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Combined Geo-Scientist (Main)
E-M-CM
Examination, 2024 SGS CMS
CHEMISTRY
Paper - II
Time Allowed : Three Hours Maximum Marks : 200
Question Paper Specific Instructions
Please read each of the following instructions carefully before attempting
questions :
There are FIFTEEN questions divided in THREE sections.
Candidate has to attempt TEN questions in all.
The ONLY question in Section A is compulsory. In Section B, SIX out of NINE questions
are to be attempted. In Section C, THREE out of FIVE questions are to be attempted.
The number of marks carried by a question/ part is indicated against it.
Neat sketches are to be drawn to illustrate answers, wherever required. These shall be
drawn in the space provided for answering the question itself.
Unless otherwise mentioned, symbols and notations have their usual standard meanings.
Assume suitable data, if necessary, and indicate the same clearly.
Attempts of questions shall be counted in sequential order. Unless struck off, attempt of a
question shall be counted even if attempted partly.
Any page or portion of the page left blank in the Question-cum-Answer Booklet must be
clearly struck off.
Answers must be written in ENGLISH only.
SGSE-M-CMS 1
Some useful fundamental constants and conversion factors
Nag = 6-022 x 1023 mol ¦
Rydberg constant = 2-178 × 108 J
= 2-998 × 108 ms!
hp = 1:38 × 10 29 JK
¿ = 1.602 × 10-19 0
76 = 9-109 × 1031 kg
F = 96485 C molt
8:314 JK! molt
h = 6-626 x 10-34 Js
7 = 3-142
1 amu 1-66 × 1027 kg
141 = 4-184 J
1 9 = 1 12 112 2
1 & = 10 cm = 10710 = 0-1 nm = 100 pm
1 atm = 760 torr = 1-01325 × 106 Pa
1 bar = 1 × 10° Pa = 0-9869 atm
1 % = 1.602 × 10719 J
1 Latm = 101-347
1 eV = 23060 cal/mol
47202 = 3-55 x 1022 cm? 82
a = 6-025 x 10-38 J m?
h, = 1-986 x 10 * Jm
h
87020
= 2-8 x 10 44 kg ”
SGSE-M-CMS 2
SECTION A
(Compulsory Section)
Ql. Answer all of the following questions : 5x 16=80
(a) Gases A and B are van der Waals gases. If van der Waals constants
(‘a’ and ‘b’) values (in SI units) are :
A B
a 21-764 3-457
-108b’ 0-024 0-024
(i) Which of these would occupy greater volume under identical
conditions ?
(ii) | Which gas has the highest critical temperature ? a
(b) From virial equation of state for a real gas
PVim = RT (1 + Ag (T)p + Ag (T) p? + «2.0... )
where the symbols have their usual meanings,
Explain :
(i) The physical significance of the second virial coefficient ‘Ag’.
(ii) The behaviour of the second virial coefficient (Ay) at low,
moderate and high temperatures.
(iii) | What happens when A, = 0? 5
(c) Differentiate between conductors, semiconductors and insulators using
band theory of solids. 5
(d) Give an account of Bravais Lattices in cubic and tetragonal crystal
system mentioning the minimum symmetry elements in them. 5
(e) What do you understand by chemical potential ? Give an account of
variation of chemical potential with temperature. 5
(f) Obtain a relation between equilibrium constant, K,, K, and K,. Under
what conditions is K, =K,=K,? 5
SGSE-M-CMS 3
(g) The rate constant for the reaction O(g) + O3(g) > 20 9(g) is
8-0 x 10-15 cm? molecule! s-! at 298 K. Express this rate constant in
dm? mol"! s-!. 5
(h) Write BET equation. Explain the terms involved in it. 5
(i) Given :
Cu2+ +2° > Cu; E°=+0-350V
Zn2+ + 2°» Zn; E°=- 0-763 V
Construct the cell using these reactions.
(i) Write and balance the total cell reaction.
(ii) Find the E° of the cell.
(iii) State whether the cell reaction will be spontaneous or not. 5
Gj) What is the source of alkaline error in pH-measurements with the glass
electrode ? 5
A
(k) Evaluate the commutator E =|. 5
qd) Interpret the physical meaning of the square of the wave function
|‘¥(x)|?. What are the dimensions of | ‘P(x) | 2? 5
(m) What is the Raman effect and how does it differ from phosphorescence
and fluorescence ? 5
(n) Hydrogen molecule gives neither vibrational nor rotational spectrum,
but is Raman active. Explain. 5
(0) The fluorescence quantum yield and observed fluorescence lifetime of
tryptophan in water are op 9 = 0:20 and Ty = 2°6 ns, respectively.
Calculate the fluorescence rate constant, kp. 5
(p) The first step in the photoinitiated reaction between hydrogen and
bromine using 511 nm radiation is
Br, + hv > 2Br
Why is hydrogen molecule not dissociated under these conditions ? as
SGSE-M-CMS a
Attempt any six questions:
Q2.
Q3.
Q5.
SECTION B
Define Boyle temperature (Tg) of a non-ideal gas. Show that for a van der
Waals gas, the Boyle temperature Tp = = where ‘a’ and ‘b’ are van der
Waals constants.
(a) Obtain Miller indices of a crystal plane which cuts through the crystal
axes at (2a, — 3b, — 3c).
(b) A bec element of density 10300 kg m- has a cell edge of 314 x10-12 m.
Calculate the atomic mass of the element.
Obtain an expression for the equilibrium constant and standard free energy
change using a general reversible reaction :
aA +bB=cC+dD
(a) The rate of decomposition of a gas A was 3-70 in some unit when 10%
had reacted and it was 2:60 in the same unit when 25% had undergone
decomposition. Calculate the order of the reaction.
(b) Explain with reasons :
(i) Physical adsorption decreases with increase in temperature, but .
chemisorption increases.
Gi) On adding detergent in water, surface tension decreases.
The pH of a buffer solution containing 0-5 mol/m? of CH3,COOH and
0:5 mol/m? of CH,COONa has been found to be 4:76. What would be the pH of
this solution after 0-02 mol/m? NaOH has been added to the buffer ? Assume
that the volume is unchanged. (Given K, = 1-80 x 10-)
SGSE-M-CMS 5
10x6=60
10
10
103
Qi.
Qs.
(a)
(b)
State the different assumptions involved in the derivation of Langmuir
adsorption isotherm.
What Raman shifts (in cm!) are expected for the first four Stokes lines
for CO, (B = 0-3906 cm} ?
Prove that the operator is is Hermitian, but < is not.
Q9. The vibrational wave numbers of He, D, and Hy are approximately 2322,
3118, and 4400 cm7!, respectively. Calculate the force constants for these
molecules and comment on the relative magnitudes of the values you obtain.
(H=1,)—2)
Q10.
(a)
(b)
Describe the Franck-Condon principle and its significance in
photochemistry.
The continuum limit for the dissociation of Bro gas
Brg (ground) = Br (ground) + Br (excited) occurs at 19,750 em7!,
The transition of a ground bromine atom to an excited one corresponds
to a wave number of 3865 cm!.
Calculate the energy for the process
Brg (ground) = 2Br (ground) in cm!.
SGSE-M-CMS 6
10
10
SECTION C
Attempt any three questions: 20x3=60
Qll. (a) Show that in a first order reaction, the time required for completion of
99% reaction is 10 times of the half-life (t1/9) of the reaction. 10
(b) The values of the rate constant (k) for the reaction 5
2N,0; (g) > 4NO, (g) + Og (g)
were determined at several temperatures. A plot of In K vs 1/T gave a
straight line of which the slope was found to be — 1-2 x 104 K. What is the
activation energy of the reaction ?
(c) For the following cell
Cd| CdCl, (sat.) || AgCl| Ag,
E = 0-675 V and a =—6:5 x 10+ VK~ at 298 K.
What is the reaction taking place in the cell ? What are the values of AG,
AH and AS at 298 K? 5
Ql2. (a) A flask of 4 dm® capacity contains Og at 101:325 kPa and 298 K. The gas
pressure is reduced to 0-10 Pa by attaching the flask to a pump.
Assuming ideal behavior, answer the following :
Ad) What will be the volume of the gas which is left behind ?
(ii) | What amount of Og and the corresponding number of molecules
are left behind in the flask ?
(iii) If now, 2 g of Nog is introduced, what will be the pressure of the
flask ? 10
(b) Evaluate the potential of a silver electrode in a solution that is saturated
with silver iodide.
(Given ay- = 1-00, K,, for Agl = 8:3 x 10-"7) 10
SGSE-M-CMS 7
Q13. (a)
(b)
Q14. (a)
(b)
(c)
(d)
Q15. (a)
HgCl, crystallizes in orthorhombic system. Using radiation with
4. = 154 pm, for the (100), (010) and (001) planes, first order reflections in
an X-ray diffractometer occur at 7°25’, 3°28’ and 10° 23’ respectively.
Calculate the dimensions of the unit cell and the number of HgCl,
molecules in the unit cell. The density of the crystal is 5-42 g cm~® and
M(HgCl,) = 271-5 g moll.
Show that the activity is the thermodynamic counterpart of gas pressure.
For a particle confined at constant potential within a cubic box,
determine the quantum numbers of
(i) the lowest excited state that is not degenerate.
Gi) __ the lowest energy level with a degeneracy of 6.
Calculate the corresponding energies (in J) if the side length of the box is
0-5 nm.
What will be the wavelength of the radiation absorbed/emitted when an
electron makes a transition between these two energy levels ? In what
region of the electromagnetic spectrum does this transition lie ?
In the uranyl oxalate actinometer, 5-1875 x 1018 molecules were
decomposed when exposed to a radiation of 1 = 365-5 nm. During this
time, the number of photons absorbed were 10-5875 x 1018. Calculate
the quantum efficiency.
135C] has a rotational constant of 10-26 cm=.
(i) Explain how the rotational constant is determined from the
microwave spectrum.
(ii) Calculate the moment of inertia of 1H®5C1.
Gii) Calculate the bond length of the HCl molecule using the above
data.
SGSE-M-CMS 8
10
10
(b) The photolysis of hydrogen iodide follows the mechanism :
HI +hv —2 5 H-+I-
H: + HI —2., Hy +1:
oe. ae
H: +1, —“4-5 HI+I-
Use the steady-state approximation to H- to construct the rate law.
What is the overall quantum yield of the process ? 10
SGSE-M-CMS 9
