Input Parameters
Temperature °C
Pressure mmHg
Selected Substance: Water

Using Antoine equation with coefficients: A = 8.07131, B = 1730.63, C = 233.426

Valid temperature range: 1°C to 100°C

Results

Enter parameters and click Calculate to see results.

Chemical Theory & Academic Context

Vapor Pressure Fundamentals

Vapor pressure is the equilibrium pressure exerted by a vapor in thermodynamic equilibrium with its condensed phases (solid or liquid) at a given temperature in a closed system. This fundamental physical chemistry concept quantifies a substance's tendency to evaporate and is crucial for understanding phase transitions, distillation, and atmospheric science.

Equations Used in This Calculator

Antoine Equation (Empirical Correlation)

log₁₀(P) = A - B/(T + C)

Where:

Variable Description Typical Units
P Vapor pressure mmHg (original), various
T Temperature °C (Celsius)
A, B, C Substance-specific Antoine coefficients (empirically determined) Dimensionless (A), °C (B, C)

Note: Antoine coefficients are temperature-range specific. Using them outside their validated range reduces accuracy.

Clausius-Clapeyron Equation (Theoretical Basis)

ln(P₂/P₁) = -(ΔHvap/R) × (1/T₂ - 1/T₁)

Derived from thermodynamic principles, this equation assumes:

  • Constant enthalpy of vaporization (ΔHvap) over the temperature range
  • Ideal gas behavior for the vapor phase
  • Negligible molar volume of liquid compared to vapor
Variable Description Units
P₁, P₂ Vapor pressures at temperatures T₁ and T₂ Consistent pressure units
T₁, T₂ Absolute temperatures Kelvin (K)
ΔHvap Enthalpy of vaporization J/mol (calculator converts kJ/mol)
R Ideal gas constant 8.314 J/(mol·K)

Method Selection Guidance

  • Antoine Equation: Preferred when accurate, experimentally determined coefficients are available for your temperature range. Typically more accurate for engineering applications.
  • Clausius-Clapeyron Equation: Used when enthalpy data is available but Antoine coefficients are not. Best for theoretical understanding and moderate temperature ranges where ΔHvap is relatively constant.
  • Auto-select logic: This calculator prioritizes the Antoine equation when both datasets are available, as it generally provides better accuracy for pure substances.

Unit System & Conversions

This calculator uses consistent scientific units internally:

  • Temperature: Calculations occur in Kelvin (K) for Clausius-Clapeyron, Celsius (°C) for Antoine
  • Pressure: Internal calculations use mmHg (torr) as base unit, with conversions to other units:
    • 1 atm = 760 mmHg (exact)
    • 1 kPa = 7.50062 mmHg
    • 1 bar = 750.062 mmHg
    • 1 torr = 1 mmHg (definition)
  • Energy: ΔHvap converted from kJ/mol to J/mol for Clausius-Clapeyron calculations

Accuracy Considerations & Limitations

Important Limitations
  • Temperature Range Validity: Antoine coefficients are valid only within specific temperature ranges. Extrapolation beyond these ranges reduces accuracy significantly.
  • Assumption of Constant ΔHvap: The Clausius-Clapeyron equation assumes ΔHvap is temperature-independent, which is only approximately true over limited ranges.
  • Pure Substances: These equations apply to pure substances. Mixtures require different approaches (Raoult's Law, activity coefficients).
  • Ideal Behavior: Assumes ideal gas behavior for vapor phase, which may not hold at high pressures or near critical points.
  • Numerical Precision: Results are rounded to 4 decimal places or scientific notation. Intermediate calculations use JavaScript's double-precision floating-point arithmetic.

Common Student Misconceptions

  1. Vapor pressure vs. boiling point: Vapor pressure equals atmospheric pressure at the boiling point, but they are distinct concepts.
  2. Temperature dependence: Vapor pressure increases exponentially with temperature, not linearly.
  3. Unit consistency: For Clausius-Clapeyron, temperature must be in Kelvin, not Celsius.
  4. Equation applicability: Different equations have different valid ranges and assumptions.
  5. ΔHvap temperature dependence: Enthalpy of vaporization decreases with increasing temperature and becomes zero at the critical point.

Sample Calculation Example

Water at 25°C using Antoine Equation

Given: A = 8.07131, B = 1730.63, C = 233.426, T = 25°C

Calculation:

  1. B/(C+T) = 1730.63/(233.426 + 25) = 1730.63/258.426 ≈ 6.697
  2. log₁₀P = A - 6.697 = 8.07131 - 6.697 ≈ 1.3743
  3. P = 101.3743 ≈ 23.76 mmHg

Result: 23.76 mmHg (matches literature value: 23.76 mmHg at 25°C)

Laboratory & Real-World Applications

  • Distillation design: Vapor pressure data determines boiling points and separation feasibility. You can further explore phase behavior using tools like the partial pressure calculator for gas mixtures.
  • Environmental science: Volatilization rates of pollutants from soil and water
  • Pharmaceutical storage: Stability of drug formulations in various climates. Understanding vapor pressure is also essential when working with colligative properties, such as in the osmotic pressure calculator.
  • Chemical engineering: Design of evaporation, drying, and crystallization processes. For related thermodynamic analysis, consider using the Gibbs free energy calculator to determine reaction spontaneity.
  • Meteorology: Humidity and cloud formation calculations

Frequently Asked Questions

Antoine coefficients are empirically fitted to experimental data. Different researchers may use different temperature ranges, data sets, or fitting methods, leading to slightly different coefficients. Always use coefficients validated for your specific temperature range.

Antoine equation: Always use Celsius, as the coefficients are calibrated for °C.
Clausius-Clapeyron equation: Always use Kelvin, as it involves thermodynamic temperature in the 1/T terms.
The calculator handles these conversions automatically based on your selected unit.

With valid coefficients and within recommended temperature ranges:
  • Antoine equation: Typically ±1-2% for pure substances
  • Clausius-Clapeyron: ±5-10% depending on temperature range and ΔHvap constancy
Accuracy decreases near critical points, at very low pressures, or when extrapolating beyond coefficient ranges.

No. This calculator is for pure substances only. Mixtures require:
  • Raoult's Law for ideal mixtures: Ptotal = Σ(xiPi°)
  • Activity coefficients for non-ideal mixtures
  • More complex equations of state for highly non-ideal systems

Related Chemistry Calculations

This tool complements other physical chemistry calculations. For instance, you can use the enthalpy calculator to determine the heat of vaporization needed for the Clausius-Clapeyron equation. Additionally, understanding the vapor pressure of pure substances is the foundation for more complex mixture calculations, such as those performed by the Raoult's Law approach (available in our partial pressure tool).

Academic Integrity & References

Formula Verification: All equations and constants used in this calculator are verified against standard physical chemistry references including:

  • Atkins, P. W., & de Paula, J. (2014). Physical Chemistry (10th ed.).
  • Poling, B. E., Prausnitz, J. M., & O'Connell, J. P. (2001). The Properties of Gases and Liquids (5th ed.).
  • NIST Chemistry WebBook (Standard Reference Data)

Educational Purpose: This tool is designed for educational use, laboratory planning, and preliminary engineering calculations. For critical applications, consult primary experimental data or rigorous thermodynamic simulations.

Last Updated: October 2025 | Formula Verification Date: November 2025

Disclaimer: While every effort is made to ensure calculation accuracy, users should verify critical results with experimental data or professional-grade software.