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Combined Geo-Scientist (Main)
Examination, 2026 feather DETACHABLE
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 under 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.
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ia useful fundamental constants and conversion factors
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Ng = 6-022 × 102
Rydberg constant = 2-178 x 107 J
-2-998 x 108 715 1
kg = 1.38 × 1023 JK}
e= 1-602 x 1019
m, = 9-109 x 10 31 kg
F = 96485 C mol!
R=8-314 JK! mor!
h = 6-626 x 10715
753-142
1 amu = 1-66 «105171
1 cal = 4-184 J
1] = 1 12 112 2
1 & = 10-8 = 1070 m=0-1 nm= 100 pm
1 atm = 760 torr = 1-01325 x 10° Pa
1 bar = 1 x 10° = 0-9869 atm
LeV=1-602 × 10791
1 Latm= 101-34 J
1 eV = 23060 cal mol!
47202 = 3-55 × 1022 cm? 5 2
8m,
e
= 6-025 x 1038 Jm?
he = 1-986 x 10 25 Jm
h
„ 28 104 kgm
1.(a)
1.(b)
1.(c)
1.(d)
1.(e)
1.(f)
1.(g)
1.(h)
1.(i)
1.G)
SECTION ‘A’
(Compulsory Section)
(Answer all of the following questions) 5x16=80
Define compressibility factor (Z). What is its significance : when its value is either
(i) 1 or (ii) <1 or (iii) >1? 5
Draw Andrew’s plot of P vs. V isotherms of a real gas at different temperatures.
2
At the critical point why (i) (=) = 0 and (ii) ced =0? 5
ov T=T, ov T=f,
" <—
What is the angle of first order X-ray diffraction for 110-planes of a simple cubic
lattice of edge length 800 pm when X-ray wavelength is 0-4 nm. 5
Which one of the following is an intrinsic semiconductor and how do you convert
it into an extrinsic semiconductor ?
(i) diamond
(iil) q@-tin
(iii) silicon
(iv) YBayCu307 5
With the help of the relation between fugacity (f) and pressure (P) of a non-ideal gas,
mention the conditions when (i) f>P, (ii) f= P and (iii) f<1. 5
Write down the relation between K, and K, of the reaction : A (g) + B (g) = C (g).
(Assuming all gases in the reaction mixture behave ideally) Under what conditions
K, will be equal to the K, ? P)
A radioactive nuclide X has two decay modes (both first order)
k, 7B
<a ; k, and k, are decay constants
> C
Express ¢,, (half-life period) of X in terms of k, and k). 5
What are the basic differences of soap and detergent though both are used for
cleaning purpose of. clothes ? 5
Construct a galvanic cell in which the following spontaneous reaction will happen.
2 Cur (aq.) = Cu* (aq.) + Cu (s). 5
Calculate the pH of an aqueous solution of a weak monoacidic base at 298 K which
has been neutralised by a strong monobasic acid to the extent of 65%. Given K, and
K,, are 20x10 and 1-0x107'4 respectively at 298 K. 5
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1.(k)
1.(1)
1.(m)
1.(n)
1.(0)
1.(p)
A student says “If a particle is in an energy eigenstate, its energy is fixed, so there
is no uncertainty in any quantity”.
Is this statement correct ? Explain your answer with a suitable example. 5
Define the expectation value of an operator. How does it differ from an eigenvalue ?
Explain with reference to energy measurements. 5
How many normal modes of vibrations are possible for the following molecules ?
(i) C6He
(ii) C4Hy
(iii) Os(CO)s;
(iv) SiCly
(v) CS) 5
(i) What is the condition for a molecular vibration to be Raman active ?
(ii) Draw the polarizability ellipsoids for symmetric stretching mode of vibration
of CO). 5
Identify the INCORRECT statement and correct it briefly :
(i) Electronic transitions occur much faster than vibrational motion.
(ii) Franck-Condon principle explains the intensity distribution of vibrational
structure of electronic spectra.
(iii) Fluorescence always originates from the lowest vibrational level of the excited
singlet state.
(iv) Phosphorescence involves a spin-forbidden transition. 5
An excited molecule can lose energy without emitting light. Name two non-radiative
decay processes and explain one reason why these processes compete with
fluorescence. 5
SECTION ‘B’
(Attempt any six questions) 10x6=60
A non-ideal gas has three characteristic temperatures; Critical temperature (T¢),
Boyle temperature (Tg) and Inversion temperature (T;). Write expressions of Tc and
Tz when the gas is van der Waals. What are the significances of Tc and Ty?
10
The elements Ne, Ar, Kr and Xe of group 18 form cubic close-packed crystalline
solids at very low temperatures. Answer the following :
(i) What type of bonding forces are involved in these solids ?
(ii) What crystal structure do they adopt ?
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5.(a)
5.(b)
(iii) How many atoms are present in the unit cells of these solids ?
(iv) What is the coordination number of each atom in these structures ?
(v) How many tetrahedral and octahedral holes per atom are present in these
crystal structures ? 10
The Gibbs-Duhem relations are :
(i) dG=E p, dn,
1
(ii) G=X nyy; For closed systems and at constant P and T
1
(iti) O=¥ nj; du,
1
(I) Mention the nature of the system
(II) Derive the expression of |14; using eqn. (i)
(III) Which one is an intensive property and why; 1; or G?
(IV) What factors can influence the value of 1; ? 10
A sample of milk kept at 25°C is found to sour 40 times rapidly as when it is kept
at 4°C. Determine the Arrhenius activation energy for this souring process in SI unit.
5
At constant P and T, for a spontaneous chemical reaction, AG must be negative but
ANG must not be necessarily negative. Explain. 5
Discuss a method to determine the partial orders and total order of the following
reaction : A(aq.) + 2B(aq.) = P(aq.) 10
The 7-dependence of E° of a galvanic cell is given by E’=A+BT +CT?.
Find the expression of A,H®° for the cell reaction. Show that when T+ the A,G°
and A,,H?® are the same. 10
For a particle in a one-dimensional box :
(i) Why is the ground state energy not zero, even though the potential inside the
box is zero ?
(ii) Why does the energy increase as n? and not linearly with n ? 5+5
Calculate the energy in joules of the rotational level (with /=1) of the rigid H,
molecule.
Given : r,, = 74-1pm
Relative mass of H atom is 1-0080 amu. 10
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10. Using a Jablonski diagram, explain the following :
(i) Why fluorescence lifetimes are typically much shorter than phosphorescence
lifetimes.
(ii) Why phosphorescence is usually observed at longer wavelengths.
(iii) Why fluorescence intensity decreases in the presence of heavy atoms.
3+3+4=10
SECTION ‘C’
(Attempt any three questions) 20x3=60
11.(a) For a solution phase reaction : A(aq.) + B(aq.) = D(aq.); derive the expression for
K,. in terms of the standard free energy change.
(i) What would be the standard state value ?
(ii) What would be the unit of K,?
(iii) What factors can influence the value of K,? 15
11.(b) Are the values of A,G°(P) and A,G°(C) the same, in general ? If not, under what
conditions will they be the same ? 5
12.(a) | Show with the help of the Hard-sphere collision theory, that a unimolecular
elementary gas phase reaction behaves kinetically as a second order reaction at very
low pressure of the reactant. 10
12.(b) Ina photochemical reaction, the following data were obtained using an actinometer :
* Number of photons absorbed per second = 2-0x 1016
* Rate of formation of product molecules = 3-6x10!© molecules s7!
(i) Calculate the quantum yield of the reaction.
(ii) What does the obtained value indicate about the nature of the mechanism ?
(iii) Name one reaction from the syllabus where such behaviour is observed.
Explain your choice. 3+4+3=10
13.(a) At 298 K, the galvanic cell :
(Pt) H(g, 1 atm) |HCl(aq, 0-1 M)|AgCl|Ag, has the EMF(E) = 0-35 V and
(=) = -18x10~ V K"1. Determine A,G, A,H and A,S of the cell reaction for the
Pp
production of 1 faraday electricity. 10
13.(b) Define buffer capacity (8) of a buffer solution. Show that B of an acetic acid-acetate
buffer solution is maximum when [salt]/[acid] is one. 10
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15.(a)
15.(b)
A particle is confined to a three-dimensional cubical box of side a.
(i) Derive the expression for the energy eigenvalues of the particle.
(ii) Define degeneracy and determine the degeneracy of the energy levels
3h" Th?
corresponding to E = and .
" - 4ma? Ama?
(iii) Explain how degeneracy reflects the underlying symmetry of the system.
8+8+4=20
The rotational constant of !2C!4N (rigid rotor) is 1-91 cm. Calculate the
equilibrium bond length (in pm) of CN. 10
A diatomic molecule shows an intense absorption (v = 0 > v= 1) at 2886 cm™!. The
anharmonicity constant of this molecule (x,) is 0-0174. Calculate the equilibrium
vibrational frequency of this molecule. 10
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