Ideal Gas Law With Compressibility Factor Calculator

Modified Ideal Gas Law:

\[ PV = ZnRT \]

Pressure (P):

Volume (V):

m³

Compressibility Factor (Z):

dimensionless

Number of Moles (n):

mol

Temperature (T):

Calculation Result:

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1. What is the Ideal Gas Law With Compressibility Factor?

The modified ideal gas law with compressibility factor (PV = ZnRT) extends the classical ideal gas law to account for real gas behavior. The compressibility factor Z indicates how much a real gas deviates from ideal gas behavior under given conditions.

2. How Does the Calculator Work?

The calculator uses the modified ideal gas law equation:

\[ PV = ZnRT \]

Where:

\( P \) — Pressure (Pascals)
\( V \) — Volume (cubic meters)
\( Z \) — Compressibility factor (dimensionless)
\( n \) — Number of moles (mol)
\( R \) — Universal gas constant (8.314 J/mol·K)
\( T \) — Temperature (Kelvin)

Explanation: The compressibility factor Z accounts for intermolecular forces and molecular volume, making the equation applicable to real gases.

3. Importance of Compressibility Factor

Details: For ideal gases, Z = 1. For real gases, Z deviates from 1 depending on pressure and temperature. At high pressures and low temperatures, Z typically becomes less than 1 due to attractive forces, while at very high pressures, Z becomes greater than 1 due to repulsive forces.

4. Using the Calculator

Tips: Enter all variables in SI units. Pressure in Pascals, volume in cubic meters, temperature in Kelvin. The compressibility factor Z must be determined from experimental data or correlations for the specific gas and conditions.

5. Frequently Asked Questions (FAQ)

Q1: What is the compressibility factor Z?
A: Z is a correction factor that accounts for the deviation of real gases from ideal gas behavior. Z = 1 for ideal gases, Z < 1 when attractive forces dominate, Z > 1 when repulsive forces dominate.

Q2: How is Z determined for real gases?
A: Z is typically determined from experimental P-V-T data or from generalized correlations like the van der Waals equation or using the principle of corresponding states.

Q3: When is the compressibility factor most important?
A: At high pressures and low temperatures, where gases deviate significantly from ideal behavior. Critical for accurate calculations in chemical engineering and high-pressure systems.

Q4: What is the range of Z values?
A: Z can range from approximately 0.2 to 4.0 depending on the gas and conditions, though most common gases under normal conditions have Z values between 0.7 and 1.3.

Q5: Can this equation be used for all gases?
A: Yes, with the appropriate Z value. However, Z must be known or estimated for the specific gas and conditions of interest.