Vapor Pressure Calculator
Vapor pressure at T₁ (e.g. 101.325 kPa = 1.013 bar)
Absolute temperature in Kelvin
Absolute temperature in Kelvin
For water at 100°C: ≈ 40.66 kJ/mol
What is Vapor Pressure?
Vapor pressure (or saturation vapor pressure) is the pressure exerted by vapor above a liquid when equilibrium is established between liquid and gas phases.
Important Properties:
- Depends on temperature
- Is substance-specific (different for water, alcohol, etc.)
- Increases exponentially with rising temperature
- Determines the boiling point of a liquid
Practical Significance:
- Distillation and evaporation
- Pressure vessels and safety valves
- Meteorology and weather
- Materials science and process engineering
Formulas
Clausius-Clapeyron Equation:
ln(P₂/P₁) = -ΔHvap/R · (1/T₂ - 1/T₁)
ln(P₂/P₁) = -ΔHvap/R · (1/T₂ - 1/T₁)
Simplified for P₂:
ln(P₂) = ln(P₁) - (ΔHvap/R) · (1/T₂ - 1/T₁)
ln(P₂) = ln(P₁) - (ΔHvap/R) · (1/T₂ - 1/T₁)
Inverse Formula for P₁:
ln(P₁) = ln(P₂) + (ΔHvap/R) · (1/T₂ - 1/T₁)
ln(P₁) = ln(P₂) + (ΔHvap/R) · (1/T₂ - 1/T₁)
Universal Gas Constant:
R = 8.314 J/(mol·K) = 0.008314 kJ/(mol·K)
R = 8.314 J/(mol·K) = 0.008314 kJ/(mol·K)
Examples
Water at 100°C
P₁ = 1.013 bar (Atmospheric Pressure)
T₁ = 373.15 K (100°C)
P₁ = 1.013 bar (Atmospheric Pressure)
T₁ = 373.15 K (100°C)
Water at 110°C
T₂ = 383.15 K (110°C)
ΔHvap ≈ 40.66 kJ/mol
Result: P₂ ≈ 1.433 bar
T₂ = 383.15 K (110°C)
ΔHvap ≈ 40.66 kJ/mol
Result: P₂ ≈ 1.433 bar
Ethanol at Room Temperature
T = 298.15 K (25°C)
ΔHvap ≈ 38.56 kJ/mol
P ≈ 0.079 bar
T = 298.15 K (25°C)
ΔHvap ≈ 38.56 kJ/mol
P ≈ 0.079 bar
Evaporation at Height
Higher temperatures for boiling point
e.g. used in pressure cookers
Higher temperatures for boiling point
e.g. used in pressure cookers
Technical Background
Clausius-Clapeyron Equation
The Clausius-Clapeyron equation describes the dependence of equilibrium vapor pressure on temperature. It is used to calculate vapor pressures at different temperatures.
Derivation
The equation is based on thermodynamic principles:
- Gibbs-Helmholtz equation
- Entropy change during phase transition
- Energy conservation (First Law)
Enthalpy of Vaporization (ΔHvap)
The energy required to vaporize 1 mole of a liquid:
- Water: 40.66 kJ/mol (at 100°C)
- Ethanol: 38.56 kJ/mol (at 25°C)
- Acetone: 30.72 kJ/mol (at 25°C)
- Benzene: 30.72 kJ/mol (at 25°C)
Practical Applications
- Pressure Vessels: Calculating operating safety
- Evaporative Cooling: Optimizing cooling systems
- Distillation: Separation processes in industry
- Psychrometry: Air humidity and dew point
- Meteorology: Cloud formation and precipitation
Range of Validity
The Clausius-Clapeyron equation is most accurate:
- At moderate pressures (not near the critical point)
- For small temperature intervals
- When ΔHvap is approximately constant
Boiling Point Definition
The boiling point is the temperature at which the vapor pressure equals the atmospheric pressure. Therefore:
- Water boils at 100°C at sea level (1.013 bar)
- Water boils at 93°C at altitude (lower atmospheric pressure)
- Water boils at 121°C in a pressure cooker (higher pressure)
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