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

In the given reaction sequence, the amount of R produced (in g) is ________.

(Given: molar mass (in g $mo{l}^{-1}$) of H = 1, C = 12, N = 14, O = 16, and S = 32)
(rounded off to two decimal places)

The wave function of a particle in a cubic box (of side L) is given by
$\psi (x,y,z)=\sqrt{32/L^3}\sin \frac{\pi x}{L}\cos \frac{\pi x}{L}\sin \frac{2\pi y}{L}\sin \frac{\pi z}{L}$.
The ratio of the energy of the state corresponding to the above wave function to the ground state energy is ________.
(rounded off to the nearest integer)

${\Phi }_1$ and ${\Phi }_2$ are normalized eigenfunctions of a Hermitian operator.
$|\psi ⟩=3i|{\Phi }_1⟩+2|{\Phi }_2⟩$ and $|\chi ⟩=-2i|{\Phi }_1⟩+5|{\Phi }_2⟩$.
The value of $⟨\psi |\chi ⟩+⟨\chi |\psi ⟩$ is ________.
(rounded off to the nearest integer)

2 mol of a monoatomic ideal gas with initial volume of 5 L and pressure 10 bar undergoes an irreversible adiabatic expansion against a constant final pressure of 1 bar. The final volume (in L) is ________.
(Given: R = $8.314\times 10^{-2}$ L bar $mo{l}^{-1}$ $K^{-1}$)
(rounded off to one decimal place)

The following figure shows an experimental liquid-liquid phase diagram of phenol and water at the vapor pressure of the system. The total amount of phenol and water (in mol) present in the phenol-rich phase when 5 mol of water was shaken with 5 mol of phenol at $40$ ${}^{\circ }C$ is ________.

(rounded off to one decimal place)