Distillation is a physical separation process that allows one to separate liquids from a mixture based on differences in their vapor pressures. In the simplest case (which we will examine) when separating a 2-component liquid mixture, the vapor phase above the liquid will always be richer in the more volatile component. Let's get some definitions down first.

Vapor Pressure

Yes, this violates my "no videos" thing on Chembook. I just had to do it. And yes, that's me in about 2013 or so. Did I look younger? Did I color my hair? - yes, and yes. Still has a nice description of vapor pressure - make sure you understand it. - Dr. McCord

A volatile liquid is one with a relatively high vapor pressure at room temperature.

So volatile relative to what? Is there a certain vapor pressure that makes a liquid volatile? Not specifically, but water is definitely NOT volatile and it has about a vapor pressure of only 24 torr at room temperature. Compare that to ethanol at 25 °C, which has a vapor pressure of 80 torr and is considered volatile. Diethyl ether is considered very volatile and has a vapor pressure of 450 torr at room temperature. Most of these volatile liquids with carbons, hydrogens, and oxygens in the formulas are also very flammable. This is a very dangerous combination - highly volatile and flammable. This means an open container of a highly volatile liquid can easily evaporate and fill an entire room with flammable vapors - one flame or spark will then equal an explosion or at least a huge fire ball.

The boiling point of a liquid is the temperature at which the vapor pressure equals the applied pressure.

The normal boiling point of a liquid is the temperature at which the vapor pressure equals normal atmospheric pressure (1 atm).

Raoult's Law

Raoult's Law is a mathematical relationship (a formula) that directly relates the vapor pressure of a liquid in a mixture with its mole fraction (a concentration term, remember?) in the mixture. The formula is simple.

\[P_{\rm A} = x_{\rm A} P^\circ_{\rm A}\]

Where \(x_{\rm A}\) is the mole fraction of liquid A in a solution (mixture) and \(P^\circ_{\rm A}\) is the vapor pressure of pure 100% A if it were all by itself. Note how this is just scaling the pure vapor pressure linearly all the way down to zero if you had none. The plot of this is really simple and is shown below for liquid A.

a plot of Raoult's Law

That plot would be all there is if the second component was just a dissolved solid with no vapor pressure of its own. However, if you have the second component to be another volatile liquid (say liquid B) then you have to also apply Raoult's Law to that liquid as well and get

\[P_{\rm B} = x_{\rm B} P^\circ_{\rm B}\]

Not a surprise at all there. So if our mixture is just A and B combined, then we can actually show both the vapor pressure of A and the vapor pressure of B on the same plot. We can even show that the mixture's vapor pressure is just a combination of the two separate liquids following the law...

\[P_{\rm total} = x_{\rm A} P^\circ_{\rm A} + x_{\rm B} P^\circ_{\rm B}\]

This too can be easily plotted on a graph like the previous one for just A. Note how the total vapor pressure for the mixture of A and B is just the combination of the two individual vapor pressures.

a plot of Raoult's Law with 2 solvents

Notice how the horizontal axis is both the mole fraction of A and B, it just runs opposite directions and remember that \(x_{\rm A} + x_{\rm B} = 1\).

Using Raoult's Law to get the Vapor Phase Composition

The equations above (and plots) are calculated via the mole fractions of the two components in the liquid phase. You can use the vapor pressures of the individual components to determine the vapor phase composition - which should be richer in the more volatile component (the one with the higher vapor pressure). To calculate the vapor phase composition, you just need to properly use Dalton's law of partial pressures for gases wherein the following must be true

\[x_{\rm A,vapor} = {P_{\rm A}\over P_{\rm A} + P_{\rm B}}\]

\[x_{\rm B,vapor} = {P_{\rm B}\over P_{\rm A} + P_{\rm B}}\]

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