At a specific temperature and pressure, 2.0\text{ moles} of a real gas occupy a volume of … — JAMB UTME

At a specific temperature and pressure, $2.0\text{ moles}$ of a real gas occupy a volume of $18.0\text{ dm}^3$ . Under the exact same conditions, $2.0\text{ moles}$ of an ideal gas occupy a volume of $22.5\text{ dm}^3$ . What is the compressibility factor ( $Z$ ) of the real gas under these conditions?

Answer: 0.8

Answer

0.8

The compressibility factor

Z

measures the deviation of a real gas from ideal gas behavior and is calculated as

Z = \frac{V_{\text{real}}}{V_{\text{ideal}}}

. Substituting the given values yields

Z = \frac{18.0}{22.5} = 0.80

. A value of

Z < 1

indicates that intermolecular attractive forces dominate, causing the real gas to occupy less volume than predicted by the ideal gas equation.

Step-by-Step Solution

Identify the formula for compressibility factor

Z = \frac{V_{\text{real}}}{V_{\text{ideal}}}

The compressibility factor

Z

quantifies deviation from ideality as the ratio of molar volume of a real gas to that of an ideal gas at the same temperature and pressure.

Substitute the given values into the equation

Z = \frac{18.0\text{ dm}^3}{22.5\text{ dm}^3}

Both volumes are measured under identical pressure, temperature, and mole count.

Calculate the numerical value

Z = 0.80

Dividing 18.0 by 22.5 gives 0.80, indicating

Z < 1

due to predominant intermolecular attraction.

Key Concept

Compressibility factor (Z = V_real / V_ideal) measuring real gas deviation

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