Can the gas be liquefied?

Yes, the gas can be liquefied. The equation of state for a real gas, given as p(v - b) = RT, provides insights into the behavior of the gas and helps determine whether it can be liquefied.

Explanation:

Equation of State:
The equation of state for a gas relates its pressure (p), volume (v), temperature (T), and a constant (R) known as the gas constant. For real gases, this equation is modified to account for the intermolecular forces and the finite size of gas particles.

Liquefaction of Gases:
Liquefaction of a gas refers to the process of converting a gas into its liquid state. This can be achieved by decreasing the temperature and/or increasing the pressure. The behavior of a gas under different conditions is described by its equation of state.

Van der Waals Equation:
The Van der Waals equation is a modification of the ideal gas law that accounts for the intermolecular forces and the volume occupied by gas particles. It is given as:

(p + a/v^2)(v - b) = RT

Where 'a' represents the attractive forces between gas particles and 'b' represents the volume occupied by gas particles.

Effect of 'b' in the Equation:
The term 'b' in the equation of state represents the volume occupied by gas particles. It accounts for the finite size of gas molecules. If the value of 'b' is significant, it implies that the gas particles occupy a considerable volume, making it more difficult to compress the gas and liquefy it.

Conclusion:
In the given equation of state, p(v - b) = RT, the presence of 'b' indicates that the volume occupied by gas particles is being considered. If 'b' is a significant value for a particular gas, it suggests that the gas particles occupy a substantial volume, making it more challenging to liquefy the gas.

Therefore, whether a gas can be liquefied or not depends on the magnitude of 'b' in the equation of state. If 'b' is relatively small, indicating that the gas particles occupy a negligible volume, the gas is more likely to be easily liquefied. However, if 'b' is significant, suggesting that the gas particles occupy a substantial volume, liquefying the gas would require higher pressures and/or lower temperatures.