UPSC Combined Geo-Scientist Main 2024 Chemistry Paper-II

 

Some useful fundamental constants and conversion factors

N_A = 6.022 × 10²³ mol⁻¹

Rydberg constant = 2.178 × 10⁻¹⁸ J

c = 2.998 × 10⁸ ms⁻¹

k_B = 1.38 × 10⁻²³ JK⁻¹

e = 1.602 × 10⁻¹⁹ C

m_e = 9.109 × 10⁻³¹ kg

F = 96485 C mol⁻¹

R = 8.314 JK⁻¹ mol⁻¹

h = 6.626 × 10⁻³⁴ Js

π = 3.142

1 amu = 1.66 × 10⁻²⁷ kg

1 cal = 4.184 J

1 J = 1 kg m² s⁻²

1 Å = 10⁻⁸ cm = 10⁻¹⁰ m = 0.1 nm = 100 pm

1 atm = 760 torr = 1.01325 × 10⁵ Pa

1 bar = 1 × 10⁵ Pa = 0.9869 atm

1 eV = 1.602 × 10⁻¹⁹ J

1 L atm = 101.34 J

1 eV = 23060 cal/mol

4π²c² = 3.55 × 10²² cm² s⁻²

h² / 8m_e = 6.025 × 10⁻³⁸ J m²

hc = 1.986 × 10⁻²⁵ Jm

h / 8π²c = 2.8 × 10⁻⁴⁴ kg m² cm⁻¹

5x16=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

·10³b' 0.024 0.024

(i) Which of these would occupy greater volume under identical conditions ?

(ii) Which gas has the highest critical temperature ?

(b) From virial equation of state for a real gas

pV_m = RT(1 + A₂(T)p + A₃(T)p² + ......)

where the symbols have their usual meanings,

Explain :

(i) The physical significance of the second virial coefficient 'A₂'.

(ii) The behaviour of the second virial coefficient (A₂) at low, moderate and high temperatures.

(iii) What happens when A₂ = 0 ?

(c) Differentiate between conductors, semiconductors and insulators using band theory of solids.

(d) Give an account of Bravais Lattices in cubic and tetragonal crystal system mentioning the minimum symmetry elements in them.

(e) What do you understand by chemical potential ? Give an account of variation of chemical potential with temperature.

(f) Obtain a relation between equilibrium constant, Kp, Kc and Kx. Under what conditions is Kp = Kc = Kx ?

UPSC Previous year question Combined Geo Scientist Main examinantion 2024 Chemistry II

(g) The rate constant for the reaction O(g) + O₃(g) → 2O₂(g) is 8.0 × 10⁻¹⁵ cm³ molecule⁻¹ s⁻¹ at 298 K. Express this rate constant in dm³ mol⁻¹ s⁻¹.

(h) Write BET equation. Explain the terms involved in it.

(i) Given:

Cu²⁺ + 2e⁻ → Cu; E⁰ = +0.350 V

Zn²⁺ + 2e⁻ → Zn; E⁰ = −0.763 V

Construct the cell using these reactions.

(i) Write and balance the total cell reaction.

(ii) Find the E⁰ of the cell.

(iii) State whether the cell reaction will be spontaneous or not.

(j) What is the source of alkaline error in pH-measurements with the glass electrode?

(k) Evaluate the commutator [x̂, d/dx].

(l) Interpret the physical meaning of the square of the wave function |Ψ(x)|². What are the dimensions of |Ψ(x)|²?

(m) What is the Raman effect and how does it differ from phosphorescence and fluorescence?

(n) Hydrogen molecule gives neither vibrational nor rotational spectrum, but is Raman active. Explain.

(o) The fluorescence quantum yield and observed fluorescence lifetime of tryptophan in water are φ_F,0 = 0.20 and T₀ = 2.6 ns, respectively. Calculate the fluorescence rate constant, k_F.

(p) The first step in the photoinitiated reaction between hydrogen and bromine using 511 nm radiation is

Br₂ + hν → 2Br

Why is hydrogen molecule not dissociated under these conditions?

10x6=60

Q2. Define Boyle temperature (T_B) of a non-ideal gas. Show that for a van der Waals gas, the Boyle temperature T_B = a/Rb, where 'a' and 'b' are van der Waals constants. 10

Q3. (a) Obtain Miller indices of a crystal plane which cuts through the crystal axes at (2a, −3b, −3c). 3

(b) A bcc element of density 10300 kg m⁻³ has a cell edge of 314 × 10⁻¹² m. Calculate the atomic mass of the element. 7

Q4. Obtain an expression for the equilibrium constant and standard free energy change using a general reversible reaction :

aA + bB ⇌ cC + dD (10)

Q5. (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. 5

(b) Explain with reasons :

(i) Physical adsorption decreases with increase in temperature, but chemisorption increases. 3

(ii) On adding detergent in water, surface tension decreases. 2

Q6. The pH of a buffer solution containing 0.5 mol/m³ of CH₃COOH and 0.5 mol/m³ of CH₃COONa has been found to be 4·76. What would be the pH of this solution after 0·02 mol/m³ NaOH has been added to the buffer ? Assume that the volume is unchanged. (Given K_a = 1·80 × 10⁻⁵) 10

Q7. (a) State the different assumptions involved in the derivation of Langmuir adsorption isotherm. 5

(b) What Raman shifts (in cm⁻¹) are expected for the first four Stokes lines for CO₂ (B = 0.3906 cm⁻¹)? 5

Q8. Prove that the operator i d/dx is Hermitian, but d/dx is not. 10

Q9. The vibrational wave numbers of H₂⁺, D₂ and H₂ are approximately 2322, 3118, and 4400 cm⁻¹, respectively. Calculate the force constants for these molecules and comment on the relative magnitudes of the values you obtain. H = 1, D = 2 10

Q10. (a) Describe the Franck-Condon principle and its significance in photochemistry. 5

(b) The continuum limit for the dissociation of Br₂ gas Br₂ (ground) = Br (ground) + Br (excited) occurs at 19,750 cm⁻¹.

The transition of a ground bromine atom to an excited one corresponds to a wave number of 3865 cm⁻¹.

Calculate the energy for the process

Br₂(ground) = 2Br(ground) in cm⁻¹.

20x3=60

Q11. (a) Show that in a first order reaction, the time required for completion of 99% reaction is 10 times of the half-life (t₁/₂) of the reaction. 10

(b) The values of the rate constant (k) for the reaction 5

2N₂O₅(g) → 4NO₂(g) + O₂(g)

were determined at several temperatures. A plot of ln K vs 1/T gave a straight line of which the slope was found to be −1·2 × 10⁴ K. What is the activation energy of the reaction ?

(c) For the following cell

Cd | CdCl₂(sat.) | AgCl | Ag,

E = 0·675 V and dE/dT = −6·5 × 10⁻⁴ V K⁻¹ at 298 K.

What is the reaction taking place in the cell ? What are the values of ΔG, ΔH and ΔS at 298 K ? 5

Q12. (a) A flask of 4 dm³ capacity contains O₂ 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 :

(i) What will be the volume of the gas which is left behind ?

(ii) What amount of O₂ and the corresponding number of molecules are left behind in the flask ?

(iii) If now, 2 g of N₂ 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 a_I⁻ = 1·00, K_sp for AgI = 8·3 × 10⁻¹⁷) (10)

Q13. (a) HgCl₂ crystallizes in orthorhombic system. Using radiation with λ = 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 HgCl₂ molecules in the unit cell. The density of the crystal is 5.42 g cm⁻³ and M(HgCl₂) = 271.5 g mol⁻¹. 10

(b) Show that the activity is the thermodynamic counterpart of gas pressure. 10

Q14. (a) 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. 2

(ii) the lowest energy level with a degeneracy of 6. 3

(b) Calculate the corresponding energies (in J) if the side length of the box is 0.5 nm. 5

(c) 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? 5

(d) In the uranyl oxalate actinometer, 5·1875 × 10¹⁸ molecules were decomposed when exposed to a radiation of λ = 365.5 nm. During this time, the number of photons absorbed were 10·5875 × 10¹⁸. Calculate the quantum efficiency. 5

Q15. (a) ¹H³⁵Cl has a rotational constant of 10·26 cm⁻¹.

(i) Explain how the rotational constant is determined from the microwave spectrum. 3

(ii) Calculate the moment of inertia of ¹H³⁵Cl. 4

(iii) Calculate the bond length of the HCl molecule using the above data. 3

(b) The photolysis of hydrogen iodide follows the mechanism :

HI + hν →(I_a) H· + I·

H· + HI →(k₂) H₂ + I·

I· + I· →(k₃) I₂

H· + I₂ →(k₄) HI + I·

Use the steady-state approximation to H· to construct the rate law. What is the overall quantum yield of the process ? 10

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