GATE CY 2024 Question Paper (03-Feb-2024) (Shift 1)

The number of metal-metal bond(s) in the complex $[({\eta }^5-Cp)Mo(CO{)}_2{]}_2$ is $x$ and in $[({\eta }^5-Cp{)}_{2}F{e}_2(CO{)}_3]$ is $y$. The value of $x+y$ is ___________.
(Assume 18 electron rule is followed.)
(Answer in integer)

${}^{1}H$ NMR spectrum of a mixture containing $C{H}_{3}Br$ ($x$ mol) and $(C{H}_3{)}_{3}CBr$ ($y$ mol) shows two singlets at 2.7 ppm and 1.8 ppm, with the relative ratio of 3:1 (integration value), respectively. The value of $x/y$ is ____________
(rounded off to the nearest integer)

The value of $\frac{e^2}{2\pi {ϵ}_0{a}_0}$ in atomic unit of energy is ___________
(e: charge of electron; $a_0$: Bohr radius; ${ϵ}_0$: permittivity of vacuum)
(rounded off to the nearest integer)

The partial vapor pressure of 0.1 molal solution of B in liquid A is 60 kPa at 300 K. The partial vapor pressure (in kPa) of a solution containing Bwith mole fraction of 0.1 in liquid A at 300 K is __________
(Assume the solute B obeys Henry's law. The molar mass of A is 80 g mol${}^{-1}$.)
(rounded off to three decimal places)

Consider the following two parallel irreversible first-order reactions, where $\ast \ast k_1=2k_2\ast \ast$ at 300 K. After complete conversion of R at 300 K, the concentration of P1 in the reaction mixture was $15{\text{ mol L}}^{-1}$. The initial concentration of R (in mol L${}^{-1}$) was _______

($\ast \ast k_1\ast \ast$ and$\ast \ast k_2\ast \ast$ are the rate constants)
(rounded off to one decimal place)