Statistical Therm & Theory Of Gases - GATE Chemistry MCQ

The value of rotational partition function for the following species at 298 K is

Four identical fermion particles are to be distributed in two energy levels E₁ and E₂. Energy E₁ is 5-fold degenerate and E₂ is 6-fold degenerate. The energy corresponding to the distribution having maximum number of arrangements is

The correct form of vibrational partition function is

The value of temperature at which 10% of the molecule in a system will be in first excited electronic state if this state is 400 kJ/mol above ground state is

The ground state of Co²⁺ ion in CoSO₄.7H₂O may be regarded as ⁴T_3/2. The entropy of the solid at temperature below 1K is derived almost entirely from electron spin. The molar entropy of the solid at these temperature is ________J/mol-K.(Round off to two decimal places).

Consider following energy levels with given number of particles

If system (III) is undergoing cooling, change in molar entropy of the system is _______J/mole-K. (Round off to one decimal place)

The exact probability distribution of rotational energy levels is the Boltzmann factor of each level Weighted by the degeneracy over the partition function
  
The plot of PRJ(T) vs J rotational quantum number for hetronuclear diatomic molecule at 100K is as follows 

If the characteristic rotaional temperature for the molecule is 2.779K. The percentage deviation between exact rotational partition function and the partition function calculated by high-temperature approximation is ____%. (answer should be an integer).

The correct form of Sackur Tetrode Equation is

The quantity remain constant in Grand Canonical Ensemble

Molar entropy of H-atom at 1000 K and 1 bar is

Using Boltzmann porbability distribution expression. The value of possible ways of distributing 7 distingusabe particle among 4 energy levels with energies 0, ε, 2ε and 3ε respectively ____(Total energy of the system remain constant at 3ε)(answer should be an integer).

Certain mass of a gas occupy 200mL at 127⁰C. If the gas is cooled to -73⁰C constant pressure, its new volume _____ mL.(an answer should be an integer).

In what mass ratio, He and O₂ gases should be mixed together to have the same partial pressures is

Nickel forms a gaseous compound of the formula Ni(CO)_x. The value of x given that under the same conditions of temperature and pressure methane effuses 3.25 times faster than the compound is _____(answer should be an integer). (Given : Ni = 58.7)

A vessel contains 80g methane at 27⁰C. The total translational kinetic energy of molecules is _____kJ. (Round off to two decimal places)

The rate of effusion of an unknown gas, X, at 480K is 1.60 times the rate of effusion of sulphur dioxide gas at 300K. The molecular weight of X is ______ (answer should be an integer).

If rotational constant for H₂O(g) at 1500⁰K are A = 27.8778cm^-1, B = 14.5042cm^-1 and C = 9.286cm^-1. The value of change in rotational free energy. (Round off to two decimal places). 
[Given: G_m - G_m(0) is _____kJmol^-1.