UPSC Previous Year Question Paper 2026 – Combined Geo-Scientist (Main) Examination | SNCS-A-CMS Chemistry Paper-II | Free PDF Download

1

N_A = 6·022×10^23 mol^−1
Rydberg constant = 2·178×10^−18 J
c = 2·998×10^8 m s^−1
k_B = 1·38×10^−23 J K^−1
e = 1·602×10^−19 C
m_e = 9·109×10^−31 kg
F = 96485 C mol^−1
R = 8·314 J K^−1 mol^−1
h = 6·626×10^−34 J s
π = 3·142
1 amu = 1·66×10^−27 kg
1 cal = 4·184 J
1 J = 1 kg m^2 s^−2
1 Å = 10^−8 cm = 10^−10 m = 0·1 nm = 100 pm
1 atm = 760 torr = 1·01325×10^5 Pa
1 bar = 1×10^5 Pa = 0·9869 atm
1 eV = 1·602×10^−19 J
1 L atm = 101·34 J
1 eV = 23060 cal mol^−1
4π^2 c^2 = 3·55×10^22 cm^2 s^−2
h^2 / 8m_e = 6·025×10^−38 J m^2
h c = 1·986×10^−25 J m
h / 8π^2 c = 2·8×10^−44 kg m

5x16=80

1. (a) Define compressibility factor (Z). What is its significance: when its value is either (i) 1 or (ii) <1 or (iii) >1 ? 5

2. (b) Draw Andrew's plot of P vs. V isotherms of a real gas at different temperatures.

At the critical point why (i) (∂P/∂V){T = T_c} = 0 and (ii) (∂^2P/∂V^2){T = T_c} = 0? (5)

[Combined Geo-Scientist (Main) Examination – Previous Year Question (Chemistry Paper-II):
Q. Explain the concept of critical temperature, critical pressure and critical volume. Derive the expressions for van der Waals constants in terms of critical constants.]

1. (c) 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

2. (d) Which one of the following is an intrinsic semiconductor and how do you convert it into an extrinsic semiconductor?

(i) diamond (ii) α-tin (iii) silicon (iv) YBa₂Cu₃O₇

1. (e) 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

2. (f) Write down the relation between K_p and K_c of the reaction: A(g) + B(g) ⇌ C(g). (Assuming all gases in the reaction mixture behave ideally) Under what conditions K_p will be equal to the K_c? 5

3. (g) A radioactive nuclide X has two decay modes (both first order)

X → B ; k₁ and k₂ are decay constants

Express t_{1/2} (half-life period) of X in terms of k₁ and k₂. 5

[Combined Geo-Scientist (Main) Examination – Previous Year Question (Chemistry Paper-II):
Q. Derive the expression for the rate constant of a first-order reaction. How is half-life related to the rate constant?]

1. (h) What are the basic differences of soap and detergent though both are used for cleaning purpose of clothes? 5

2. (i) Construct a galvanic cell in which the following spontaneous reaction will happen. 2Cu⁺(aq) ⇌ Cu²⁺(aq) + Cu(s). 5

3. (j) 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_b and K_w are 2.0 × 10^−5 and 1.0 × 10^−14 respectively at 298 K. 5

4. (k) 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

5. (l) Define the expectation value of an operator. How does it differ from an eigenvalue? Explain with reference to energy measurements. 5

6. (m) How many normal modes of vibrations are possible for the following molecules?

(i) C₆H₆ (ii) C₄H₂ (iii) Os(CO)₅ (iv) SiCl₄ (v) CS₂

1. (n) (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 CO₂. 5

[Combined Geo-Scientist (Main) Examination – Previous Year Question (Chemistry Paper-II):
Q. State the Franck-Condon principle. Explain how it accounts for the vibrational structure of electronic spectra.]

1. (o) 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

1. (p) 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) 10×6 = 60

1. A non-ideal gas has three characteristic temperatures; Critical temperature (T_C), Boyle temperature (T_B) and Inversion temperature (T_i). Write expressions of T_C and T_B when the gas is van der Waals. What are the significances of T_C and T_B? 10

2. 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?

[Combined Geo-Scientist (Main) Examination – Previous Year Question (Chemistry Paper-II):
Q. What are the differences between crystalline and amorphous solids? Give examples of each.]

1. The Gibbs-Duhem relations are:

(i) dG = Σ_i μ_i dn_i (ii) G = Σ_i n_i μ_i For closed systems and at constant P and T (iii) 0 = Σ_i n_i dμ_i

(I) Mention the nature of the system (II) Derive the expression of μ_i using eqn. (i) (III) Which one is an intensive property and why; μ_i or G ? (IV) What factors can influence the value of μ_i ?

1. (a) 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

2. (b) At constant P and T, for a spontaneous chemical reaction, Δ_rG must be negative but Δ_rH must not be necessarily negative. Explain. 5

3. Discuss a method to determine the partial orders and total order of the following reaction: A(aq.) + 2B(aq.) = P(aq.) 10

4. The T-dependence of E° of a galvanic cell is given by E° = A + BT + CT². Find the expression of Δ_rH° for the cell reaction. Show that when T → ∞ the Δ_rG° and Δ_rH° are the same. 10

5. 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 n² and not linearly with n ? 5+5

[Combined Geo-Scientist (Main) Examination – Previous Year Question (Chemistry Paper-II):
Q. Derive the expression for the energy levels of a particle in a one-dimensional box. What is the significance of the quantum number n?]

1. Calculate the energy in joules of the rotational level (with J = 1) of the rigid H₂ molecule.

Given: r_H₂ = 74.1 pm

Relative mass of H atom is 1·0080 amu. 10

1. 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) 20×3 = 60

1. (a) For a solution phase reaction: A(aq.) + B(aq.) ⇌ D(aq.) derive the expression for K_c in terms of the standard free energy change.

(i) What would be the standard state value?

(ii) What would be the unit of K_c?

(iii) What factors can influence the value of K_c?

1. (b) Are the values of Δ_rG°(P) and Δ_rG°(C) the same, in general? If not, under what conditions will they be the same? 5

2. (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

3. (b) In a photochemical reaction, the following data were obtained using an actinometer:

• Number of photons absorbed per second = 2·0×10^16

• Rate of formation of product molecules = 3·6×10^16 molecules s^−1

(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

[Combined Geo-Scientist (Main) Examination – Previous Year Question (Chemistry Paper-II):
Q. Define quantum yield. Explain the difference between primary and secondary photochemical processes.]

1. (a) At 298 K, the galvanic cell:

(Pt) H₂(g, 1 atm) | HCl(aq, 0·1M) | AgCl | Ag, has the EMF(E) = 0·35 V and

(dE/dT)_P = −18×10^−4 V K^−1. Determine Δ_rG, Δ_rH and Δ_rS of the cell reaction for the production of 1 faraday electricity. 10

1. (b) Define buffer capacity (β) of a buffer solution. Show that β of an acetic acid-acetate buffer solution is maximum when [salt]/[acid] is one. 10

2. 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 corresponding to E = 3h²/4ma² and 7h²/4ma².

(iii) Explain how degeneracy reflects the underlying symmetry of the system. 8 + 8 + 4 = 20

1. (a) The rotational constant of ¹²C¹⁴N (rigid rotor) is 1.91 cm^−1. Calculate the equilibrium bond length (in pm) of CN. 10

2. (b) A diatomic molecule shows an intense absorption (ν = 0 → ν = 1) at 2886 cm^−1. The anharmonicity constant of this molecule (x_e) is 0.0174. Calculate the equilibrium vibrational frequency of this molecule. 10

UPSC Previous Year Question Paper 2026 – Combined Geo-Scientist (Main) Examination | SNCS-A-CMS Chemistry Paper-II | Free PDF Download link

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