which
will be called E ntro py, soon.]
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Q-11
14
A heat engine carries one mole of an ideal mono-atomic gas around the cycle as shown in the figure, the amount
of heat added in the process A B and heat removed in the process CA are :
(A) qAB = 450 R and qCA = –450 R
(B) qAB = 450 R and qCA = –225 R
(C) qAB = 450 R and qCA = –375 R
(D) qAB = 375 R and qCA = –450 R
S ol n :
Q-12
Two moles of Helium gas undergo a reversible cyclic process as showin in figure. Assuming gas to be ideal, what
is the net work involved in the cyclic process c?
(A) – 100 R n4
(B) +100R n4
(C) + 200R n4
(D) –200R n4
S ol n :
Q-13
Select the correct set of statement /s :
I.
Work done by the surrounding in case of infinite stage expansion is more than single stage expansion
II.
Irreversible work is always greater than reversible work. (with sign)
III.
On an ideal gas in case of single stage expansion and compression system as well as surrounding are
restored back to their original states
IV.
If gas is in thermodynamic equilibrium is taken from state A to state B, by four successive single stage
expansions. Then we can plot 4 points on the P-V indicator diagram.
(A) II
(B) I, II, III, IV
(C) II, IV
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(D) I, II, IV
THEMODYNAMICS
15
Q-14
Consider the reaction at 300 K
H 2 (g) + Cl2 (g)
2H Cl (g) ;
H º = – 185 kJ
If 2 mole of H 2 completely react with 2 mole of Cl2 to form H Cl. What is U º for this reaction ?
(A) 0
(B) – 185 kJ
(C) 370 kJ
(D) – 370 kJ
S ol n :
Q-15
For the real gases reaction 2CO (g) + O 2 (g)
2C O 2 (g) ; H = – 560 kJ. In 10 litre rigid vessel at 500 K, thee
initial pressure is 70 bar and after the reaction it becomes 40 bar. The change in internal energy is :
(A) – 557 kJ
(B) – 530 kJ
(C) – 563 kJ
(D) None of these
S ol n :
Q-16
A gas expands adiabatically at constant pressure such that T
(A) 1.30
(B) 1.50
(C) 1.70
V –1 / 2 . The value of
of the gas will be:
(D) 2
S ol n :
Q-17
P-V plot for two gases (assuming ideal) during adiabatic processes are given in the figure. Plot A and plot B
should correspond respectively to :
(A) He and H 2
(B) H 2 and He
(C) SO 3 and CO 2
(D) N 2 and Ar
S ol :
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Q-18
3
1 mole of an idal gas A (C v,m = 3R) and 2 mole of an ideal gas B are Cv,m = 2 R taken in a container and
expanded reversible and adiabatically from 1 litre to 4 litre starting from initial temperature of 320 K. E or U
for the process is :
(A) –240 R
(B) –240 R
(C) 480 R
(D) –960 R
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16
ABHYAAS - IV
LEVEL - II
Enthalpy of reaction, Hess’s Law
Q-1
For reduction of ferric oxide by hydrogen,
Fe2 O 3(s) + 3 H 2(g)
2 Fe(s) + 3 H 2 O( ) ;
H º 300 = - 35 kJ. The reaction was found to be too exothermic.
To be convenient, it is desirable that
H º should be at the most - 26 kJ . At what temperature is it possible ?
C P[Fe2 O 3] = 105, C P[Fe(s)] = 25, C P[H 2 O( )] = 75, C P[H 2(g)] = 29 (all are in J/mol)
C P[Fe2 O 3] = 105, C P[Fe(s)] = 25, C P[H 2 O( )] = 75, C P[H 2(g)] = 29
S ol n :
Q-2
Set up the Hess’ law cycle to find the standard enthalpy of combustion of hydrazine using the follow ing
thermochemical reactions.
(i) 2NH 3(g) + 3N 2 O(g)
4N 2(g) + 3H 2 O( ) + 1011 kJ
(ii) N 2 O(g) + 3H 2(g)
N 2 H 4( ) + H 2 O( ) + 317 kJ
(iii) 4NH 3(g) + O 2(g)
2N 2 H 4( ) + 2H 2 O( ) + 286 kJ
(iv) H 2(g) +
1
O (g)
2 2
Also find
H f (N 2 H 4). Is N 2 H 4 an endothermic compound?
H 2 O( ) + 286 kJ
S ol n :
Q-3
In Haber's process of manufacturing of ammonia :
2NH 3(g) ; H025°C = –92.2 kJ
N 2(g) + 3H 2(g)
Molecule
CP
JK -1
mol–1
N 2(g)
H 2(g)
NH 3(g)
29.1
28.8
35.1
If C P is independent of temperature, then reaction at 100°C as compared to that of 25° C will be :
(A) More endothermic
(B) Less endothermic
(C) More exothermic
(D) Less exothermic
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THEMODYNAMICS
17
Q-4
In the reaction, CO 2(g) + H 2(g)
CO(g) + H 2 O(g);
H = 2.8 kJ,
(A) heat of reaction
(B) heat of combustion
(C) heat of formation
(D) heat of solution
H represents
S ol :
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Q-5
For the following reaction,
C (diamond) + O 2
CO 2(g) ; H = –94.3 kcal
C (graphite) + O 2
C O 2(g) ; H = –97.6 kcal
The heat required to change 1 g of C (diamond)
(A) 1.59 kcal
(B) 0.1375 kcal
C (graphite) is
(C) 0.55 kcal
(D) 0.275 kcal
S ol n :
Q-6
C (s) + O 2 (g)
CO (g) +
O 2(g)
1
O (g)
2 2
H = –94.3 kcal /mol
CO 2 (g);
H = – 67.4 kcal /mo!
2O (g);
CO (g)
Calculate
(A) 171
CO 2 , (g);
H = 117.4 kcal /mol
C (g) + O(g) ;
H for C (s)
H = 230.6 kcal /mol
C (g) in kcal /mol.
(B) 154
(C) 117
(D) 145
S ol n :
Q-7
The difference between
(A) – 13.6 kJ
H and
E (on a molar basis) for the combustion of n-octane ( ) at 25° C would be :
(B) – 1.14 kJ
(C) – 11.15 kJ
(D) + 11.15 kJ
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Q-8
18
From the following data of
C(s) +
1
O (g)
2 2
H, of the following reactions,
CO (g)
C(s) + H 2 O (g)
H = – 110 kJ
CO (g) + H 2(g)
H = 132 kJ
What is the mole composition of the mixture of steam and oxygen on being passed over coke at 1273 K, to
maintain constant temperature :
(A) 0.5 : 1
(B) 0.6 : 1
(C) 0.8 : 1
(D) 1 : 1
S ol n :
Q-9
If heat of dissociation of CH Cl2 CO O H is 0.7 kcal /mole then
CH Cl2 CO O H + KO H
H for the reaction :
CH Cl2 CO OK + H 2 O
(A) – 13 kcal
(B) + 13 kcal
(C) – 14.4 kcal
C 2 H 6 (g) + 3.5 O 2 (g)
2C O 2 (g) + 3H 2 O (g)
(D) – 13.7 kcal
S ol n :
Q-10
Svap (H 2 O, ) = x1 cal K -1 (boiling point = T 1)
H f (H 2 O, )
= x2
H f (CO 2)
= x3
H f (C 2 H 6)
= x4
Hence,
H for the reaction is -
(A) 2x3 + 3x2 – x4
(B) 2x3 + 3x2 – x4 + 3x1 T 1
(C) 2x3 + 3x2 – x4 – 3x1 T 1
(D) x1 T 1 + X 2 + X 3 – x4
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THEMODYNAMICS
19
Q-11
In the reaction CS2 ( ) + 3O 2 (g)
CO 2 (g) + 2SO 2 (g)
H = – 265 kcal
The enthalpies of formation of C O 2 and SO 2 are both negative and are in the ratio 4 : 3. The enthalpy of
formation of CS2 is +26kcal /mol. Calculate the enthalpy of formation of SO 2 .
(A) – 90 kcal /mol
(B) – 52 kcal /mol
(C) –78 kcal /mol
(D) –71.7 kcal /mol
S ol n :
Enthalpy of formation, Combustion
Q-12
The heat of combustion of ethyl alcohol is –300 kcal. If the heats of formation of CO 2 (g) and H 2 O( ) are–94.3
and –68.5 kcal respectively, calculate the heat of formation of ethyl alcohol.
S ol n :
Q-13
When 0.36g of glucose was burned in a bomb calorimeter (Heat capacity 640 JK -1) the temperature rose by 10
K. Calculate the standard molar enthalpy of combustion.
S ol n :
Q-14
Find out the heat evolved in combustion if 112 litres (at STP) of water gas (mixture of equal volume of H 2(g) and
CO (g)).
H 2(g) + 1 / 2 O 2 (g)
CO (g) + 1 / 2 O 2(g)
H 2 O(g)
CO 2(g)
H = – 241.8 kJ
H = – 283 kJ
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Q-15
20
If H 2 + 1 / 2 O 2
K + H2O
H 2 O,
H = – 68 kcal
KO H (aq) + 1 / 2 H 2 ,
H = – 48 kcal
KO H (aq),
H = – 14 kcal
KO H + water
Find the heat of formation of KO H.
S ol n :
Q-16
Use the following data to calculate the enthalpy of formation of As 2 O 3
(i) As2 O 3(s) + [(3H 2 O + aq)]
(ii) As(s) +
3
Cl (g)
2 2
2H 3 AsO 3(aq)
AsCl3 ( )
(iii) AsCl3( ) + (3 H 2 O + aq)
(iv) H Cl(g) + aq
H Cl (aq)
(v)
1
1
H 2(g) + Cl2(g)
2
2
(vi) H 2(g) +
1
O (g)
2 2
H 3 AsO 3(aq) + 3H Cl(aq)
H Cl(g)
H 2 O( )
;
H = +7550 cal
;
H = –71390 cal
;
;
H = –17580 cal
H = –17315 cal
;
H = –22000 cal
;
H = –68360 cal
S ol n :
Q-17
Which of the reaction defines molar
(A) CaO(s) + CO 2(g)
(B)
(D)
CaCO 3 (s)
1
1
Br2 ( ) + H 2 (g)
2
2
(C) N 2 (g) + 2H 2 (g) +
H f°?
HBr(g)
3
O (g)
2 2
1
1
I (s) + H 2 (g)
2 2
2
NH 4 NO 3 (s)
HI (g)
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21
Q-18
Given, H 2(g) + Br2(g)
2HBr(g), H 01 and standard enthalpy of condensation of bromine is H 02 , standardd
enthalpy of formation of HBr at 250 C is
(A) H 01 / 2
(B) H 01 / 2 + H 02
(C) H 01 / 2 - H 02
(D) ( H 01- H 02) / 2
S ol n :
Q-19
The standard heat of combustion of solid boron is equal to :
(A) H °f (B 2 O 3)
(B) 1 / 2 H °f (B 2 O 3)
(C) 2 H °f (B 2 O 3)
(D) 1 / 2 H °f (B 2 O 3)
S ol n :
Enthalpy of Vapourisation, Neutralisation, Bond Energy etc.
Q-20
The heats of neutralization of
(i) CH C 2 - CO O H by NaO H is 12830 cals ;
(ii) H C by NaO H is 13680 calories,
(iii) NH 4 O H by H C is 12270 calories .
What is the heat of neutralization of dichloro acetic acid by NH 4 O H ? Calculate also the heats of ionization of
dichloro acetic acid & NH 4 O H.
S ol n :
Q-21
Calcualte the bond energy of Cl–Cl bond from the following data :
CH 4(g) + Cl2(g)
CH 3 Cl(g) + H Cl(g); H = – 100.3 kJ. Also the bond enthalpies of C–H, C–Cl, H–Cl bonds
are 413, 326 and 431 kJ mol–1 respectively.
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Q-22
22
Calculate H º r for the reaction CH 2 Cl2 (g)
C(g) + 2H(g) + 2Cl(g). The average bond enthalpies of C–H and
C–Cl bonds are 414 kJ mol and 330 kJ mol .
–1
–1
S ol n :
Q-23
Calculate the enthalpy change ( H) of the following reaction
2C 2 H 2(g) + 5O 2(g)
4C O 2(g) + 2H 2 O(g) given average bond enthalpies of various bonds, i.e., C–H,
C C, O = O, C = O, O–H as 414, 814, 499, 724 and 640 kJ mol–1 respectively..
S ol n :
Q-24
Calculate free energy change for the reaction at 27º C
H 2(g) + C 2(g)
2H–C (g)
by using the bond energy and energy data
Bond energies of H–H, C –C and H–C bonds are 435 kJ mol–1 , 240 kJ mol–1 and 430 kJ mol–1 respectively.
Standard entropies of H 2 , C
2
and H C are 131, 223 and 187 JK –1 mol–1 respectively.
S ol n :
Q-25
2 mole of zinc is dissolved in H Cl at 25º C. The work done in open vessel is :
(A) –2.477 kJ
(B) –4.955 kJ
(C) 0.0489 kJ
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(D) None
THEMODYNAMICS
23
Q-26
A solution is 500 ml of 2 M KO H is added to 500 ml of 2 M H Cl and the mixture is well shaken. The rise in
temperature T 1 is noted. The experiment is then repeated using 250 ml of each solution and rise in temperature
T 2 is again noted. Assume all heat is taken by the solution
(A) T 1 = T 2
(B) T 1 is 2 times as large as T 2
(C) T 2 is twice of T 1
(D) T 1 is 4 times as large as T 2
S ol :
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Q-27
One mole of anhydrous MgCl2 dissolves in water and librates 25 cal /mol of heat.
H hydration of MgCl2 = –30 cal /
mol. Heat of dissolution of MgCl2 .H 2 O is
(A) +5 cal /mol
(B) –5 cal /mol
(C) 55 cal /mol
(D) –55 cal /mol
S ol n :
Q-28
The following is (are) endothermic reaction(s) :
(A) Combustion of methane.
(B) Decomposition of water
(C) Dehydrogenation of ethane to ethylene.
(D) Conversion of graphite to diamond.
S ol n :
Q-29
T he bond dissoci a t ion energy of gaseous H 2 , C l 2 a nd H C l are 1 0 4 , 5 8 a nd 1 0 3 kc a l mol –1
respectively. The enthalpy of formation for H Cl gas will be
(A) – 44.0 kcal
(B) – 22.0 kcal
(C) 22.0 kcal
(D) 44.0 kcal
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Q-30
24
The average O–H bond energy in H 2 O with the help of following data
(1) H 2 O( )
H 2 O(g) ; H = + 40.6 KJ mol–1
(2) 2H(g)
H 2 (g) ; H = – 435.0 KJ mol–1
(3) O 2(g)
2O(g) ; H = + 489.6 KJ mol–1
(4) 2H 2 (g) + O 2 (g)
(A) 584.9 KJ mol–1
2H 2 O( ) ; H = – 571.6 KJ mol–1
(B) 279.8 KJ mol–1
(C) 462.5 KJ mol–1
(D) 925 KJ mol–1
S ol n :
Q-31
Heat of hydrogenation of ethene is x1 and that of benzene is x2 . Hence, resonance energy is :
(A) x1 – x2
(B) x1 + x2
(C) 3x1 – x2
(D) x1 – 3x2
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25
THEMODYNAMICS
ABHYAAS - V
LEVEL - II
Second Law and Entropy Calculation
Q-1
One mole of monoatomic gas was taken through a cyclic process as shown in figure.
Calculate
dqrev
T .
ABCA
S ol n :
Q-2
From the given T-S diagram of a reversible carnot engine, find
(i) work delivered by engines in each cycle
(ii) heat taken from the source in each cycle.
(iii) Ssink in each cycle.
S ol n :
Q-3
Two moles of an ideal gas is expanded isothermally and irreversibly at 27º C from volume V 1 to 2.5 V 1 and 4.17
kJ heat is absorbed from surroundings. Determine Ssys, Ssurr and Suniv.
S ol n :
Q-4
One gram sample of oxygen undergoes free expansion from 0.75 L to 3.0 L at 298 K. Calculate S, q , w,
H
and E.
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Q-5
26
One mole of ideal monoatomic gas was taken through isochoric heating from 100 K to 1000 K. Calculate
Ssystem, Ssurr and Stotal in
(i) when the process carried out reversibly
(ii) when the process carried out irreversibly (one step)
S ol :
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Q-6
Predict which of the following reaction (s) has a positive entropy change ?
I. Ag+ (aq) + Cl– (aq)
AgCl (s)
II. NH 4 Cl (s)
NH 3 (g) + H Cl (g)
III. 2NH 3 (g)
N 2 (g) + 3H 2 (g)
(A) I and II
(B) III
(C) II and III
(D) II
S ol :
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Q-7
Which of the following reactions is associated with the most negative change in entropy ?
(A) 2SO 2 (g) + O 2 (g)
2SO 3 (g)
(B) C 2 H 4 (g) + H 2 (g)
(C) C (s, graphite)
(D) 3C 2 H 2 (g)
C 2 H 6 (g)
C6H6 ( )
S ol :
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Q-8
5
When two mole of an ideal gas Cp,m = 2 R heated from 300 K to 600 K at constant pressure. The change inn
entropy of gas ( S) is :
(A)
3
R ln 2
2
(B) –
3
R ln 2
2
(C) 5R ln 2
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(D)
5
R ln 2
2
THEMODYNAMICS
27
Q-9
In previous problem calcualte Sgas if process is carried out at constant volume :
(A) 5R ln 2
(B)
3
R ln 2
2
(C) 3R ln 2
(D) –3R ln 2
S ol n :
Q-10
When one mole of an ideal gas is comressed to half of its initial volume and simultaneously heated to twice its
initial temperature, the change in entropy of gas ( S) is :
(A) C p, m ln 2
(B) C v, m ln 2
(C) R ln 2
(D) (C v, m – R) ln 2
S ol n :
Q-11
The entropy change when two moles of ideal monoatomic gas is heated from 200 to 300 º C reversibly and
isochorically ?
3
300
(A) 2 R ln 200
5
573
(B) 2 R ln 273
573
(C) 3R ln 473
3
573
(D) 2 R ln 473
S ol n :
Q-12
If one mole of an ideal gas Cp,m = 5 R
2
is expanded isothermally at 300 K until it’s volume is tripled, then
change in entropy of gas is :
(A) zero
(B) infinity
5
(C) 2 R ln 3
(D) R ln 3
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Q-13
28
In previous problem if expansion is carried out freely (Pext = 0), then :
(A) W = 0
(B) W = RT ln 3
(C) S = R ln 3
(D) Q = RT ln 3
S ol n :
Q-14
Two mole of an ideal gas is expanded irreversibly and isothermally at 37º C until its volume is doubled and 3.41
kJ heat is absorbed from surrounding. Stotal (system + surrounding) is :
(A) –0.52 J/ K
(B) 0.52 J/ K
(C) 22.52 J/ K
(D) 0
S ol n :
Q-15
1 mole of an ideal gas at 25°C is subjected to expand reversibly and adiabatically to ten times of its initial volume.
Calculate the change in entropy during expansion (in J k–1 mol–1)
(A) 19.15
(B) – 19.15
(C) 4.7
(D) zero
S ol n :
Q-16
One mole of an ideal diatomic gas (C v = 5 cal) was transformed from initial 25° C and 1 L to the state when
temperature is 100°C and volume 10 L. The entropy change of the process can be expressed as (R = 2 calories /
mol / K)
298
(A) 3 ln 373 + 2 ln 10
373
1
(C) 7 ln 298 + 2 ln 10
373
(B) 5 ln 298 + 2 ln 10
373
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(D) 5 ln 298 + 2 ln 10
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THEMODYNAMICS
29
Q-17
What is the change in entropy when 2.5 mole of water is heated from 27º C to 87º C ? Assume that the heat
capacity is constant. (C p,m (H 2 O) = 4.2 J/g-K ln (1.2) = 0.18)
(A) 16.6 J/ K
(B) 9 J/ K
(C) 34.02 J/ K
(D) 1.89 J/ K
S ol n :
Q-18
For a perfectly crystalline solid C p,m = aT 3 + bT, where a and b constant. If C p,m is 0.40 J/ K mol at 10 K and 0.92
J/ K mol at 20 K, then molar entropy at 20 K is :
(A) 0.92 J/ K mol
(B) 8.66 J/ K mol
(C) 0.813 J/ K mol
(D) None of these
S ol n :
Q-19
The entropy of vaporization of benzene is 85 JK –1 mol–1 . When 117 g benzene vaporizes at it’s normal boiling
point, the entropy change of surrounding is :
(A) –85 JK –1
(B) –85
1.5 JK –1
(C) 85
1.5 JK –1
(D) None of these
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30
ABHYAAS - VI
LEVEL - II
Gibbs free Energy
Q-1
Find E , H, S and G in expanding reversibly one litre of one mole of an ideal gas to 100 L at a constant
temperature of 27° C.
S ol n :
Q-2
C alculate free energy when 1 mole of a an ionic salt MX (s) is dissolved in water at 25 ° C . Given
Lattice energy of MX = 780 kJ mol–1
Hydration energy of MX = – 775.0 kJ mol–1
Entropy change of dissolution at 25° C = 45 J mol–1 K –1
S ol n :
Q-3
Estimate the temperature range for which the following standard reaction is product-favoured.
SiO 2 (s) + 2C(s) + 2Cl2 (g)
SiCl4 (g) + 2CO(g)
H ° = + 33 kJ / mole and S° = 225 J/mole.K
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Q-4
A gaseous reactant A forms two different product, in parallel reaction, B and C as follows :
A
B; H º = –3kJ, Sº = 20JK –1 ;
A
C; H º = –3.6 kJ, Sº = 10 JK –1
Discuss the relative stability of B and C on the basis of Gibb’s free energy change at 27º C.
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Q-5
Calculate the total entropy change for the transition at 368 K of 1 mol of sulphur from the monoclinic to the
rhombic solid state and
H = – 401.7 J mol–1 for the transition. Assume the surroundings to be an ice-water.
Both at 0º C :
(A) – 1.09 JK –1
(B) 1.47 JK –1
(C) 0.38 JK –1
(D) None of these
S ol n :
Q-6
Which of the following statement (s) is / are correct?
Statement (i) : The entropy of isolated system with P–V work only, is always maximized at equilibrium.
Statement (ii) : It is possible for the entropy of close system to decrease substantially in an irreversible process.
Statement (iii) : Entropy can be created but not destroyed.
Statement (iv) : Ssystem is zero for reversible process in an isolated system.
(A) Statement i, ii, iii,
(B) Statement ii, iv
(C) Statement i, ii, iv
(D) All of these
S ol n :
Q-7
Calculate standard entropy change in the reaction
Fe2 O3 (s) + 3H 2 (g)
2Fe (s) + 3H 2 O ( )
Given : Sºm (Fe2 O 3 , S) = 87.4 , Sºm (Fe, S) = 27.3, Sºm (H 2 , g) = 130.7, Sºm (H 2 O, ) = 69.9 JK –1 mol–1 .
(A) –212.5 JK –1 mol–1
(B) –215.2 JK –1 mol–1
(C) –120.9 JK –1 mol–1
(D) None of these
S ol :
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Q-8
Calculate the entropy change (J / mol K) of the given reaction. The molar entropies [J / K-mol] are given in
brackets after each substance.
2PbS (s) [91.2] + 3O 2 (g) [205.1]
(A) –113.5
(B) - 168.3
2PbO (s) [66.5] + 2SO 2 (g) [248.2]
(C) + 72.5
(D) - 149.2
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Q-9
Given
32
Sº = –266 and the listed [Sºm values]
r
calculate Sº for Fe3 O 4 (s) :
4Fe3 O 4 (s) [..............] + O 2 (g) [205]
(A) +111.1
(B) +122.4
6Fe2 O 3 (s) [87]
(C) 145.75
(D) 248.25
S ol n :
Q-10
Which of the following conditions regarding a chemical process ensures its spontaneity at all temperature ?
(A) H > 0, G < 0
(B) H < 0, S > 0
(C) H < 0, S < 0
(D) H > 0, S < 0
S ol n :
Q-11
For isothermal expansion in case of an ideal gas :
(A) H = 0
(B) E = 0
(C) G = –T. S
(D) T final = T initial
S ol n :
Q-12
When reaction is at standard state at equilibrium, then :
(A) H º = 0
(B) Sº = 0
(C) equilibrium constant K = 0
(D) equilibrium constant K = 1
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Q-13
For the gas - phase decomposition,
(A) H < 0, S < 0
Q-14
PCl5 (g)
(B) H > 0, S > 0
PCl3 (g) + Cl2 (g) :
(C) H > 0, S < 0
(D) H < 0, S > 0
What is the free energy change ( G) when 1.0 mole of water at 100º C and 1 atm pressure is converted into
steam at 100º C and 1 atm pressure ?
(A) 80 cal
(B) 540 cal
(C) 620 cal
(D) Zero
S ol n :
Q-15
The enthalpy change for a given reaction at 298 K is – x J mol –1 (x being positive). If the reaction occurs
spontaneously at 298 K, the entropy change at that temperature
(A) can be negative but numerically larger than x / 298
(B) can be negative but numerically smaller than x / 298
(C) cannot be negative
(D) cannot be positive
S ol :
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Q-16
A reaction has H = – 33 kJ and S = – 58
J
. This reaction would be :
K
(A) spontaneous at all temperatures
(B) non-spontaneous at all temperatures
(C) spontaneous above a certain temperature
(D) spontaneous below a certain temperature
S ol n :
Q-17
For a reaction A (g)
B(g) at equilibrium. The partial pressure of B is found to be one fourth of the partial
pressure of A. The value of
(A) RT n 4
G ° of the reaction A
(B) – RT n 4
B is
(C) RT log 4
(D) – RT log 4
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34
ANSWERS
A BHYAAS-I
Q-1
State function : (A) (B) (D) (E) ; Path function : (C) (F) (G)
Q-2
Extensive Property : (B) (C) ; Intensive Property : (A) (D) (E) (F) (G)
Q-3
Intensive property – B, D, E, F, G, H ; Extensive property – A, C
Q-4
(C)
Q-6
(i) Open system
Q-5
(C)
(ii) Closed system
(iii) Open system
Q -8
(A)
(B)
(C) T
(D) F
Q-14
30 J
(iv) Isolated system
(v) Isolated system
Q -7
(D)
Q-12
(A) F
Q-13
70 J
(B) F
Q -9
(E) T
Q -10
(B)
Q -11
(C, D)
(F) T
Q-15
249.37 J
A BHYAAS-II
Q -1
2 g ice,
Q -2
10 2 J
Q -3
5065.8 J
Q -4
E = 0.993 kcal,
Q -5
(B)
Q -6
(A)
Q -7
(A)
Q -8
(D)
Q -9
(C)
Q -10
5200 kJ
Q -11
(D)
Q -12
(B)
Q -13
(C)
Q -14
(B)
Q -15
(D)
Q -16
(C)
H = 1 kcal
A BHYAAS-III
Q-1
T 2 = 100 K, w = – 5.016 KJ
state
1
2
3
Q-2
P ath
1
2
3
Q-3
2
3
1
P
1 atm
1
0.5
N ame of
p rocess
sobaric
Isochoric
Isothermal
Cyclic
V
22.4
44.8
44.8
T
273
546
273
q
w
5 / 2 R(273)
-3 / 2 R(273)
-273 R ln 2
R (273) - 273 R ln 2
E
-R (273)
0
273 R ln 2
(273) + 273 R
3 / 2 R (273)
-3 / 2 R (273)
0
0
H
5 / 2 R (273)
-5 / 2 R (273)
0
0
(i) w AB = – 1496.52 Joule, wBC = – 1446.63 Joule, w CD = 0, wDA = 1728.48 Joule;
(ii) qAB = 5237.82 Joule, qBC = 1446.63 Joule, qCD = – 3741.3 Joule, qDA = –1728.18 Joule;
(iii) H AB = 6235.5 Joule,
Q-4
H BC = 0,
H CD = – 6235.5 Joule,
H DA = 0 Joule
U = w = – 1247.1 J ; H = – 1745.94 J
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35
Q-5
Q-6
w = -3.2kJ, q = 0, T = -38K, U = -3.2kJ, H = - 4.42 kJ
E = 34.46 kJ
Q-7
27.91 kJmol–1 , t = 514 sec.
Q-8
w = —240 L.atm.
Q-9
–10 L. atm, –10 L. atm, –19000 L. atm
Q-10
(A) – 816 J (B) + 2026 J (C) 1210 J
Q-11
(C)
Q-18
(D)
Q-12
(A)
Q-13
(A)
Q-14
(D)
Q-15
(B)
Q-16
(B)
Q-17
(B)
A BHYAAS-IV
Q-1
408.43 K
Q-2
Q-3
(C)
Q-4
(A)
Q-5
(D)
Q-6
(D)
Q-7
(C)
Q-8
(B)
Q-9
(A)
Q-10
(B)
Q-11
(D)
Q-12
(–94.1 kcal)
Q-13
–3.2 MJ mol . Q-14
1312 kJ
Q-15
–102 kcal
Q-16
– 154.68 kcal
Q-17
(B,C,D)
Q-18
(D)
Q-19
(B)
Q-20
–11420 cal., –850 cal., –1410 cal.
Q-21
243.7 kJ mol
Q-22
1488 kJ mol . Q-23
– 2573 kJ/mole
Q-24
-191 kJ
Q-25
(B)
Q-26
(A)
Q-27
(A)
Q-28
(B,C,D)
Q-29
(B)
Q-30
(C)
Q-31
(C)
-1
-1
H comb = – 622.7 kJ mol–1 ,
-1
H f = 50.7 kJ mol–1 , Yes
A BHYAAS-V
dq rev.
T
Q-1
dS =
Q-2
(i) 30 kJ,
dq rev.
= S. As 'S' being a state function, S = 0 in a cyclic process.
T
(ii) + 60 kJ,
(iii) 100 J/ K
Q-3
Ssystem = 15.32 J, Ssurr = – 13.9 J, Suniv = 1.42 J
Q-4
S = 0.36 JK –1 , W = q = H = 0
Q-5
(i) Rev. Process Ssystem =
dq rev.
= 0.
T
3
3
R In 10; Ssurrr = – R In 10 STotal = 0
2
2
(ii) Irr. Process Ssystem =
3
3
3
R In 10; Ssurrr = – R (0.9); Stotal = R (1.403)
2
2
2
Q-6
(C)
Q-7
(D)
Q-8
(C)
Q-9
(C)
Q-10
(D)
Q-11
(C)
Q-12
(D)
Q-13
(A, C)
Q-14
(B)
Q-15
(D)
Q-16
(B)
Q-17
(C)
Q-18
(D)
Q-19
(B)
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36
A BHYAAS-VI
Q-1
For an ideal gas, at constant temperature, E = 0 and H = 0;
V2
Ssys = R n V = 2.303 × 2 log 100 = 9.2 cal K –1 mol–1
1
Q-2.
Q-4
Q-5
Q-10
At constant temperature, G = H – T.
– 8.41 kJ mol–1 .
G º indicates that B is more stable than
(C)
Q-6
(D)
(B)
Q-11 (A, B, C, D)
S=0
Q-3
C.
Q-7
Q-12
Q-15
(B)
Q-17
Q-16
(D)
– 300 × 9.2 = – 2760 cal mol–1
T > 146.7 K
(B)
(D)
Q-8
Q-13
(A)
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(B)
(B)
Q-9
Q-14
(C)
(D)