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:
- Z > 1 and attractive forces are dominant
- Z > 1 and repulsive forces are dominant
- Z < 1 and attractive forces are dominant
- Z < 1 and repulsive forces are dominant
The Correct Option is C
Solution and Explanation
To determine the correct option about the gas and its compressibility factor (Z), we need to analyze the given information and apply concepts regarding real gases and their deviations from ideal behavior.
An ideal gas follows the equation:
PV = nRT.
The compressibility factor Z is defined as:
Z = \frac{PV}{nRT}.
When Z is equal to 1, the gas behaves ideally. If Z \ne 1, the gas exhibits real behavior:
- Z > 1: Indicates that the gas is expanded more than the ideal gas. This occurs when repulsive forces are dominant.
- Z < 1: Indicates that the gas is more compressed than the ideal gas. This occurs when attractive forces are dominant.
According to the problem, the molar volume of the gas is 20% smaller than that of an ideal gas under the same conditions. This implies the gas is more compressed due to attractive forces between molecules.
Hence, the compressibility factor Z < 1.
So, the correct option is:
Z < 1 and attractive forces are dominant.
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