Question

A gas at 350 K and 15 bar has molar volume 20 percent smaller than that for an ideal gas under the same conditions. The correct option about the gas and its compressibility factor (Z) is:

• A. Z > 1 and attractive forces are dominant
• B. Z > 1 and repulsive forces are dominant
• C. Z < 1 and attractive forces are dominant
• D. Z < 1 and repulsive forces are dominant

Answer 1

The Correct Option is C

The problem presents a real gas situation at 350 K and 15 bar where the molar volume is 20% smaller than that for an ideal gas at the same conditions. We are asked to determine the compressibility factor (Z) and whether attractive or repulsive forces are dominant. Let us solve this step-by-step:

1. The compressibility factor, Z, is defined as the ratio of the molar volume of the real gas (V_{\text{real}}) to the molar volume of the ideal gas (V_{\text{ideal}}) under the same conditions: Z = \frac{V_{\text{real}}}{V_{\text{ideal}}}.
2. According to the problem, the molar volume of the gas is 20% less than that of an ideal gas. Therefore, V_{\text{real}} = 0.8 \cdot V_{\text{ideal}}.
3. Substitute into the Z expression: Z = \frac{0.8 \cdot V_{\text{ideal}}}{V_{\text{ideal}}} = 0.8. As Z is less than 1, it implies the gas is compressible under the given conditions.
4. A compressibility factor Z \lt 1 typically indicates that the intermolecular attractive forces are dominant. These forces cause the gas particles to come closer than they would in an ideal gas, hence reducing the volume.

Given this understanding, the correct option is "Z < 1 and attractive forces are dominant." This indicates that the presence of significant attractive forces between gas molecules causes the gas to have a smaller volume than expected for an ideal gas, thereby making Z \lt 1.