Reduced Molar Volume of Real Gas using Clausius Equation given Critical and Actual Parameters Calculator

Formula:

\[ V'_{m,r} = \frac{\left(\frac{[R] \times T_{rg}}{p + \frac{a}{T_{rg}}} + b'\right)}{V_{m,c}} \]

Temperature of Real Gas (T_rg):

Pressure (p):

Clausius Parameter (a):

Clausius Parameter (b'):

Critical Molar Volume (V_m,c):

m³/mol

Reduced Molar Volume (V'_m,r):

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1. What is Reduced Molar Volume of Real Gas?

Definition: Reduced Molar Volume for Real Gas of a fluid is computed from the ideal gas law at the substance's critical pressure and temperature per mole.

Purpose: This calculator helps determine the reduced molar volume of real gases using the Clausius equation, which accounts for deviations from ideal gas behavior.

2. How Does the Calculator Work?

The calculator uses the formula:

\[ V'_{m,r} = \frac{\left(\frac{[R] \times T_{rg}}{p + \frac{a}{T_{rg}}} + b'\right)}{V_{m,c}} \]

Where:

\( V'_{m,r} \) — Reduced molar volume (dimensionless)
\( [R] \) — Universal gas constant (8.314 J/mol·K)
\( T_{rg} \) — Temperature of real gas (K)
\( p \) — Pressure (Pa)
\( a \) — Clausius parameter a (empirical constant)
\( b' \) — Clausius parameter b (empirical constant)
\( V_{m,c} \) — Critical molar volume (m³/mol)

Explanation: The formula accounts for molecular interactions (a) and finite molecular volume (b) that deviate from ideal gas behavior.

3. Importance of Reduced Molar Volume

Details: Calculating reduced properties helps predict gas behavior under various conditions and is essential in thermodynamics and chemical engineering applications.

4. Using the Calculator

Tips: Enter all required parameters with appropriate units. Default values are provided for Clausius parameters a and b, and critical molar volume.

5. Frequently Asked Questions (FAQ)

Q1: What are typical values for Clausius parameters?
A: Parameters a and b are substance-specific. For example, for CO₂: a ≈ 0.3653 Pa·m⁶/mol², b ≈ 4.28×10⁻⁵ m³/mol.

Q2: How do I find critical molar volume?
A: Critical molar volume is a substance property found in chemical databases or calculated from critical temperature and pressure.

Q3: Why use reduced properties?
A: Reduced properties allow generalized correlations that work for many substances (law of corresponding states).

Q4: What's the range for reduced molar volume?
A: Typically between 0 and 1, where 1 represents the critical point.

Q5: How accurate is the Clausius equation?
A: It's moderately accurate for gases at moderate pressures but less accurate near the critical point.