What Is the Compressibility Factor?
The compressibility factor calculator determines the compressibility factor (Z) using a version of the ideal gas law corrected for non-ideal (real) gases. This factor is useful to determine the mass and volume of non-ideal gases. You can generate several results from the calculator to draw a compressibility factor chart. Read on to understand what the compressibility factor is and how to calculate it.
How Is the Compressibility Factor Defined?
The behavior of an ideal gas can be generalized using the equation we know as the ideal gas law. However, this equation can only be applied in specific conditions and for ideal gases. To account for the behavior of real gases, the equation is modified by including a dimensionless entity known as the compressibility factor, Z.
For a gas having volume V and n number of moles at pressure P and temperature T, with gas constant R, the compressibility factor is written as:
Z = (P · V) ÷ (n · R · T)
The compressibility factor is used to determine the deviation of the thermodynamic properties of real gases from ideal gas behavior. It can also be defined as the ratio of the actual volume of a gas to the ideal volume of the gas for a given temperature and pressure:
Z = Vactual ÷ Videal
- Z = 1 — the gas behaves exactly like an ideal gas.
- Z > 1 — repulsive intermolecular forces dominate; the gas is less compressible than an ideal gas (common at high pressures).
- Z < 1 — attractive intermolecular forces dominate; the gas is more compressible than an ideal gas (common near the condensation point).
How Do I Use the Compressibility Factor Calculator?
Follow the steps below to calculate the compressibility factor, Z:
- Step 1: Enter the gas pressure, P.
- Step 2: Give the gas volume, V.
- Step 3: Input the amount of substance in moles, n.
- Step 4: Insert the universal gas constant, R. The constant is set to its default value automatically for the chosen unit system: 8.314 J/(K·mol) in SI units, or 10.73164 (psi·ft³)/(lb-mol·°R) in the FPS (US customary) system.
- Step 5: Fill in the temperature of the gas, T (use absolute temperature — Kelvin for metric, Rankine for imperial).
- Step 6: The calculator uses the compressibility factor equation to return the value of the compressibility factor, the ideal volume, and the percentage deviation from ideal behavior.
🙋 You may need help with conversions — use a temperature conversion tool and a pressure conversion calculator to quickly change between units.
Unit Systems
| Quantity | Metric (SI) | Imperial (FPS / US) |
|---|---|---|
| Pressure, P | Pa | psi |
| Volume, V | m³ | ft³ |
| Amount, n | mol | lb-mol |
| Gas constant, R | 8.314 J/(K·mol) | 10.73164 (psi·ft³)/(lb-mol·°R) |
| Temperature, T | K | °R |
Example: Using the Compressibility Factor Calculator
Consider 1 mole of a gas at a pressure of 101 325 Pa and a temperature of 273.15 K, occupying a measured volume of 0.0224 m³. Using R = 8.314 J/(K·mol):
- Z = (P × V) ÷ (n × R × T)
- Z = (101 325 × 0.0224) ÷ (1 × 8.314 × 273.15)
- Z = 2 269.68 ÷ 2 271.02 ≈ 0.9994
A value of Z very close to 1 confirms that, under these near-standard conditions, the gas behaves almost exactly like an ideal gas. The ideal volume is Videal = nRT/P ≈ 0.022414 m³, and the deviation from ideal behavior is only about −0.06%.
FAQs
- What does a compressibility factor of 1 mean?
- A value of Z = 1 means the gas behaves as a perfect ideal gas. The actual volume equals the volume predicted by the ideal gas law, so there is no measurable deviation.
- Why can the compressibility factor be greater than 1?
- At high pressures, repulsive forces between molecules become significant, so the real gas occupies more volume than the ideal gas law predicts. This makes Z greater than 1.
- Why can the compressibility factor be less than 1?
- Near the condensation point or at moderate pressures, attractive forces pull molecules together, so the gas occupies less volume than predicted. This makes Z less than 1.
- Which temperature scale should I use?
- Always use an absolute temperature scale: Kelvin (K) in the metric system and Rankine (°R) in the imperial system. Never use Celsius or Fahrenheit directly in the equation.
- Can I build a compressibility chart with this tool?
- Yes. By keeping the temperature and amount of substance fixed and varying the pressure (and the corresponding measured volume), you can generate several Z values and plot a compressibility factor chart.