Compressibility Factor Calculator Formula

Understand the math behind the compressibility factor calculator. Each variable explained with a worked example.

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Formulas Used

Compressibility Factor (Z)

z_factor = (pressure * volume) / (0.08206 * temp)

Variables

VariableDescriptionDefault
pressurePressure (P)(atm)100
volumeMolar Volume (V_m)(L/mol)0.2
tempTemperature (T)(K)300

How It Works

Compressibility Factor

Formula

Z = PV_m / (RT)

Where:

  • Z = compressibility factor (dimensionless)
  • P = pressure (atm)
  • V_m = molar volume (L/mol)
  • R = 0.08206 L·atm/(mol·K)
  • T = temperature (K)

    • For an ideal gas, Z = 1. Z < 1 means attractive forces dominate; Z > 1 means repulsive forces dominate.

    Worked Example

    A gas at 100 atm, 300 K, has a molar volume of 0.2 L/mol.

    pressure = 100volume = 0.2temp = 300
    1. 01Z = PV_m / (RT)
    2. 02Z = (100 × 0.2) / (0.08206 × 300)
    3. 03Z = 20 / 24.618
    4. 04Z = 0.8124

    Frequently Asked Questions

    What does Z = 1 mean?

    Z = 1 means the gas behaves ideally. The actual molar volume equals the ideal molar volume predicted by PV = nRT.

    What causes Z < 1?

    Intermolecular attractions pull molecules closer together, reducing the volume below ideal predictions. This is common at moderate pressures.

    What causes Z > 1?

    At very high pressures, molecular volume and repulsive forces become significant, causing the gas to occupy more volume than predicted.

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