Chemistry UPSC PYQ 2024

(a) (i) Calculate the coefficient of viscosity of air at (I) 298 K and (II) 0 K. Assume that the collision cross-section (πσ2) of air is 0·28 (nm)2 and the average molar mass of air is 29 g mol−1. (ii) Arrange Boyle’s temperatures of the gases Ar, CH4 and C6H6 in increasing order and give reasons. (b) (i) Which of the following liquids has greater surface tension: Ethanol or Dimethyl ether? Explain with reasons. (ii) Calculate the difference in pressure across the liquid–air interface for a water droplet of radius 150 nm. (c) (i) Calculate the change in Helmholtz energy for a reversible isothermal compression of 1 mol of an ideal gas from 100·0 L to 22·4 L at 298 K. (ii) Why does a tyre get hot when air is pumped into it? Can a tyre be inflated without a rise in temperature? Calculate the coefficient of viscosity of air at 298 K and 0 K. [10M] Arrange Boyle’s temperatures of Ar, CH4 and C6H6 in increasing order and justify. [5M] Identify which liquid—ethanol or dimethyl ether—has the greater surface tension and explain. [5M] Calculate the pressure difference across the liquid–air interface of a water droplet (radius 150 nm). [5M] Determine the change in Helmholtz energy for isothermal compression of an ideal gas from 100 L to 22·4 L at 298 K. [10M] Explain why a tyre gets hot during inflation and whether it can be inflated without a temperature rise. [5M] <!--qid:MAINS_2024_Chemistry-I_Q3-->

(a) State Heisenberg’s uncertainty principle. Show that for a particle in a one-dimensional box having length from 0 to L, the two normalised eigen functions corresponding to the eigenvalues E1 and E2 (quantum numbers 1 and 2 respectively) are orthogonal to each other. (b) (i) Calculate the bond order for the following: (I) Oxygen, (II) Superoxide, (III) Peroxide, (IV) Dioxygenyl ion. Which of them has the highest stability? (ii) Draw the molecular orbital diagram for CO. (c) (i) Calculate the limiting radius ratio for crystals with coordination numbers 3 and 6. (ii) Explain stoichiometric defects with an example. Calculate bond orders for O2, O2− (superoxide), O22− (peroxide) and O2+ (dioxygenyl) and identify the most stable species. [10M] Draw the molecular orbital diagram for CO. [10M] Calculate the limiting radius ratio for coordination numbers 3 and 6. [10M] Explain stoichiometric defects with an example. [10M] <!--qid:MAINS_2024_Chemistry-I_Q2-->

The mass spectral data of diethyl ether is as under: m/z 74, m/z 59, m/z 45, m/z 31, m/z 29. Explain the fragmentation pattern. <!--qid:MAINS_2024_Chemistry-II_Q3-->

Using the following data, calculate the bond length of HCl : I = 2.70 × 10^−47 kg m^2 ; 1 a.m.u. = 1.661 × 10^−27 kg. <!--qid:MAINS_2024_Chemistry-II_Q4-->

Answer the following: Consider the following reactions: C6H5-CH2-CH2-Br + EtO⁻ → C6H5-CH=CH2 (Rate = k_H) C6H5-CD2-CD2-Br + EtO⁻ → C6H5-CH=CHD (Rate = k_D) It was observed that k_H / k_D = 7.1. Based on this data, predict the mechanism and justify your answer. [10M] Consider the following reaction: CH2=CH-CH=CH2 + HBr → CH3-CH(Br)-CH=CH2 + CH3-CH=CH-CH2Br At −80 °C, the 1,2-addition product predominates while at −45 °C the 1,4-addition product predominates. Justify. [5M] Identify the major product X in the following reaction, explain its mechanism and name the reaction: C6H5-CHO + CH2(COOC2H5)2 (pyridine) → X [10M] Predict the structure of X in the following reaction and name the reaction. Justify that it is a syn-elimination: tert-Butyl alcohol (with CS2, NaOH; then CH3I) → X → (elimination product) [5M] <!--qid:MAINS_2024_Chemistry-II_Q2-->

Answer ALL the parts (a) to (e): Classify the following as aromatic, nonaromatic or antiaromatic: (1) Azulene (2) Pyridine (3) Sydnone (4) Cyclooctatetraene (5) Cyclopentadienyl cation [5M] Though the following compound contains a keto group, it does not undergo nucleophilic addition reactions. Explain. [5M] <!--qid:MAINS_2024_Chemistry-II_Q1-->

(a) (i) Determine the distance from the nucleus at which the electron is most expected in the hydrogen atom in its ground state. [Given: The normalised radial function for hydrogen-like systems is R10(1s) = 2 (Z/a0)3/2 e−ρ/2 where ρ = 2Zr/na0 and a0 is the first Bohr orbit radius. Other notations have their usual meanings.] (ii) Sodium bromide and sodium iodide have higher lattice energies than expected from theoretical calculations. Justify. (b) (i) The 235U isotope undergoes fission when bombarded with neutrons. However, its natural abundance is only 0·72 percent. To separate it from more abundant 238U isotope, U is first converted to UF6 which is easily vaporised above room temperature. The mixture of 235UF6 and 238UF6 gases is then subjected to many stages of effusion. Calculate the separation factor, that is enrichment of 235U relative to 238U after one stage of effusion. (ii) Define ‘unit cell’. Draw all the Bravais lattices for a cubic system. (c) Use the following data to determine the normal boiling point of mercury. What assumptions must you make in order to do the calculations? Hg(l) ΔHf° = 0, S° = 77·4 J K−1 mol−1 Hg(g) ΔHf° = 60·78 kJ mol−1, S° = 174·7 J K−1 mol−1 (d) (i) The compound dichlorodifluoromethane (CCl2F2) has a normal boiling point of –30 °C, a critical temperature of 112 °C, and a corresponding critical pressure of 40 atm. If the gas is compressed to 18 atm at 20 °C, will the gas condense? Give your answer on the basis of graphical presentation. (ii) Define overvoltage. Mention the applications of overvoltage. (e) The activation energy for the decomposition of hydrogen peroxide 2 H2O2(aq) → 2 H2O(l) + O2(g) is 42 kJ mol−1, whereas when the reaction is catalysed by enzyme catalase it is 7·0 kJ mol−1. Calculate the temperature that would cause the uncatalysed reaction to proceed as rapidly as the enzyme-catalysed decomposition at 20 °C. Assume the frequency factor A to be the same in both cases.2f:["$","section","2024",{"className":"mb Determine the distance from the nucleus at which the electron is most expected in the hydrogen atom in its ground state. [5M] Sodium bromide and sodium iodide have higher lattice energies than expected from theoretical calculations. Justify. [5M] Calculate the separation factor (enrichment of 235U relative to 238U) after one stage of effusion of a UF6 gas mixture. [5M] Define ‘unit cell’. Draw all the Bravais lattices for a cubic system. [5M] Will CCl2F2 gas condense when compressed to 18 atm at 20 °C? Give your answer on the basis of graphical presentation. [5M] Define overvoltage and mention its applications. [5M] <!--qid:MAINS_2024_Chemistry-I_Q1-->