Engineering
Clausius-Clapeyron Vapor Pressure & Raoult's Law binary mixture formulas
Predict pure-component vapor pressure across temperature via P2 = P1 * EXP((-dHvap/R) * (1/T2 - 1/T1)) and ideal mixture bubble pressure via Raoult's Law.
Approximate vapor pressure and a separate ideal-mixture example
The integrated Clausius–Clapeyron form assumes constant molar vaporization enthalpy over the temperature interval, approximately ideal vapor and negligible liquid volume compared with vapor. The water example is a model estimate, not a steam-table value; enthalpy changes with temperature and extrapolation near critical conditions is unsuitable. Temperatures are kelvin and enthalpy J/mol.
The binary-mixture example is independent of the water calculation. Both saturation pressures must refer to the same mixture temperature. Assume an ideal liquid solution, ideal vapor and vapor–liquid equilibrium. B6 is a liquid mole fraction, not a mass or volume fraction. Raoult partial pressures sum to the bubble pressure; Dalton’s relation gives vapor composition. Nonideal mixtures need a different model.
| Thermodynamic Input | Cell | Distillation Example | Calculated Pressure / Composition |
|---|---|---|---|
| Water Ref (T1, P1, dH_vap) | B2=373.15 K, B3=101.325 kPa | B4 = 40,650 J/mol | 1 atm normal boiling point |
| Target Temp T2 | B5 = 353.15 K (80 C) | Clausius-Clapeyron EXP | P2 = 48.25 kPa |
| Raoult Binary Mix (x_A = 0.40) | B6=0.40, PA*=100, PB*=40 kPa | 0.40*100 + 0.60*40 | P_total = 64.00 kPa |
| Vapor Enrichment y_A | (0.40 * 100) / 64.00 | 40 / 64 | y_A = 0.6250 (62.5% A in vapor!) |
Clausius-Clapeyron vapor pressure P2 at temperature T2 (Kelvin)
Ensure dH_vap (B4) is in J/mol (multiply kJ/mol by 1,000) to match R = 8.3144626 J/(mol*K).
=IF(OR(COUNT(B2:B5)<>4,MIN(B2:B5)<=0),"Invalid inputs",ROUND(B3 * EXP((-B4 / 8.3144626) * (1 / B5 - 1 / B2)), 2))Raoult's Law total mixture pressure & Dalton vapor mole fraction y_A
A has the higher supplied saturation pressure here, so its vapor mole fraction exceeds its liquid mole fraction. That conclusion reverses when B is more volatile. Use the unrounded total pressure when calculating composition.
=IF(OR(COUNT(B6:B8)<>3,B6<0,B6>1,MIN(B7:B8)<0),"Invalid inputs",ROUND(B6 * B7 + (1 - B6) * B8, 2))Equilibrium vapor mole fraction of A
At zero total vapor pressure the fraction is undefined and the formula reports No vapor pressure.
=IF(OR(COUNT(B6:B8)<>3,B6<0,B6>1,MIN(B7:B8)<0),"Invalid inputs",IF(B6*B7+(1-B6)*B8=0,"No vapor pressure",ROUND((B6 * B7) / (B6 * B7 + (1 - B6) * B8), 4)))Try the example
Use the original values or change them to test your understanding.