GATE CY 2023 Question Paper (05-Feb-2023) (Shift 2)

For the non-dissociative adsorption of a gas on solid,

(i) the Freundlich isotherm is given by 𝜃 = 𝑘𝑝${}^{1\text{⁄n}}$ where 𝜃 is surface coverage, 𝑝 is pressure, 𝑘 and 𝑛 are empirical constants; and

(ii) the BET isotherm is given by $\frac{\mathrm{p}}{\mathrm{p}\ast -\mathrm{p}}=\frac{\theta }{\mathrm{c}}+\theta (\mathrm{c}-1)\left(\frac{\mathrm{p}}{\mathrm{q}\ast }\right)$

where 𝑝${}^{\text{∗}}$ and 𝑐 are empirical constants, and 𝑝 < 𝑝${}^{\text{∗}}$ .

The correct statement(s) is(are)

Two different enzyme catalysis reactions I and II have identical Y-intercepts for the Lineweaver-Burke (equation given below) plots. The slope for reaction I is twice than that of reaction II.

If the initial concentrations of enzymes in I and II are same, the correct statement(s) is(are)

$\frac{1}{\mathrm{v}}=\frac{1}{{\mathrm{v}}_{\max }}+\frac{{\mathrm{K}}_{\mathrm{M}}}{{\mathrm{v}}_{\max }}\frac{1}{[\mathrm{S}]}$

where 𝜈 and 𝜈 𝑚𝑎𝑥 are rate and maximum rate; 𝐾 𝑀 is Michaelis-Menten constant, and [S] is substrate concentration.

The enthalpy change for the exothermic reaction between BeI2 and HgF₂ is _______kJ mol⁻¹ (rounded off to the nearest integer)

(Given: Bond dissociation energy (in kJ mol⁻¹ ) for Be−F = 632, Be−I = 289, Hg−F = 268 and Hg−I = 145)

The number of carbon atoms connected to the metal center in [W(C₆₀)(CO)₅] is _______ (rounded off to the nearest integer) (Given: atomic number of W is 74)

Two-component solid-liquid system of naphthalene-benzene forms a simple eutectic mixture. Assuming that naphthalene-benzene forms an ideal solution, the mole fraction of naphthalene in benzene at 300 K and 1 bar is _______ (rounded off to two decimal places)

(Given: Freezing point (T${}_{fp}$) and enthalpy of fusion (ΔH${}_{fus}$) of naphthalene are 353 K and 19.28 kJ mol⁻¹ , respectively and gas constant (R) =8.31 J K⁻¹ mol⁻¹)