GATE CY 2022 Question Paper (06-Feb-2022) (Shift 2)

EMF of the following cell

Cu│CuSO₄(aq, 1.0 mol/kg)│Hg₂SO₄(s)│Hg(l)│Pt

at 25 °C and 1 bar is 0.36 V. The value of the mean activity coefficient (rounded off to three decimal places) of CuSO₄ at 25 °C and 1 bar is

[Given: Standard electrode potential values at 25 °C for

Cu²⁺ + 2e⁻ → Cu and

Hg₂SO₄ + 2e⁻ → 2Hg + $\mathrm{S}{\mathrm{O}}_4^{2-}$

are 0.34 V and 0.62 V, respectively.

Consider: RT/F at 25 °C = 0.0256 V]

The radius of gyration (in nm, rounded off to one decimal place), for three dimensional random coil linear polyethylene of molecular weight 8,40,000 is

[Given: C-C bond length = 0.154 nm]

The activation energy of the elementary gas-phase reaction O₃ + NO → NO₂ + O₂ is 10.5 kJ mol⁻¹. The value of the standard enthalpy of activation (rounded off to two decimal places in kJ mol⁻¹) at 25 °C is

[Given: R is 8.314 J mol⁻¹ K⁻¹]

In a collection of molecules, each molecule has two non-degenerate energy levels that are separated by 5000 cm⁻¹. On measuring the population at a particular temperature, it was found that the ground state population is 10 times that of the upper state. The temperature (in K, rounded off to the nearest integer) of measurement is

[Given: Value of the Boltzmann constant = 0.695 cm⁻¹ K⁻¹]

The change in entropy of the surroundings (in J K⁻¹, rounded off to two decimal places) to convert 1 mol of supercooled water at 263 K to ice at 263 K at 1 bar is

[Consider: Δ${}_{fus}$ H° at 273 K = 6.0 kJ mol⁻¹, and the molar heat capacity of water is higher than that of ice by 37.0 J K⁻¹ mol⁻¹ in the temperature range of 263 K to 273 K]