Vapor Pressure Formula
Pressure exerted by vapor in equilibrium with its liquid phase
Key Formulas
Clausius-Clapeyron Equation
ln(P₂/P₁) = -ΔHᵥₐₚ/R × (1/T₂ - 1/T₁)
Relates vapor pressure to temperature
Raoult's Law (Ideal Solutions)
Pₛₒₗᵤₜᵢₒₙ = χₛₒₗᵥₑₙₜ × P°ₛₒₗᵥₑₙₜ
Vapor Pressure Lowering
ΔP = χₛₒₗᵤₜₑ × P°ₛₒₗᵥₑₙₜ
Variables & Constants
P (Vapor Pressure)
Measured in atm, kPa, or mmHg
T (Temperature)
Absolute temperature in Kelvin (K)
ΔHᵥₐₚ (Heat of Vaporization)
Energy to vaporize 1 mol, in kJ/mol
R (Gas Constant)
8.314 J/(mol·K)
χ (Mole Fraction)
Ratio of moles (0 to 1)
P° (Pure Vapor Pressure)
Vapor pressure of pure solvent
Worked Examples
Example 1: Clausius-Clapeyron Application
Problem: Water has vapor pressure 23.8 mmHg at 25°C and ΔHᵥₐₚ = 40.7 kJ/mol. Find vapor pressure at 100°C.
Given:
P₁ = 23.8 mmHg, T₁ = 298 K
T₂ = 373 K, ΔHᵥₐₚ = 40,700 J/mol
R = 8.314 J/(mol·K)
Solution:
ln(P₂/23.8) = -40,700/8.314 × (1/373 - 1/298)
ln(P₂/23.8) = -4895 × (-0.000675)
ln(P₂/23.8) = 3.30
P₂/23.8 = e³·³⁰ = 27.1
P₂ = 645 mmHg ≈ 760 mmHg (boiling point!)
Example 2: Raoult's Law (Vapor Pressure Lowering)
Problem: Add 10.0 g glucose (C₆H₁₂O₆, 180 g/mol) to 100 g water. P°(water) = 23.8 mmHg at 25°C. Find new vapor pressure.
Solution:
n(glucose) = 10.0/180 = 0.0556 mol
n(water) = 100/18 = 5.56 mol
χ(water) = 5.56/(5.56 + 0.0556) = 0.990
P(solution) = 0.990 × 23.8
P(solution) = 23.6 mmHg
ΔP = 23.8 - 23.6 = 0.2 mmHg lowering
Example 3: Finding ΔHᵥₐₚ
Problem: Ethanol has P = 44 mmHg at 20°C and P = 135 mmHg at 40°C. Find ΔHᵥₐₚ.
Solution:
ln(135/44) = -ΔHᵥₐₚ/8.314 × (1/313 - 1/293)
1.124 = -ΔHᵥₐₚ/8.314 × (-0.000218)
ΔHᵥₐₚ = 1.124 × 8.314 / 0.000218
ΔHᵥₐₚ = 42,900 J/mol = 42.9 kJ/mol
Common Mistakes
Forgetting to Convert to Kelvin
T must be in Kelvin: K = °C + 273.15
Unit Mismatch in ΔHᵥₐₚ
If ΔHᵥₐₚ in kJ/mol, multiply by 1000 to get J/mol for R = 8.314 J/(mol·K)
Boiling Point Definition
Liquid boils when vapor pressure = atmospheric pressure (760 mmHg at sea level)
Raoult's Law Limitations
Only accurate for ideal solutions; fails for strong solute-solvent interactions