Question

Identify the correct statements from the following
(A) The compressibility factor (Z) for an ideal gas is 1
(B) Uranium isotopes (\( ^{235}U \) and \( ^{238}U \)) are separated by converting them into \( UF_6 \) vapours
(C) Decrease in temperature increases the kinetic energy of gas molecules

• A. A, B, C
• B. A, C only
• C. B, C only
• D. A, B only

Hint:

Recall the definition of the compressibility factor for ideal gases. Understand the industrial process for uranium isotope separation, which involves the volatile \( UF_6 \) compound. Remember the relationship between the kinetic energy of gas molecules and temperature: kinetic energy is directly proportional to temperature.

Answer 1

The Correct Option is D

Let's analyze each statement:
Option (A) **The compressibility factor (Z) for an ideal gas is 1.
** The compressibility factor \( Z \) is defined as \( Z = \frac{PV}{nRT} \), where \( P \) is pressure, \( V \) is volume, \( n \) is the number of moles, \( R \) is the ideal gas constant, and \( T \) is temperature.
For an ideal gas, the equation of state is \( PV = nRT \), so \( Z = \frac{nRT}{nRT} = 1 \).
This statement is correct.

Option (B) **Uranium isotopes (\( ^{235}U \) and \( ^{238}U \)) are separated by converting them into \( UF_6 \) vapours.
** The separation of uranium isotopes \( ^{235}U \) and \( ^{238}U \) is industrially achieved using the gaseous diffusion method.
Uranium is converted to uranium hexafluoride (\( UF_6 \)), which is a volatile solid that sublimes to form a gas at relatively low temperatures.
The slight mass difference between \( ^{235}UF_6 \) and \( ^{238}UF_6 \) molecules allows for their separation by passing the gaseous \( UF_6 \) through a series of porous barriers.
The lighter \( ^{235}UF_6 \) diffuses slightly faster than the heavier \( ^{238}UF_6 \).
This statement is correct.

Option (C) **Decrease in temperature increases the kinetic energy of gas molecules.
** The average kinetic energy of gas molecules is directly proportional to the absolute temperature \( T \) (in Kelvin).
The relationship is given by \( KE_{avg} = \frac{3}{2} kT \), where \( k \) is the Boltzmann constant.
Therefore, a decrease in temperature leads to a decrease in the average kinetic energy of gas molecules, not an increase.
This statement is incorrect.
Based on the analysis, statements A and B are correct, while statement C is incorrect.
Therefore, the correct option is (D) A, B only.