List of top Physical Chemistry Questions asked in GATE CY

In the EPR spectrum of an aqueous solution of VOSO₄ at room temperature, the total number of hyperfine splitting signals is

In thermogravimetric analysis, 12.45 mg of CuSO₄.5H₂O was subjected to heating under N₂ atmosphere. At a particular temperature, there was a weight loss of 3.6 mg. The number of water molecule(s) lost per formula unit is _____.
(Given molar mass (in g mol^-1) of H = 1.0, O = 16.0, S = 32.0, and Cu = 63.5)
(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 B with 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)

Critical micellar concentration of a surfactant is 0.008 M in water at 25 °C. If the aggregation number of the micelles is 80, the concentration of the micelles (in M) present in 0.088 M aqueous solution of the surfactant at 25 °C is

The correct statement(s) about ⁴D_5/2 state of an atom is (are) :

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 × 10^-2 L bar mol^-1 K^-1)
(rounded off to one decimal place)

The molecule XY₂ is microwave active and its vibration-rotation spectrum shows only P and R transitions. In the correct structure,

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 °C is _______.

(rounded off to one decimal place)

The correct statement(s) related to an ensemble is (are) :

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)

Φ₁ and Φ₂ are normalised eigenfunctions of a Hermitian operator.
|Ψ〉 = 3i |Φ₁〉 + 2|Φ₂〉 and |X〉 = -2i |Φ₁〉 + 5 |Φ₂〉
The value of 〈Ψ|X〉 + 〈X|Ψ〉 is _______.
(rounded off to the nearest integer)

The turnover frequency (in h^-1) of a reaction where 5 mol% of a catalyst is required for 90% conversion in 3 h is ______.
(rounded off to the nearest integer)

ΔS° (in J mol^-1 K^-1) for the given reaction at 298 K is ________.
[Cu(H₂O)6]²⁺ + en ⇌ [Cu(H₂O)₄(en)]²⁺ + 2H₂O
(Given: log K₁ = 10.6, where K₁ is the equilibrium constant. ΔH° =-54 kJ mol^-1 and R = 8.314 J mol^-1 K^-1)
(rounded off to two decimal places)

Among the following, the correct statement(s) is (are) :

Among the following, the correct statement(s) is (are) :

Consider the following reaction sequence where M and N are the major products.
The correct option(s) is (are)

The correct statement for a thermally initiated radical polymerization in a solution is :
(Assume: Steady-state and equal reactivity of the propagating radicals, termination reactions are only by combination, and no chain transfer reaction.
Given: Rp = rate of polymerization, DP = degree of polymerization, [I] = initiator concentration, and [M] = monomer concentration.)

If q_t and Q_t,m are the molecular and molar translational partition functions of X₂, respectively, then In(Q_t,m) =
(N is the Avogadro number)

Ψ₁, Ψ₂, Ψ₃ and Ψ₄ are four Hückel molecular orbitals of benzene with orbital energies E₁, E₂, E₃, and E₄, respectively.
Ψ₁ = \(\frac{1}{2}\)(Ф_B + Ф_C - Ф_E - Ф_F)
Ψ₂ = \(6^{-\frac{1}{2}}\)(Ф_A - Ф_B + Ф_C - Ф_D + Ф_E - Ф_F)
Ψ₃ = \(6^{-\frac{1}{2}}\)(Ф_A + Ф_B + Ф_C + Ф_D + Ф_E - Ф_F)
Ψ₄ = \(12^{-\frac{1}{2}}\)(2Ф_A + Ф_B - Ф_C - 2Ф_D - Ф_E + Ф_F)
The correct order of the orbital energies is
(The six carbon atoms of benzene are denoted by A to F and Ф_J, is the 2p_z, orbital of J^th carbon of benzene.)

Consider the following six vibrational modes :
symmetric stretching of CO₂, O-H symmetric stretching of H₂O, stretching of HCl, stretching of H₂, N-H symmetric stretching of NH₃, and bending of CO₂.
Among these modes, if k number of modes are IR active but Raman inactive, l number of modes are IR inactive but Raman active, and m number of modes are both IR and Raman active.
k, l, and m, respectively, are

The value of \(\frac{e^2}{2\piε_0a_0}\) in atomic unit of energy is _______.
(e: charge of electron; a₀: Bohr radius; ∈₀: permittivity of vacuum)
(rounded off to the nearest integer)

Consider the following two parallel irreversible first-order reactions, where k₁ = 2k₂ at 300 K. After complete conversion of R at 300 K, the concentration of P1 in the reaction mixture was 15 mol L^-1. The initial concentration of R (in mol L^-1) was

(k1 and k2 are the rate constants)
(rounded off to one decimal place)

The non-dissociative adsorption of a gas on a given surface at a fixed temperature follows Langmuir isotherm. The plot(s) which give(s) a straight line is (are)
[Given: V = volume of the adsorbed gas, P = pressure of the gas]

 k₁=2k₂, find the initial concentration of A.