Phase Equilibrium
Vapor Pressure
Calculate vapor pressures using Antoine equation. Essential for flash calculations, storage tank design, and RVP blending.
1. Fundamentals
Vapor pressure is the equilibrium pressure exerted by vapor over its liquid at a given temperature. Higher T → more molecules escape → higher VP.
Temperature
Exponential rise
VP roughly doubles every 20°F.
Molecular weight
Lighter = higher VP
Propane > Butane > Octane.
Polarity
H-bonding lowers VP
Water VP lower than MW suggests.
Boiling point
VP = 1 atm
Definition of normal boiling point.
Key Relationships
Clausius-Clapeyron (approximate):
ln(P₂/P₁) = (ΔHᵥₐₚ/R) × (1/T₁ - 1/T₂)
Trouton's Rule (estimate ΔHᵥₐₚ):
ΔHᵥₐₚ ≈ 10.5 × R × Tᵦₚ [kJ/mol]
Where: R = 8.314 J/mol·K, T in Kelvin
2. Antoine Equation
Antoine Equation:
log₁₀(P) = A - B/(C + T)
Where:
P = Vapor pressure (mmHg or bar, depends on constants)
T = Temperature (°C or K, depends on constants)
A, B, C = Compound-specific constants
Unit conversion:
mmHg → psia: divide by 51.715
mmHg → kPa: multiply by 0.13332
bar → psia: multiply by 14.504
Antoine Constants (NIST)
| Compound | A | B | C | T Range (°C) | P units |
|---|---|---|---|---|---|
| Methane | 6.61184 | 389.93 | 266.00 | -181 to -161 | mmHg |
| Ethane | 6.80266 | 656.40 | 256.00 | -142 to -75 | mmHg |
| Propane | 6.82973 | 803.81 | 247.04 | -108 to -25 | mmHg |
| n-Butane | 6.82485 | 935.86 | 238.73 | -78 to 19 | mmHg |
| i-Butane | 6.78866 | 899.81 | 241.94 | -83 to 7 | mmHg |
| n-Pentane | 6.87632 | 1075.82 | 233.36 | -50 to 58 | mmHg |
| n-Hexane | 6.87601 | 1171.17 | 224.41 | -25 to 92 | mmHg |
| n-Heptane | 6.89386 | 1264.37 | 216.64 | -2 to 124 | mmHg |
| n-Octane | 6.91874 | 1351.99 | 209.15 | 19 to 152 | mmHg |
| Water | 8.07131 | 1730.63 | 233.43 | 1 to 100 | mmHg |
| Methanol | 8.08097 | 1582.27 | 239.73 | 15 to 84 | mmHg |
| Ethanol | 8.11220 | 1592.86 | 226.18 | 20 to 93 | mmHg |
Source: NIST Chemistry WebBook. Always verify T range before use.
Example: n-Butane at 100°F
T = 100°F = 37.8°C
A = 6.82485, B = 935.86, C = 238.73
log₁₀(P) = 6.82485 - 935.86/(238.73 + 37.8)
= 6.82485 - 3.3843
= 3.4405
P = 10^3.4405 = 2,758 mmHg = 53.3 psia
→ n-Butane at 100°F: VP = 53.3 psia (requires pressure vessel)
⚠ Do not extrapolate. Antoine accuracy degrades rapidly outside the valid temperature range. For extended ranges, use Wagner equation or EOS models.
3. Mixtures (Raoult's Law)
Raoult's Law (ideal mixtures):
Pᵢ = xᵢ × Pᵢ° (partial pressure of component i)
P_total = Σ(xᵢ × Pᵢ°) (bubble point pressure)
yᵢ = xᵢ × Pᵢ° / P_total (vapor composition)
Where:
xᵢ = liquid mole fraction
Pᵢ° = pure component vapor pressure at T
yᵢ = vapor mole fraction
Example: 40% Propane / 60% n-Butane at 100°F
Given: x_C3 = 0.40, x_C4 = 0.60
P°_C3 = 188 psia, P°_C4 = 53 psia (at 100°F)
Bubble point pressure:
P = (0.40)(188) + (0.60)(53) = 75.2 + 31.8 = 107 psia
Vapor composition:
y_C3 = (0.40 × 188) / 107 = 0.70 (70% propane)
y_C4 = (0.60 × 53) / 107 = 0.30 (30% butane)
→ Vapor enriched in propane (70% vs 40% in liquid)
This drives distillation separation
Non-Ideal Mixtures
For polar/nonpolar mixtures, add activity coefficients:
Modified Raoult's Law:
Pᵢ = xᵢ × γᵢ × Pᵢ°
Where γᵢ = activity coefficient from:
- Wilson, NRTL, UNIQUAC (polar systems)
- Use process simulators for γᵢ values
| System Type | γ Value | Recommended Model |
|---|---|---|
| Ideal (similar HCs) | γ ≈ 1.0 | Raoult's Law / Peng-Robinson |
| Slightly non-ideal | γ = 0.8-1.2 | Peng-Robinson with kij |
| Polar/nonpolar | γ = 1.5-5+ | NRTL, UNIQUAC |
| Aqueous alcohols | γ = 2-10+ | NRTL, Wilson |
| Azeotropes | Variable | NRTL with experimental data |
4. Engineering Applications
Flash Calculations
| Parameter | Vapor Pressure Role |
|---|---|
| K-value (ideal) | Kᵢ = Pᵢ°/P_system |
| Bubble point | Σ(xᵢ × Kᵢ) = 1 |
| Dew point | Σ(yᵢ / Kᵢ) = 1 |
| Flash drum sizing | Higher VP → more vapor → larger diameter |
Reid Vapor Pressure (RVP)
| Parameter | RVP | TVP |
|---|---|---|
| Standard | ASTM D323 | ASTM D6378 |
| Temperature | 100°F (fixed) | Actual storage T |
| V/L ratio | 4:1 (fixed) | Actual tank |
| Use | Gasoline spec | Tank venting |
| Typical gasoline | 7-15 psi | Varies with T |
Summer gasoline: RVP 7.0-7.8 psi (EPA limit). Winter: 13.5-15 psi.
Storage Tank Venting (API 2000)
Breathing losses ∝ VP
Higher vapor pressure → more evaporation → larger vent required
Normal venting:
- Thermal breathing (day/night T swing)
- Filling/emptying operations
- Use TVP at max storage temperature
Emergency venting:
- Fire case: VP at elevated T (per API 2000 Table 4)
- Size for vapor generation rate at fire conditions
Relief Valve Sizing
Fire relief for liquid-full vessels:
- Step 1: Determine max T from fire heat input (API 521)
- Step 2: Calculate VP at T_max using Antoine
- Step 3: Size PSV for vapor generation at VP
References
- NIST Chemistry WebBook – Antoine constants
- ASTM D323 – Reid Vapor Pressure
- API 2000 – Venting Atmospheric Storage Tanks
- API 521 – Pressure Relief and Depressuring Systems
- Perry's Chemical Engineers' Handbook, Section 2
Ready to calculate?
→ Vapor Pressure Calculator