Understanding Vapor Pressure Calculation: Fundamentals and Applications

Vapor pressure calculation determines the pressure exerted by a vapor in equilibrium with its liquid. This article explores key formulas, data, and real-world applications.

Learn how to accurately compute vapor pressure using empirical and theoretical models. Detailed tables, formulas, and examples guide expert-level understanding.

• Calculate vapor pressure of water at 80°C using Antoine equation.
• Determine vapor pressure of ethanol at 25°C with Clausius-Clapeyron relation.
• Estimate vapor pressure of benzene at 50°C from tabulated constants.
• Find vapor pressure of acetone at 30°C using empirical correlations.

Comprehensive Tables of Vapor Pressure Values for Common Substances

Accurate vapor pressure data is essential for chemical engineering, environmental science, and process design. The following tables present vapor pressure values for widely used substances across typical temperature ranges.

These values serve as benchmarks for validating vapor pressure calculations using various models. Note that vapor pressure increases exponentially with temperature, approaching atmospheric pressure at the boiling point.

Key Formulas for Vapor Pressure Calculation and Variable Definitions

Vapor pressure can be calculated using several empirical and theoretical equations. Each formula has specific variables and applicability ranges. Below are the most widely used equations with detailed explanations.

Antoine Equation

The Antoine equation is an empirical relationship widely used for vapor pressure estimation:

• P: Vapor pressure (usually in mmHg or kPa depending on constants)
• T: Temperature (°C)
• A, B, C: Substance-specific Antoine constants

The constants A, B, and C are determined experimentally and vary with the temperature range. For example, for water between 1°C and 100°C:

• A = 8.07131
• B = 1730.63
• C = 233.426

These constants yield vapor pressure in mmHg.

Clausius-Clapeyron Equation

The Clausius-Clapeyron equation relates vapor pressure to temperature based on enthalpy of vaporization:

• P: Vapor pressure (Pa or atm)
• ΔH_vap: Enthalpy of vaporization (J/mol)
• R: Universal gas constant (8.314 J/mol·K)
• T: Absolute temperature (Kelvin)
• C: Integration constant determined from reference data

This equation assumes ΔH_vap is constant over the temperature range, which is an approximation valid for small intervals.

Antoine Constants Table for Common Substances

Other Empirical Correlations

Additional models include the Wagner equation, Antoine extended forms, and the DIPPR correlation, which provide higher accuracy over wider temperature ranges but require more parameters.

Detailed Explanation of Variables and Typical Values

• Temperature (T): Usually in °C for Antoine, Kelvin for Clausius-Clapeyron. Accurate temperature measurement is critical.
• Vapor Pressure (P): Pressure exerted by vapor in equilibrium, units vary (kPa, mmHg, atm). Conversion factors: 1 atm = 101.325 kPa = 760 mmHg.
• Enthalpy of Vaporization (ΔH_vap): Energy required to vaporize one mole, typically 30-50 kJ/mol for common liquids.
• Constants A, B, C: Empirically derived, substance and temperature range dependent.
• Gas Constant (R): 8.314 J/mol·K, universal constant used in thermodynamic equations.

Real-World Applications: Case Studies in Vapor Pressure Calculation

Case 1: Vapor Pressure of Water at 80°C Using Antoine Equation

Objective: Calculate the vapor pressure of water at 80°C.

Given Antoine constants for water (1-100°C): A = 8.07131, B = 1730.63, C = 233.426.

Applying the Antoine equation:

Calculate denominator:

Calculate fraction:

Calculate exponent:

Calculate vapor pressure:

Convert to kPa:

This matches well with tabulated data (~47.4 kPa), confirming the accuracy of the Antoine equation for this temperature.

Case 2: Estimating Vapor Pressure of Ethanol at 25°C Using Clausius-Clapeyron Equation

Objective: Calculate vapor pressure of ethanol at 25°C using Clausius-Clapeyron, given vapor pressure at 20°C.

Known data:

• Vapor pressure at 20°C (P₁) = 5.95 kPa
• Temperature T₁ = 293.15 K (20°C)
• Temperature T₂ = 298.15 K (25°C)
• Enthalpy of vaporization ΔH_vap = 38.56 kJ/mol = 38560 J/mol
• Gas constant R = 8.314 J/mol·K

Clausius-Clapeyron rearranged for P₂:

Calculate the right side:

Calculate exponent:

Calculate P₂:

Tabulated vapor pressure of ethanol at 25°C is approximately 7.87 kPa, showing good agreement.

Additional Considerations and Advanced Topics

For precise engineering applications, vapor pressure calculations must consider:

• Non-ideal behavior: Real gases and mixtures deviate from ideality; activity coefficients and fugacity corrections may be necessary.
• Temperature range validity: Empirical constants are valid only within specified temperature ranges.
• Mixture effects: Raoult’s law and Dalton’s law govern vapor pressures in mixtures, requiring component vapor pressures and mole fractions.
• Pressure units consistency: Always ensure units of vapor pressure and constants match to avoid calculation errors.

Advanced models such as the Wagner equation or DIPPR correlations provide enhanced accuracy for industrial process simulations. These models incorporate additional parameters and temperature dependencies.

References and Further Reading

• NIST Chemistry WebBook – Authoritative source for thermophysical properties.
• CHERIC Database – Chemical engineering research information center.
• Engineering Toolbox: Vapor Pressure of Water – Practical data and calculators.
• Yaws, C.L., “Thermophysical Properties of Chemicals and Hydrocarbons,” Elsevier, 2015.
• Poling, B.E., Prausnitz, J.M., O’Connell, J.P., “The Properties of Gases and Liquids,” 5th Edition, McGraw-Hill, 2000.