Van Der Waals Gas Pressure Calculator

Van der Waals Equation:

\[ P = \frac{nRT}{V - nb} - a\left(\frac{n}{V}\right)^2 \]

Number of moles (n):

mol

Gas constant (R):

J/mol·K

Temperature (T):

Volume (V):

m³

Van der Waals constant (a):

Pa·m⁶/mol²

Van der Waals constant (b):

m³/mol

Calculated Pressure (P):

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1. What is the Van der Waals Equation?

The Van der Waals equation is a thermodynamic equation of state that modifies the ideal gas law to account for molecular size (b) and intermolecular forces (a). It provides a more accurate description of real gas behavior than the ideal gas law.

2. How Does the Calculator Work?

The calculator uses the Van der Waals equation:

\[ P = \frac{nRT}{V - nb} - a\left(\frac{n}{V}\right)^2 \]

Where:

\( P \) — Pressure (Pa)
\( n \) — Number of moles (mol)
\( R \) — Gas constant (8.314 J/mol·K)
\( T \) — Temperature (K)
\( V \) — Volume (m³)
\( a \) — Van der Waals constant (Pa·m⁶/mol²)
\( b \) — Van der Waals constant (m³/mol)

Explanation: The first term accounts for volume correction (excluded volume), while the second term accounts for intermolecular attraction.

3. Importance of Van der Waals Equation

Details: The equation is crucial for understanding real gas behavior, especially under high pressure or low temperature conditions where gases deviate from ideal behavior.

4. Using the Calculator

Tips: Enter all values in SI units. Typical values for 'a' range from 0.003 to 1.5 Pa·m⁶/mol², and for 'b' from 2×10⁻⁵ to 5×10⁻⁵ m³/mol depending on the gas.

5. Frequently Asked Questions (FAQ)

Q1: Why use Van der Waals instead of ideal gas law?
A: The Van der Waals equation provides more accurate results for real gases, especially under high pressure or near the condensation point.

Q2: What are typical values for a and b?
A: For common gases: a (Pa·m⁶/mol²) - H₂: 0.0247, N₂: 0.1408, CO₂: 0.3640; b (m³/mol) - H₂: 2.66×10⁻⁵, N₂: 3.91×10⁻⁵, CO₂: 4.27×10⁻⁵.

Q3: When is the ideal gas law sufficient?
A: At high temperatures and low pressures where intermolecular forces and molecular volume become negligible.

Q4: What are the limitations of Van der Waals equation?
A: It's less accurate near critical points and for strongly polar or associating molecules.

Q5: How does temperature affect the correction terms?
A: The attraction term (a) becomes less significant at higher temperatures as kinetic energy dominates intermolecular forces.