Question

The 'Fugacity Coefficient ($\phi = f/P$)' of a real gas approaches unity when

• A. the pressure approaches infinity
• B. the temperature approaches $0\text{ K}$
• C. the pressure approaches zero
• D. the gas is compressed into a liquid

Hint:

At very low pressures, all real gases behave ideally.
Consequently, any non-ideal property multiplier (like the fugacity coefficient $\phi$ or compressibility factor $Z$) must approach 1 as $P \to 0$.

Answer 1

The Correct Option is C

Step 1: Understanding the Question:
This question deals with fugacity and the fugacity coefficient, which are thermodynamic concepts used to describe the non-ideal behavior of real gases.
The question asks for the thermodynamic limit under which a real gas exhibits ideal gas behavior.

Step 2: Key Formula or Approach:
The fugacity coefficient ($\phi$) is defined by the relation:
\[ \phi = \frac{f}{P} \] Where:
$f$ is the fugacity of the gas.
$P$ is the pressure of the gas.
For an ideal gas, fugacity is exactly equal to the system pressure ($f = P$), which yields:
\[ \phi = 1 \]

Step 3: Detailed Explanation:

• Real gases deviate from ideal behavior due to intermolecular attractive/repulsive forces and the physical volume occupied by the gas molecules.

• When the pressure of a real gas approaches zero ($P \to 0$), the volume of the system becomes very large, and the molecules are spaced extremely far apart.

• At this infinite dilution limit, intermolecular interactions become negligible, and the molecular volume is negligible compared to the total volume.

• Under this condition, the real gas behaves exactly like an ideal gas.

• Since ideal gas behavior is reached at $P \to 0$, the fugacity ($f$) approaches the pressure ($P$), meaning that the fugacity coefficient ($\phi = f/P$) approaches 1 (unity):
\[ \lim_{P \to 0} \phi = 1 \]

Step 4: Final Answer:
The fugacity coefficient approaches unity when the pressure approaches zero, corresponding to option (C).