At −90°C, solid CO₂ has a much lower vapor pressure — it sublimes much more slowly at this temperature.
Understanding the Clausius-Clapeyron Equation
The Clausius-Clapeyron equation describes the relationship between vapor pressure and temperature for a substance. It is derived from thermodynamics and is fundamental for understanding phase transitions, boiling points, and atmospheric pressure effects.
The Equation
ln(P₂/P₁) = −(ΔH_vap / R)(1/T₂ − 1/T₁)
Where R = 8.314 J/(mol·K), the universal gas constant
P₂ = P₁ × exp[−(ΔH_vap/R)(1/T₂ − 1/T₁)]
Explicit form for calculating final vapor pressure
Variable Definitions
Symbol
Meaning
Typical Units
P₁
Initial vapor pressure
atm, mmHg, Pa, etc.
P₂
Final vapor pressure
atm, mmHg, Pa, etc.
T₁
Initial temperature (absolute)
Kelvin (K)
T₂
Final temperature (absolute)
Kelvin (K)
ΔH_vap
Enthalpy of vaporization
kJ/mol
R
Universal gas constant
8.314 J/(mol·K)
Common Enthalpies of Vaporization
Substance
Formula
Normal Boiling Point (°C)
ΔH_vap (kJ/mol)
Water
H₂O
100.0
40.65
Ethanol
C₂H₅OH
78.37
38.56
Acetone
C₃H₆O
56.08
29.10
Benzene
C₆H₆
80.10
30.72
Methanol
CH₃OH
64.70
35.21
Ammonia
NH₃
−33.34
23.35
How to Use the Calculator
1
Choose a substance from the preset dropdown or enter your own ΔH_vap value in kJ/mol.
2
Select calculation mode: Calculate P₂ (vapor pressure) from known T₂, or calculate T₂ (temperature) from known P₂.
3
Enter initial conditions: Provide T₁ (initial temperature) and P₁ (initial vapor pressure at T₁).
4
Enter the target value: T₂ (final temperature) if calculating P₂, or P₂ (target vapor pressure) if calculating T₂.
5
Toggle temperature units between °C and K as needed — the calculator converts automatically.
Key Concepts
🌡️ Vapor Pressure
The pressure exerted by a vapor in thermodynamic equilibrium with its condensed phase at a given temperature.
🔥 Enthalpy of Vaporization
The heat energy required to convert one mole of liquid to gas at constant temperature and pressure.
💨 Boiling Point
The temperature at which the vapor pressure of a liquid equals the external pressure surrounding the liquid.
📈 Temperature Dependence
Vapor pressure increases exponentially with temperature. The Clausius-Clapeyron equation models this relationship accurately over moderate temperature ranges.
🧪
Clausius-Clapeyron
Applies the fundamental thermodynamic equation for accurate vapor pressure calculations at different temperatures.
🔥
Enthalpy Presets
Pre-loaded enthalpy of vaporization values for common substances: water, ethanol, acetone, benzene, and more.
🔄
Dual Calculation Modes
Calculate vapor pressure at a given temperature or find the temperature needed to reach a target vapor pressure.
🌡️
Unit Conversion
Toggle between Celsius and Kelvin with automatic conversion. See results in both scales.
Vapor pressure is the pressure exerted by a vapor in thermodynamic equilibrium with its condensed phases (solid or liquid) at a given temperature in a closed system. The equilibrium vapor pressure is an indication of a liquid's evaporation rate. It relates to the tendency of particles to escape from the liquid (or solid).
A substance with a high vapor pressure at normal temperatures is often referred to as volatile. The vapor pressure of any substance increases non-linearly with temperature according to the Clausius-Clapeyron relation. At the normal boiling point of a liquid, the vapor pressure is equal to the standard atmospheric pressure (1 atm or 101.325 kPa).
Why Vapor Pressure Matters
Understanding vapor pressure is critical in many fields of science and engineering. In chemistry, vapor pressure determines how quickly a solvent evaporates and affects distillation processes. In meteorology, vapor pressure is essential for understanding humidity and weather patterns. In chemical engineering, vapor-liquid equilibrium data is fundamental for designing separation processes like distillation columns and evaporators.
The Clausius-Clapeyron equation is one of the most important relationships in physical chemistry because it connects the macroscopic property of vapor pressure to the molecular property of enthalpy of vaporization. This allows scientists and engineers to predict how substances behave under different temperature and pressure conditions without performing extensive experimental measurements.
Temperature and Vapor Pressure
As temperature increases, the kinetic energy of molecules in a liquid increases, allowing more molecules to escape into the vapor phase. This causes the vapor pressure to rise. The relationship is exponential rather than linear — a small increase in temperature can cause a significant increase in vapor pressure. This is why water boils more vigorously at higher temperatures and why volatile liquids evaporate quickly even at room temperature.
Applications of the Clausius-Clapeyron Equation
🫖 Cooking at High Altitudes
At higher altitudes, atmospheric pressure is lower, so water boils at a lower temperature. The Clausius-Clapeyron equation explains why cooking times must be adjusted.
🔬 Distillation Design
Chemical engineers use vapor pressure data to design distillation columns that separate mixtures based on differences in boiling points and volatilities.
🌪️ Weather Prediction
Vapor pressure is directly related to relative humidity. Meteorologists use these relationships to predict cloud formation, precipitation, and storm intensity.
⚡ Power Generation
Steam turbines in power plants rely on the vapor pressure of water at high temperatures. Understanding the P-T relationship optimizes thermodynamic efficiency.
Frequently Asked Questions
What is the Clausius-Clapeyron equation used for?
The Clausius-Clapeyron equation is used to calculate the vapor pressure of a substance at different temperatures, or conversely, to find the temperature at which a substance reaches a specific vapor pressure. It is fundamental for understanding boiling points, distillation processes, phase transitions, and atmospheric phenomena.
Does the Clausius-Clapeyron equation work for all substances?
The Clausius-Clapeyron equation works well for most substances over moderate temperature ranges where the enthalpy of vaporization remains approximately constant. It assumes ideal gas behavior for the vapor phase and neglects the molar volume of the liquid relative to the gas. For high accuracy over wide temperature ranges, more complex equations like the Antoine equation are often used.
What is the normal boiling point?
The normal boiling point of a liquid is the temperature at which its vapor pressure equals 1 atmosphere (101.325 kPa or 760 mmHg). For water, the normal boiling point is 100°C (212°F). At higher altitudes where atmospheric pressure is lower, water boils at a lower temperature because less vapor pressure is needed to match the external pressure.
What is enthalpy of vaporization?
The enthalpy of vaporization (ΔH_vap) is the amount of heat energy required to convert one mole of a liquid into vapor at constant temperature and pressure. It is a measure of the strength of intermolecular forces in the liquid. Water has a relatively high ΔH_vap (40.65 kJ/mol) due to strong hydrogen bonding, which is why it takes more energy to boil water compared to many other liquids.
Why must temperature be in Kelvin for this equation?
The Clausius-Clapeyron equation requires absolute temperature (Kelvin) because it is derived from thermodynamic principles that use the reciprocal of temperature (1/T). Using Celsius or Fahrenheit would produce mathematically incorrect results since these scales are relative, not absolute. The Kelvin scale starts at absolute zero (−273.15°C), where molecular motion theoretically ceases. The conversion is simple: K = °C + 273.15.
How accurate is the Clausius-Clapeyron equation?
The Clausius-Clapeyron equation is most accurate over small to moderate temperature ranges (typically 20-30°C) where ΔH_vap can be considered constant. Its accuracy typically ranges from 1-5% over such ranges. For wider temperature spans, ΔH_vap varies with temperature, and more sophisticated models like the Antoine equation or Wagner equation are preferred for higher accuracy.
⚠️ Important Note: This Vapor Pressure Calculator is for educational and professional reference purposes. The Clausius-Clapeyron equation assumes constant enthalpy of vaporization and ideal gas behavior. For precise engineering applications, consult experimental data or more advanced thermodynamic models. Always verify critical values with authoritative sources.