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Combined Geo-Scentst (Main)
Examination-2025 BGSP-B-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.
BGSP-B-CMS/65 1 [P.T.0.
[061] 1311302-4 1010000
Some useful fundamentaltsribladts\and conversion factors
, =6.022 1023 mol"!
Rydberg constant = 2-178x10718
c=2-998x108 ms!
kg =1-38 ×10-23 JK!
e=1-602x10 19
716 = 9 . 109 × 10 `3! kg
F = 96485 mol"!
R=8-314 JK"! mol"
h=6-626x10 8
7 =3-142
1 amu = 1 . 66 × 10 27 kg
1 cal = 4. 184 J
1 J >1 [8 25 2
1A =10 8 cm = 10 10 m = 0 . 1 nm = 100 pm
1 atm = 760 torr =1-01325x10° Pa
1 bar =1x10° Pa =0-9869 atm
1 eV =1-602x10719 J
1 L atm = 101 . 34
1 eV = 23060 cal mol!
4722 = 3 . 55 ×1022 cm? 7
h?
8m,
= 6 . 025 10 38 J 712
he = 1 . 986 10 25 Jm
h
87162
= 92. 821071 kg m
BGSP-B-CMS/65 2
SECTION—A
( Compulsory Section )
1. Answer all of the following questions : 5x 16=80
(a) Z (compressibility factor) versus P plots of Hy and He gas are always above the
plot of ideal gases. Explain why. 5
(b) Calculate the temperature and pressure of 1 mole of HS, which will
correspond to the state of 1 mole of Nj at 25 °C and 1-0 atm pressure.
Given : P, (atm) T, (K)
Ny 33-5 126-3
H,S 88-3 373-2 5
(c) Draw the qualitative band structure of p-type and n-type semiconductors. 5
(a) Mg2SiO, crystallizes in an orthorhombic crystal system. What are the
maximum and minimum symmetry elements it can possess? 5
(e) For closed system, at constant pressure, Gibbs’ free energy (G) decreases with
increase of temperature and vice versa. Justify with reasons. 5
(ff) For a gas obeying the equation of state P(V,, -b)=RT, (i) Z (compressibility
factor) > 1 and (i) f (fugacity) > P. Justify with reasons. 5
(g) The mechanism of a chemical reaction is
A+B—>C+D
2C>F
F+B—>2A+G
Give the overall balanced equation and classify each species as reactant,
product, intermediate or catalyst. Give reasons. 5
(h) For a specific H* ion catalyzed solution-phase reaction, draw the plot of
log (rate constant) versus pH of the solution. State the values of slope and
intercept. 5
() Can a salt bridge made from filter paper dipped in KCl solution be used to
make a cell consisting of silver and lead half-cells? Justify your answer. 5
BGSP-B-CMS/65 3 [P20
@) Given that Elst =-0-41 V and Ee = ~2-33 V, calculate the value of
/Cr 3+ / Ce
equilibrium constant for the following reaction at room temperature (25 °C) :
Ce(s)+Cr°* (aq) = Ce** (aq) +Cr(s) 5
(k) What are the conditions for an acceptable wave function? 5
() Prove that there is no acceptable solution to the time-independent Schrédinger
equation for the particle in one-dimensional box with E =0 (dimensions of the
box are x=0 and x=a). 5
(m) ‘Discrete energy levels’ and ‘condition of resonance’ are essential conditions for
discontinuous line spectrum. Explain. 5
(n) Which one of the following molecules is rotational spectrum active and why?
CO, and CO 5
(o) Explain briefly about measuring the intensity of radiation using a chemical
actinometer. 5
(p) How do watch hands glow in the dark? 5
SECTION—B
Attempt any six questions : 10x6=60
2. A gas at 350K and 12 atm has a molar volume 12 percent larger than the
calculated from the perfect gas law.
(a) Calculate the compressibility factor under these conditions. Which forces
(attractive or repulsive) are dominating under these conditions?
(b) Calculate the molar volume of the gas. 10
3. Explain the limitations of powder X-ray diffraction to analyze samples with the
following conditions :
(a) An alloy consisting of Co and Ni
(b) Powders with average crystallite size in sub-micron scale 10
BGSP-B-CMS/65 4
4.
5.
10.
Show that
oH
.
an; 5, V, nj (171) 10
The Debye-Htckel limiting equation is
logio(¥;)=-AZ? VI
(a) Write down the significance of each symbol with unit.
(b) What are the factors on which A depends?
(c) Derive the following equation :
logiolvs)=-A|Z,Z_|VI 10
5-0 kg of a catalyst adsorbs 400 of 112 gas at 1 bar and 300K to form a
monolayer. What is the surface area of the catalyst if the area occupied per
molecule of Ny is 16x107!° m?? 10
(0) Derive the expressions to determine AG’ and &5 of an electrochemical cell
reaction by emf () measurements.
(b) Find the cell reaction and its AS” of the cell
(8 (aq) || Fe>* , Fe2* () 29
Given : | | =1.14 ×10-3 - at 298K
21 > 10
Explain how degeneracy can occur for a particle in a rectangular box witha#b#c. 10
Whether spectral lines of Balmer spectrum are equispaced? Give reason(s) with your
answer. 10
For the reaction
11 () + Bry -- 2HBr@g)
show that the rate of the reaction varies as the square root of the intensity of the
absorbed radiation. 10
BGSP-B-CMS/65 5 190,
Attempt any three questions :
11.
12.
13.
SECTION—C
(a) The fugacity coefficient of a certain gas at 200K and SObar is 0-72.
Calculate the difference of its chemical potential from that of an ideal gas in the
same state.
(b) The value of K, for the reaction (at 298 K)
_1 3
NH3 (g) = rea ep Me (g)
is 1-36x10°°. Determine the corresponding value of its Ke.
(c) Derive the expression oe clearly mentioning assumption(s)
RT
and approximation(s) used, and discuss the effect of temperature on the
value of K, (with graphical sketch also) for any solution-phase dimerization
reaction.
(a) For a second-order reaction A— P, show that the time required for 75% of
the reaction (to.75) is equal to 3 xto.5.
(b) Sucrose is hydrolyzed in presence of H* ion as catalyst. At any initial
concentration of sucrose, the half-lives at pH = 5 and pH = 4 are 500 min and
50 min respectively. Find out the values of exponents a and bin the rate law
_ d[sucrose]
= k[sucrose]® [H* |?
ae [ }° {H*]
(c) The adsorption of a gas is described by the Langmuir isotherm with
a =0-75 kPa! at 298K. Calculate the pressure at which the fractional
surface coverage is (i) 0-15 and (ii) 0-95.
Given the reaction
2M+6H* >2M** +3H,
for which AHj9g =-3-00 kcal, the entropies are 6-5cal/K for M, -22-2cal/K
for M** 31-2 cal/K for Hy and -10-0 cal/K for H* ; AG; for H* is 0-00. Calculate—
(a) the standard free energy of formation of M°*;
(b) E° for the half-reaction M°* +3e7 > M.
BGSP-B-CMS/65 6
20x3=60
14. Let A and B be Hermitian operators and c be the constant.
(a) Show that cA is Hermitian if c is a real number and cA is not Hermitian
if c is not a real number.
(b) Show that (A +B) is a Hermitian. 20
15. (a) Symmetric stretching vibration of linear CO, molecule is vibrational spectrum
inactive but vibrational Raman spectrum active. Give reason(s). 5
(b) Spectral lines of microwave spectrum of rigid diatomic molecules are
equispaced. So energy levels are also equispaced. Justify or criticize with
reasons. 5
(c) The microwave spectrum of H°°Cl consists of equispaced spectral lines,
separated by 6-26 x10!! hertz. What is the—
(j totational constant (B);
(i) moment of inertia (I) in SI unit;
(ii) equilibrium bond length (79) in SI unit? 10
BGSP-B-CMS/65 7 25SS—144
