List of top Physical Chemistry Questions asked in IIT JAM CY

The rotational spectrum of HF has equally spaced lines that are 40.9 cm$^{-1}$ apartThe moment of inertia of HF is $Y \times 10^{-47}$ kg m$^2$The value of Y is _ _ _. (rounded off to three decimal places)

A free particle of mass $m$ confined within the walls of a one-dimensional box of length $a$ (with the potential outside the box being infinity), is in the eigenstate having quantum number $n = 4$The magnitude of uncertainty in the measurement of momentum of the particle is $Y \times \frac{h}{a}$The value of $Y$ is _ _ _. (answer in integer)

If the radial wavefunction of the 3p orbital of a hydrogen-like atom is

At a constant pressure, the entropy of mixing of 1 mole of oxygen with 3 moles of nitrogen at 25 $^\circ$C is _ _ _ J K$^{-1}$. (rounded off to two decimal places)

For the dissociation reaction,

The mobility of Na$^+$ ions in water at 298 K is $5.19 \times 10^{-8}$ m$^2$ s$^{-1}$ V$^{-1}$If the effective radius of a Na$^+$ ion is $Y \times 10^{-12}$ m, the value of $Y$ is _ _ _. (rounded off to two decimal places)

At pH 7, the reaction for the oxidation of NADH at 298 K and a pressure of 1 atm is given below:

The Debye temperatures ($\theta_D$) of diamond and copper are 2230 K and 343 K, respectivelyThe maximum value of the frequency of the atomic oscillations of diamond is Y times the maximum value of the frequency of the atomic oscillations of copperThe value of Y is _ _ _. (rounded off to two decimal places)

A system consists of 110 particlesEach particle can have only two non-degenerate energy states $\epsilon_1$ and $\epsilon_2$ with $\epsilon_2 > \epsilon_1$The energy difference between these two states is 0.10 eVThe temperature at which only 10 particles of the system will be present in the energy state $\epsilon_2$ is _ _ _ K. (rounded off to two decimal places)

At 30$^\circ$C, the half-life for the decomposition of a compound is 100 seconds and the value of the half-life is independent of the initial concentration of the reactantThe time required for 30\% of the reactant to be consumed is _ _ _ seconds. (rounded off to one decimal place)

The number of normal modes of vibration in benzene is _ _ _. (answer in integer)

The Langmuir isotherm for the adsorption of a gas on a solid surface can be expressed as $\theta = \frac{Kp}{1+Kp}$The correct statement(s) about this isotherm is/are

The possible value(s) of energy ($E$) obtained from setting the following determinant equal to zero is/are

For the transformation of 1 mole of an ideal gas from an initial temperature of 27$^\circ$C and an initial pressure of 1 atm to a final temperature of 327$^\circ$C and a final pressure of 17 atm, the change in enthalpy, $\Delta H$, is _ _ _ kJ

In the van der Waals equation of state, the volume correction factor (b) arises from the repulsive interactions between the gas moleculesConsidering the molecules to behave as hard spheres of radius r, b = Y $\times$ V$_{\text{molecule}}$ $\times$ N$_A$The value of Y is _ _ _.

For the reaction NO$_2$Cl $\rightarrow$ NO$_2$ + $\frac{1}{2}$Cl$_2$, the proposed mechanism involves the following two elementary steps:
NO$_2$Cl $\xrightarrow{k_1}$ NO$_2$ + Cl
NO$_2$Cl + Cl $\xrightarrow{k_2}$ NO$_2$ + Cl$_2$
Assuming steady state approximation for Cl, the correct expression for the rate of formation of NO$_2$ is

The Lennard-Jones (LJ) potential of interaction between two molecules as a function of distance ($r$), is given by $V_{LJ}(r) = 4\epsilon \left[ \left(\frac{\sigma}{r}\right)^{12} - \left(\frac{\sigma}{r}\right)^6 \right]$, where $\epsilon$ and $\sigma$ are constantsThe expression of $r$ at which $V_{LJ}(r)$ reaches minimum is _ _ _.

For an ideal gas, the isothermal compressibility $k_T = -\frac{1}{V}\left(\frac{\partial V}{\partial P}\right)_T$ is _ _ _.

For first-order diffraction, the smallest value of $d_{hkl}$ that can be detected with X-ray having a wavelength of 1.54 is _ _ _ .

A pair of isosteric compounds is

For a zero-order reaction P→Q, the concentration of P becomes half of its initial concentration in 30 minutes after starting the reaction.
The concentration of P becomes zero at ____ minutes. (rounded off to the nearest integer)

Mobility of ions Li⁺ , Na⁺ , K⁺ , Ag⁺ in water at 298 K follows the order

A salt QCl of a certain metal Q is electrolyzed to its elements. 40 g of metal Q is formed at an electrode. The volume of Cl₂ formed at the other electrode at 1 atm pressure and 298 K is _______ litres. (rounded off to one decimal place)
[Given: The gas constant 𝑅 = 0.082 L atm mol⁻¹ K⁻¹ , the molar mass of Q is 40 g mol⁻¹ and Cl₂ is assumed to be an ideal gas]

The unit cell of a two-dimensional square lattice with lattice parameter a is indicated by the dashed lines as shown below:

The percentage (%) area occupied by the grey circles (of radius r) inside the unit cell is _______. (rounded off to the nearest integer)

The ratio of osmotic pressures of aqueous solutions of 0.01 M BaCl₂ to 0.005 M NaCl is
[Given: Both compounds dissociate completely in water]