Molar Volume using Modified Berthelot Equation given Critical and Actual Parameters Calculator

Molar Volume Formula:

\[ V_m = \frac{[R] \times T}{p} \times \left(1 + \left(\frac{\frac{9p}{P_c}}{128 \times \frac{T}{T_c}}\right) \times \left(1 - \frac{6}{\frac{T^2}{T_c^2}}\right)\right) \]

Temperature (T):

Pressure (p):

Critical Pressure (P_c):

Critical Temperature (T_c):

Molar Volume (V_m):

Unit Converter ▲

Unit Converter ▼

From:	To:

1. What is Molar Volume using Modified Berthelot Equation?

Definition: This calculator estimates the molar volume of a real gas using the Modified Berthelot equation, which accounts for deviations from ideal gas behavior.

Purpose: It helps chemists and engineers determine the volume occupied by one mole of a real gas under specific temperature and pressure conditions.

2. How Does the Calculator Work?

The calculator uses the formula:

\[ V_m = \frac{[R] \times T}{p} \times \left(1 + \left(\frac{\frac{9p}{P_c}}{128 \times \frac{T}{T_c}}\right) \times \left(1 - \frac{6}{\frac{T^2}{T_c^2}}\right)\right) \]

Where:

\( V_m \) — Molar volume (m³/mol)
\( [R] \) — Universal gas constant (8.314 J/mol·K)
\( T \) — Temperature (K)
\( p \) — Pressure (Pa)
\( P_c \) — Critical pressure (Pa)
\( T_c \) — Critical temperature (K)

Explanation: The equation modifies the ideal gas law to account for real gas behavior using critical parameters.

3. Importance of Molar Volume Calculation

Details: Accurate molar volume calculations are essential for gas storage, chemical reactions, and industrial processes involving gases.

4. Using the Calculator

Tips: Enter the temperature, pressure, critical pressure, and critical temperature. All values must be positive.

5. Frequently Asked Questions (FAQ)

Q1: What is the Modified Berthelot equation?
A: An empirical equation that improves upon the ideal gas law by incorporating critical parameters to better predict real gas behavior.

Q2: When is this equation most accurate?
A: For moderate pressures (not too high) and temperatures above the critical temperature.

Q3: Where can I find critical parameters for gases?
A: Critical properties are tabulated in chemical engineering handbooks and online databases.

Q4: How does this compare to the Van der Waals equation?
A: The Modified Berthelot is simpler but less accurate at very high pressures than Van der Waals.

Q5: What units should I use?
A: Temperature in Kelvin, pressure in Pascals, and the result will be in m³/mol.