Steam Distillation Volatility: Why the Formula Holds
Steam distillation is a technique used to separate immiscible liquids — typically an organic compound (like an essential oil) and water. The key idea is that the mixture boils when the sum of the vapor pressures equals the external pressure, even though each component's individual boiling point is higher.
The Core Formula
For a mixture of two immiscible liquids (A and water), the total vapor pressure at a given temperature is:
Ptotal=PA∘+Pwater∘
where PA∘ and Pwater∘ are the vapor pressures of the pure components at that temperature.
The mixture boils when:
Ptotal=Patm
Why This Works — The Reasoning
1. Immiscibility → No Mutual Solubility
Since the two liquids do not mix, each exists as a pure phase (not a solution). There is no Raoult's law deviation — each liquid exerts its own pure vapor pressure independently.
- In a solution, the vapor pressure of a component is lowered by the presence of the other (Raoult's law).
- In an immiscible mixture, each liquid behaves as if the other is not there — they are separate layers.
2. Vapor Pressure Adds Independently
Because the liquids are immiscible, the vapor above the mixture contains molecules from both pure phases. The total pressure is simply the sum:
Ptotal=PA∘+Pwater∘
This is Dalton's law of partial pressures applied to two independent pure vapors.
3. Boiling Occurs When Total Pressure Equals Atmospheric Pressure
Boiling happens when the vapor pressure of the liquid equals the external pressure. Here, the "liquid" is the two-phase system. So:
PA∘+Pwater∘=Patm
This temperature is lower than the boiling point of either pure component — because each contributes only part of the required pressure.
The Composition of the Distillate
The mole fraction of each component in the vapor (and hence in the distillate) is given by:
yA=PtotalPA∘,ywater=PtotalPwater∘
Since the vapor is in equilibrium with the pure liquids, the mass ratio in the distillate is:
mwatermA=Pwater∘⋅MwaterPA∘⋅MA
where MA and Mwater are molar masses. …