List of top Physical Chemistry Questions asked in GATE CY

The Brunauer-Emmett-Teller (BET) surface area measurement data for adsorption of \(\mathrm{N_2}\) gas at 77 K on 1.0 g of an adsorbent fits into a straight line, when \(\dfrac{z}{(1-z)V}\) is plotted against \(z\). The slope and intercept of the straight line are \(6 \times 10^{-4}\) mm\(^{-3}\) and \(4 \times 10^{-6}\) mm\(^{-3}\), respectively. The surface area (in m\(^2\) g\(^{-1}\)) of the adsorbent is (rounded off to one decimal place).
(Given: 1 mm\(^3\) of \(\mathrm{N_2}\) gas corresponds to \(2.7 \times 10^{16}\) molecules and each molecule occupies 0.16 nm\(^2\). \(V\) is the volume of gas adsorbed in mm\(^3\), \(z\) is \(p/p_o\), where \(p\) is the pressure of the \(\mathrm{N_2}\) gas and \(p_o\) is equilibrium vapour pressure of liquid \(\mathrm{N_2}\))

The orbital angular momentum (\(\mathbf{L}\)) of an electron is \(\sqrt{12}\,\hbar\). The minimum angle between \(\mathbf{L}\) and its \(z\)-component (in degrees) is (rounded off to one decimal place).

In a calibrated pH meter comprising of glass electrode-standard calomel electrode, the potential for a buffer solution of pH 4.01 is measured as 0.814 V at 25\(^{\circ}\)C. For a \(4.0 \times 10^{-3}\) M solution of acetic acid, the measured potential (in V) is (rounded off to three decimal places).
(Given: \(K_a\) of acetic acid at 25\(^{\circ}\)C = \(1.75 \times 10^{-5}\); \(2.303RT/F = 0.059\); Assume: \(a_{H^+} = [H^+]\))

If the translational partition function for \(\mathrm{H_2}\) confined in a 1 L vessel at 300 K is \(y \times 10^{27}\), then the value of \(y\) is (rounded off to one decimal place).
(Given: Atomic mass (in amu): H = 1.008; 1 amu = \(1.661 \times 10^{-27}\) kg; \(h = 6.626 \times 10^{-34}\) J s; \(k = 1.381 \times 10^{-23}\) J K\(^{-1}\))

The positions of two atoms in spherical polar coordinates \((r, \theta, \Phi)\) are \((1, \frac{\pi}{2}, \frac{\pi}{2})\) and \((1, \frac{\pi}{4}, \frac{3\pi}{2})\), where the distance is in \(\overset{\circ}{\mathrm{A}}\) and the angles are in radian. The interatomic distance (in \(\overset{\circ}{\mathrm{A}}\)) is (rounded off to two decimal places).

The correct statement(s) for a surface catalyzed unimolecular gaseous reaction is(are)

For a reaction between neutral molecules \(\mathrm{X}\) and \(\mathrm{Y}\) in a solution at temperature \(T\), the measured rate of reaction is equal to the rate of diffusion. Assume \(\mathrm{X}\) is stationary and \(\mathrm{Y}\) is moving. If the diameter of the molecule \(\mathrm{X}\) is five times that of \(\mathrm{Y}\), then the rate constant for the reaction is
(\(\eta\) is viscosity of the solvent; \(k\) is the Boltzmann constant)

For the following electrochemical cells, liquid junction potentials affect the cell potential (\(E_{cell}\)).
I. \(\mathrm{Electrode\text{-}1 \mid 0.1\ M\ KCl \parallel 0.1\ M\ NaCl \mid Electrode\text{-}2}\)
II. \(\mathrm{Electrode\text{-}1 \mid 0.1\ M\ HCl \parallel 0.01\ M\ HCl \mid Electrode\text{-}2}\)
III. \(\mathrm{Electrode\text{-}1 \mid 0.01\ M\ KCl \parallel 0.01\ M\ HCl \mid Electrode\text{-}2}\)
The correct order of their \(E_{cell}\) at \(25^{\circ}\mathrm{C}\) is

The correct option for the average value of kinetic energy and the average value of potential energy of a one-dimensional harmonic oscillator with frequency \(\nu\) in its ground state is:

For the following reaction,
\[ 2\,\mathrm{Pb_3O_4(s)} \rightleftharpoons 6\,\mathrm{PbO(s)} + \mathrm{O_2(g)} \] The correct option showing the number of phases (P), number of components (C) and degrees of freedom (F) is:

If the ionic mobility of \(\mathrm{Ag^+}\) ion in a very dilute aqueous solution of \(\mathrm{AgNO_3}\) at \(298\ \mathrm{K}\) is \(y\times10^{-8}\ \mathrm{m^2\,V^{-1}\,s^{-1}}\), then the value of \(y\) is (rounded off to two decimal places).

(Given: viscosity of water at \(298\ \mathrm{K} = 8.94\times10^{-4}\ \mathrm{kg\,m^{-1}\,s^{-1}}\); \(k = 1.38\times10^{-23}\ \mathrm{J\,K^{-1}}\); \(F = 96500\ \mathrm{C\,mol^{-1}}\); \(R = 8.314\ \mathrm{J\,mol^{-1}\,K^{-1}}\); Stokes radius of \(\mathrm{Ag^+} = 0.15\ \mathrm{nm}\))

In a \(^1\mathrm{H}\) NMR spectrum obtained from a spectrometer operating at a magnetic field of \(14.1\ \mathrm{T}\), two resonances are observed at \(1.25\) ppm and \(5.75\) ppm. The separation between the two resonances (in Hz) is (rounded off to one decimal place).

(Given: gyromagnetic ratio (\(\gamma\)) of \(\mathrm{H} = 2.675\times10^{8}\ \mathrm{T^{-1}\,s^{-1}}\))

The maximum work (\(|W_{max}|\), in kJ) that can be obtained by complete combustion of \(1.0\) mol of \(\mathrm{CH_4}\) at constant pressure and \(25^{\circ}\mathrm{C}\) is (rounded off to one decimal place).

(Given: \(\Delta S = -241.60\ \mathrm{J\,K^{-1}\,mol^{-1}}\); \(\Delta H = -890.01\ \mathrm{kJ\,mol^{-1}}\); \(R = 8.314\ \mathrm{J\,mol^{-1}\,K^{-1}}\))

The total number of symmetry operations (order, \(h\)) present in the point group of \([\mathrm{PdCl_6}]^{2-}\) is \(x\) and that in trans-\([\mathrm{PdBr_2Cl_4}]^{2-}\) is \(y\). The value of \(x-y\) is (in integer).

The microwave spectrum of gaseous \(\mathrm{HF}\) consists of a series of lines separated by \(41.11\ \mathrm{cm^{-1}}\). The bond length (in \(\mathrm{\mathring{A}}\)) of \(\mathrm{HF}\) is (rounded off to two decimal places).

(Given: Atomic mass (in amu): \(\mathrm{H} = 1.008\), \(\mathrm{F} = 18.998\); \(1\ \mathrm{amu} = 1.661\times10^{-27}\ \mathrm{kg}\); \(h = 6.626\times10^{-34}\ \mathrm{J\,s}\); \(c = 2.998\times10^{8}\ \mathrm{m\,s^{-1}}\))

A 0.005 M solution of compound X transmits 80% of the incident light of wavelength (\(\lambda\)) 500 nm. The absorbance of 0.01 M solution of X is (rounded off to three decimal places).
(Given: path length = 1.0 cm)

For the wavefunction \(\Phi = x(a-x)\), where \(a\) is a constant, the correct statement(s) is(are)

The correct statement(s) about spherical harmonics \((Y_l^m)\) is(are)

For the following reaction,
\(\mathrm{A + B \rightleftharpoons X^{\ddagger} \rightarrow product}\)
If the value of \(\Delta^{\ddagger}U^{o} = \dfrac{5}{2}RT\), then the value of \(\Delta^{\ddagger}H^{o}\) is
(\(X^{\ddagger}\) is an activated complex; \(\Delta^{\ddagger}U^{o}\) is the standard change in internal energy; \(\Delta^{\ddagger}H^{o}\) is the standard enthalpy of activation; \(R\) is the gas constant; \(T\) is the temperature)

Among the following, the one for which the infrared active vibrational modes are Raman inactive and vice versa is

The point group of \(\mathrm{CH_2=C=CH_2}\) is