Statistical Thermodynamics - Physical Chemistry - Chemistry Previous Year Questions

1

2008 · Chemistry · Physical Chemistry · Statistical Thermodynamics

Chemistry (CY) 2008

At T = 300 K, the thermal energy (k_BT) in cm^-1 is approximately

A

20000

B

8000

C

5000

D

200

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2

2008 · Chemistry · Physical Chemistry · Statistical Thermodynamics

Chemistry (CY) 2008

The residual entropy of the asymmetric molecule N₂O in its crystalline state is 5.8 J K^-1 mol^-1 at absolute zero. The number of orientations that can be adopted by N₂O in its crystalline state is

A

4

B

3

C

2

D

1

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3

2008 · Chemistry · Physical Chemistry · Statistical Thermodynamics

Chemistry (CY) 2008

A certain molecule can be treated as having only a doubly degenerate state lying at 360 cm^-1 above the nondegenerate ground state. The approximate temperature (K) at which 15% of the molecules will be in the upper state is

A

500

B

150

C

200

D

300

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4

2008 · Chemistry · Physical Chemistry · Statistical Thermodynamics

Chemistry (CY) 2008

A box of volume V contains one mole of an ideal gas. The probability that all N particles will be found occupying one half of the volume leaving the other half empty is

A

1/2

B

2/N

C

(1/2)^N

D

(1/2)^6N

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5

2012 · Chemistry · Physical Chemistry · Statistical Thermodynamics

Chemistry (CY) 2012

The molecular partition function of a system is given by
\(q(T) = \left(\frac{k_B T}{hc}\right)^{3/2} \left(\frac{8\pi^2 m k_B T}{h^2}\right)^{5/2}\), where the symbols have their usual meanings.
The heat capacity at constant volume for this system is

A

3R

B

6R

C

9R/2

D

3R/2

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6

2012 · Chemistry · Physical Chemistry · Statistical Thermodynamics

Chemistry (CY) 2012

A and B are friends. They decide to meet between 1 PM and 2 PM on a given day. There is a condition that whoever arrives first will not wait for the other for more than 15 minutes. The probability that they will meet on that day is

A

1/4

B

1/16

C

7/16

D

9/16

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7

2013 · Chemistry · Physical Chemistry · Statistical Thermodynamics

Chemistry (CY) 2013

The moment of inertia of a homonuclear diatomic molecule is 7.5 × 10^-45 kg m². Its rotational partition function at 500 K is __________.

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8

2013 · Chemistry · Physical Chemistry · Statistical Thermodynamics

Chemistry (CY) 2013

In a factory, two machines M1 and M2 manufacture 60% and 40% of the autocomponents respectively. Out of the total production, 2% of M1 and 3% of M2 are found to be defective. If a randomly drawn autocomponent from the combined lot is found defective, what is the probability that it was manufactured by M2?

A

0.35

B

0.45

C

0.5

D

0.4

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9

2014 · Chemistry · Physical Chemistry · Statistical Thermodynamics

Chemistry (CY) 2014

The molecular partition function for a system in which the energy levels are equispaced by ε, is

A

\(\frac{1}{1 + e^{β ε}} \)

B

\(\frac{1}{1 - e^{β ε}} \)

C

\(\frac{1}{1 + e^{-β ε}} \)

D

\(\frac{1}{1 - e^{-β ε}} \)

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10

2014 · Chemistry · Physical Chemistry · Statistical Thermodynamics

Chemistry (CY) 2014

The ratio of molecules distributed between two states is 9.22 × 10⁶ at 300 K. The difference in energy (in kJ mol^–1) of the two states is ______________

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11

2016 · Chemistry · Physical Chemistry · Statistical Thermodynamics

Chemistry (CY) 2016

Consider a two-state system at thermal equilibrium with equal degeneracy where the excited state is higher in energy than the ground state by 0.1 eV. The ratio of the population of the excited state to that of the ground state, at a temperature for which \(k_BT = 0.05\) eV, is __________.

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12

2019 · Chemistry · Physical Chemistry · Statistical Thermodynamics

Chemistry (CY) 2019

Consider a two-state system at thermal equilibrium having energies 0 and 2k_BT for which the degeneracies are 1 and 2, respectively. The value of the partition function at the same absolute temperature T is __________. (Round off to two decimal places)
(k_B is the Boltzmann constant)

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13

2019 · Chemistry · Physical Chemistry · Statistical Thermodynamics

Chemistry (CY) 2019

Consider a system of three identical and distinguishable non-interacting particles and three available nondegenerate single particle energy levels having energies 0, ε and 2ε. The system is in contact with a heat bath of temperature T K. A total energy of 2ε is shared by these three particles. The number of ways the particles can be distributed is __________.

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14

2023 · Chemistry · Physical Chemistry · Statistical Thermodynamics

Chemistry (CY) 2023

For an ideal gas, the molecular partition function in the canonical ensemble, that is proportional to the system volume (\(V\)), is the

A

vibrational partition function

B

rotational partition function

C

electronic partition function

D

translational partition function

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15

2024 · Chemistry · Physical Chemistry · Statistical Thermodynamics

Chemistry (CY) 2024

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

A

an ensemble is a collection of an infinite number of imaginary replications of the system of interest.

B

all members of an ensemble are macroscopically identical and also have identical microstates.

C

an ensemble average of any macroscopic property of the system is equal to the value of the property averaged over a sufficiently long time.

D

all systems in a canonical ensemble need NOT have the same composition.

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16

2024 · Chemistry · Physical Chemistry · Statistical Thermodynamics

Chemistry (CY) 2024

If qₜ and Qₜ,ₘ are the molecular and molar translational partition functions of X₂, respectively, then ln(Qₜ,ₘ) = (N is the Avogadro number)

A

N ln qₜ - N ln N

B

N ln qₜ - ln N

C

N ln qₜ + N ln N + N

D

N ln qₜ - N ln N + N

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17

2025 · Chemistry · Physical Chemistry · Statistical Thermodynamics

Chemistry (CY) 2025

The translational, vibrational, and rotational molecular partition functions for a system containing ideal diatomic gas molecules in the canonical ensemble (N, V, T) are written as \(q_{trans}\), \(q_{vib}\), and \(q_{rot}\), respectively. The option that correctly defines their thermodynamic variable(s) dependency is

A

\(q_{trans}(T,V), q_{vib}(T,V), q_{rot}(T,V)\)

B

\(q_{trans}(T,V), q_{vib}(T), q_{rot}(T)\)

C

\(q_{trans}(T), q_{vib}(T,V), q_{rot}(T)\)

D

\(q_{trans}(T,V), q_{vib}(T), q_{rot}(T,V)\)

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18

2025 · Chemistry · Physical Chemistry · Statistical Thermodynamics

Chemistry (CY) 2025

An approximate partition function Q(N, V, T) of a gas is given below.
Q(N, V, T) = (1/N!) [(2πmk_B T / h²)^3N/2] (V - Nb)^N
The equation of state(s) for this gas is/are
[Note: b is a parameter independent of volume.]

A

P(V - Nb) = N k_B T

B

P V^(N-b) = k_B T

C

P V = N k_B T

D

P(V - Nb) = N k_B

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19

2025 · Chemistry · Physical Chemistry · Statistical Thermodynamics

Chemistry (CY) 2025

The mean energy of a molecule having two available energy states at ε = 0 J and ε = 4.14 × 10^-21 J at 300 K is ______ × 10^-21 J (rounded off to two decimal places).
[Given: Boltzmann constant (k_B) = 1.38 × 10^-23 J K^-1]

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20

2007 · Chemistry · Physical Chemistry · Statistical Thermodynamics

Chemistry (CY) 2007

The correct statement(s) among the following is/are
(i) The vibrational energy levels of a real diatomic molecule are equally spaced.
(ii) At 500K, the reaction A → B is spontaneous when ΔH = 18.83 kJ mol^-1 and ΔS = 41.84 J K^-1 mol^-1.
(iii) The process of fluorescence involves transition from a singlet electronic state to another singlet electronic state by absorption of light.
(iv) When a constant P is added to each of the possible energies of a system, its entropy remains unchanged.

A

only i

B

only ii

C

both i and iii

D

both ii and iv

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