# Raoult's Law and Distillation

### 1 Solutions of volatile liquids

The popular liquor vodka consists mainly of ethanol (ethyl alcohol) and water in roughly equal portions. Ethanol and water both have substantial vapor pressures, so both components contribute to the total pressure of the gas phase above the liquid in a closed container of the two liquids.

One might expect the vapor pressure of a solution of ethanol and water to be directly proportional to the sums of the values predicted by Raoult's law for the two liquids individually, but in general, this does not happen. The reason for this can be understood if you recall that Raoult's law reflects a single effect: the smaller proportion of vaporizable molecules (and thus their reduced escaping tendency) when the liquid is diluted by otherwise "inert" (non-volatile) substance.

Note

Dmitri Mendeleev, the inventor of the periodic table, is also claimed to be the first person to determine the alcoholic content of Vodka. Liquors that can be legally sold as "vodka" in the EU must have an alcoholic content of at least 37.5 percent (v/v); some vodkas go as high as 50 percent ethanol.

#### Ideal solutions

There are some solutions whose components follow Raoult's law quite closely. An example of such a solution is one composed of hexane C6H14 and heptane C7H16. The total vapor pressure of this solution varies in a straight-line manner with the mole fraction composition of the mixture.

Figure 7.2.1: Raoult's law plot for a mixture of hexane and heptane.

Note that

• the mole fraction scales at the top and bottom run in opposite directions, since by definition,

$X_{hexane} = 1 – X_{heptane}$

• $$P_{total}$$ is the sum of the Raoult's law plots for the two pure compounds, indicating that this solution behaves ideally.

An ideal solution is one whose vapor pressure follows Raoult's law throughout its range of compositions. Experience has shown solutions that approximate ideal behavior are composed of molecules having very similar structures. Thus hexane and heptane are both linear hydrocarbons that differ only by a single –CH2group.

This provides a direct clue to the underlying cause of non-ideal behavior in solutions of volatile liquids. In an ideal solution, the interactions are there, but they are all energetically identical. Thus in an ideal solution of molecules A and B, A—A and B—B attractions are the same as A—B attractions. This is the case only when the two components are chemically and structurally very similar.

Note that this differs in a fundamental way from the definition of an ideal gas, defined as a hypothetical substance that follows the ideal gas law. The kinetic molecular theory that explains ideal gas behavior assumes that the molecules occupy no space and that intermolecular attractions are totally absent.

The definition of an ideal gas is clearly inapplicable to liquids, whose volumes directly reflect the volumes of their component molecules. And of course, the very ability of the molecules to form a condensed phase is due to the attractive forces between the molecules. So the most we can say about an ideal solution is that the attractions between its all of its molecules are identical — that is, A-type molecules are as strongly attracted to other A molecules as to B-type molecules. Ideal solutions are perfectly democratic: there are no favorites.

#### Real Solutions

Real solutions are more like real societies, in which some members are "more equal than others." Suppose, for example, that unlike molecules are more strongly attracted to each other than are like molecules. This will cause A–B pairs that find themselves adjacent to each other to be energetically more stable than A–A and B–B pairs. At compositions in which significant numbers of both kind of molecules are present, their tendencies to escape the solution — and thus the vapor pressure of the solution, will fall below what it would be if the interactions between all the molecules were identical. This gives rise to a negative deviation from Raoult's law. The chloroform-acetone system, illustrated above, is a good example.

Figure 7.2.2: Systems with negative deviation (left) and positive deviation (right) of Raoult's law.

Conversely, if like molecules of each kind are more attracted to each other than to unlike ones, then the molecules that happen to be close to their own kind will be stabilized. At compositions approaching 50 mole-percent, A and B molecules near each other will more readily escape the solution, which will therefore exhibit a higher vapor pressure than would otherwise be the case. It should not be surprising molecules as different as benzene and $$CS_2$$ should interact more strongly with their own kind, hence the positive deviation illustrated here.

You will recall that all gases approach ideal behavior as their pressures approach zero. In the same way, as the mole fraction of either component approaches unity, the behavior of the solution approaches ideality. This is a simple consequence of the fact that at these limits, each molecule is surrounded mainly by its own kind, and the few A-B interactions will have little effect. Raoult's law is therefore a limiting law:

$P_i = \lim_{x_i \rightarrow 0} P^o X_i$

it gives the partial pressure of a substance in equilibrium with the solution more and more closely as the mole fraction of that substance approaches unity.

### 2 Separation of volatile liquids by distillation

Distillation is a process whereby a mixture of liquids having different vapor pressures is separated into its components. At first one might think that this would be quite simple: if you have a solution consisting of liquid A that boils at 50°C and liquid B with a boiling point of 90°C, all that would be necessary would be to heat the mixture to some temperature between these two values; this would boil off all the A (whose vapor could then be condensed back into pure liquid A), leaving pure liquid B in the pot. But that overlooks that fact that these liquids will have substantial vapor pressures at all temperatures, not only at their boiling points.

To fully understand distillation, we will consider an ideal binary liquid mixture of A and B. If the mole fraction of A in the mixture is XA, then by the definition of mole fraction, that of B is

$X_B = 1 – X_A$

Since distillation depends on the different vapor pressures of the components to be separated, let's first consider the vapor pressure vs. composition plots for a hypothetical mixture at some arbitrary temperature at which both liquid and gas phases can exist, depending on the total pressure.

Figure 7.2.3:

In this diagram, all states of the system (that is, combinations of pressure and composition) in which the solution exists solely as a liquid are shaded in green. Since liquids are more stable at higher pressures, these states occupy the upper part of the diagram. At any given total vapor pressure such as at , the composition of the vapor in equilibrium with the liquid (designated by xA) corresponds to the intercept with the diagonal equilibrium line at . The diagonal line is just an expression of the linearity between vapor pressure and composition according to Raoult's law.

Figure 7.2.4:

The blue shading in plot on the right shows all the states in which the vapor is the only stable phase. The upper boundary of this region is defined by the equilibrium line which in this case is curved. As before, the intersection  of the pressure  line  with the equilibrium curve defines the mole fractions of A and B present in the vapor. (Note that mole fractions of gases, which we are dealing with here, are conventionally represented by y, hence yA and yB.)

The curvature of the equilibrium line arises from the need to combine Raoult's law with Dalton's law of partial pressures which applies to gaseous mixtures.

Figure 7.2.5:

The two plots immediately above refer to the same solution at the same total vapor pressure . We can therefore combine them into a single plot, which we show here.

The two liquid-vapor equilibrium lines (one curved, the other straight) now enclose an area in which liquid and vapor can coexist; outside of this region, the mixture will consist entirely of liquid or of vapor. At this particular pressure , the intercept  with the upper boundary of the two-phase region gives the mole fractions of A and B in the liquid phase, while the intercept  with the lower boundary gives the mole fractions of the two components in the vapor.

Take a moment to study this plot, and to confirm that

• because both intercepts occur on equilibrium lines, they describe the compositions of the liquid and vapor that can simultaneously exist;
• the compositions of the vapor and liquid are not the same;
• in the vapor, the mole fraction of B (the more volatile component of the solution) is greater than that inf the liquid;
• in the liquid, the mole fraction of A (the less volatile component) is smaller than that of the vapor.

Hence the very important rule:

The vapor in equilibrium with a solution of two or more liquids is always richer in the more volatile component.

#### Boiling point diagrams

The rule shown above suggests that if we heat a mixture sufficiently to bring its total vapor pressure into the two-phase region, we will have a means of separating the mixture into two portions which will be enriched in the more volatile and less volatile components respectively. This is the principle on which distillation is based.

Figure 7.2.6:

But what temperature is required to achieve this? Again, we will spare you the mathematical details, but it is possible to construct a plot similar to the one above except that the vertical axis represents temperature rather than pressure. This kind of plot is called a boiling point diagram.

• The shape of the two-phase region is bi-convex, as opposed to the half-convex shape of the pressure-composition plot.
• The slope of the two-phase region is opposite to what we saw in the previous plot, and the areas corresponding to the single-phase regions are reversed. This simply reflects the fact that liquids having a higher vapor pressure boil at lower temperatures, and vice versa.
• The horizontal line that defines the temperature is called the tie line. Its intercepts with the two equilibrium curves specify the composition of the liquid and vapor in equilibrium with the mixture at the given temperature.
• The vapor composition line is also known as the dew point line — the temperature at which condensation begins on cooling.
• The liquid composition line is also called the bubble point line — the temperature at which boiling begins on heating.

#### Distillation and temperature

The tie line shown above is for one particular temperature. But when we heat a liquid to its boiling point, the composition will change as the more volatile component (B in these examples) is selectively removed as vapor. The remaining liquid will be enriched in the less volatile component, and its boiling point will consequently rise. To understand this process more thoroughly, let us consider the situation at several points during the distillation of an equimolar solution of A and B.

 We begin with the liquid at T1, below its boiling point. When the temperature rises to T2, boiling begins and the first vapor (and thus the first drop of condensate) will have the composition y2. As the more volatile component B is boiled off, the liquid and vapor/condensate compositions shift to the left (orange arrows). At T4, the last trace of liquid disappears. The system is now entirely vapor, of composition y4.

Notice that the vertical green system composition line remains in the same location in the three plots because the "system" is defined as consisting of both the liquid in the "pot" and that in the receiving container which was condensed from the vapor. The principal ideas you should take away from this are that

• distillation can never completely separate two volatile liquids;
• the composition of the vapor and thus of the condensed distillate changes continually as each drop forms, starting at y2 and ending at y4 in this example;
• if the liquid is completely boiled away, the composition of the distillate will be the same as that of the original solution.

#### Laboratory distillation setup

The apparatus used for a simple laboratory batch distillation is shown here. The purpose of the thermometer is to follow the progress of the distillation; as a rough rule of thumb, the distillation should be stopped when the temperature rises to about half-way between the boiling points of the two pure liquids, which should be at least 20-30 C° apart (if they are closer, then fractional distillation, described below, becomes necessary).

Figure 7.2.7: Fractional distillation setup. An Erlenmeyer flask is used as a receiving flask. Here the distillation head and fractionating column are combined in one piece. Image used with permission from Wikipedia

Condensers are available in a number of types. The simple Liebig condenser shown above is the cheapest and therefore most commonly used in student laboratories. Several other classic designs increase the surface area separating the vapor/distillate and cooling water, leading to greater heat exchange efficiency and allowing higher throughput.

Figure 7.2.8:

absolute ethanol "), the most common method is the use of zeolite-based molecular sieves to absorb the remaining water. Addition of benzene can break the azeotrope, and this was the most common production method in earlier years. For certain critical uses where the purest ethanol is required, it is synthesized directly from ethylene.

### 4 Special Distillation Methods

Here be briefly discuss two distillation methods that students are likely to encounter in more advanced organic lab courses.

#### Vacuum distillation

Many organic substances become unstable at high temperatures, tending to decompose, polymerize or react with other substances at temperatures around 200° C or higher. A liquid will boil when its vapor pressure becomes equal to the pressure of the gas above it, which is ordinarily that of the atmosphere. If this pressure is reduced, boiling can take place at a lower temperature. (Even pure water will boil at room temperature under a partial vacuum.) "Vacuum distillation" is of course a misnomer; a more accurate term would be "reduced-pressure distillation". Vacuum distillation is very commonly carried out in the laboratory and will be familiar to students who take more advanced organic lab courses. It is also sometimes employed on a large industrial scale.

Figure 7.2.9vacuum connection at lower right

The vacuum distillation setup is similar that employed in ordinary distillation, with a few additions:

• The vacuum line is connected to the bent adaptor above the receiving flask.
• In order to avoid uneven boiling and superheating ("bumping"), the boiling flask is usually provided with a fine capillary ("ebulliator") through which an air leak produces bubbles that nucleate the boiling liquid.
• The vacuum is usually supplied by a mechanical pump, or less commonly by a water aspirator or a "house vacuum" line.
• The boiling flask is preferably heated by a water- or steam bath, which provides more efficient heat transfer to the flask and avoids localized overheating. Prior to about 1960, open flames were commonly used in student laboratories, resulting in occasional fires that enlivened the afternoon, but detracted from the student's lab marks.
• A Claisen-type distillation head (below) provides a convenient means of accessing the boiling flask for inserting an air leak capillary or introducing additional liquid through a separatory funnel. This Claisen-Vigreux head includes a fractionation column.

Figure 7.2.10: A Claisen-type distillation head

#### Steam distillation

Strictly speaking, this topic does not belong in this unit, since steam distillation is used to separate immiscible liquids rather than solutions. But because immiscible liquid mixtures are not treated in elementary courses, we present a brief description of steam distillation here for the benefit of students who may encounter it in an organic lab course. A mixture of immiscible liquids will boil when their combined vapor pressures reach atmospheric pressure. This combined vapor pressure is just the sum of the vapor pressures of each liquid individually, and is independent of the quantities of each phase present.

Figure 7.2.11:

Because water boils at 100° C, a mixture of water and an immiscible liquid (an "oil"), even one that has a high boiling point, is guaranteed to boil below 100°, so this method is especially valuable for separating high boiling liquids from mixtures containing non-volatile impurities. Of course the water-oil mixture in the receiving flask must itself be separated, but this is usually easily accomplished by means of a separatory funnel since their densities are ordinarily different.

There is a catch, however: the lower the vapor pressure of the oil, the greater is the quantity of water that co-distills with it. This is the reason for using steam: it provides a source of water able to continually restore that which is lost from the boiling flask. Steam distillation from a water-oil mixture without the introduction of additional steam will also work, and is actually used for some special purposes, but the yield of product will be very limited. Steam distillation is widely used in industries such as petroleum refining (where it is often called "steam stripping") and in the flavors-and-perfumes industry for the isolation of essential oils

The term essential oil refers to the aromas ("essences") of these [mostly simple] organic liquids which occur naturally in plants, from which they are isolated by steam distillation or solvent extraction. Steam distillation was invented in the 13th Century by Ibn al-Baiter, one of the greatest of the scientists and physicians of the Islamic Golden Age in Andalusia.

### 5 Industrial-scale distillation, petroleum fractionation

Distillation is one of the major "unit operations" of the chemical process industries, especially those connected with petroleum and biofuel refining, liquid air separation, and brewing. Laboratory distillations are typically batch operations and employ relatively simple fractionating columns to obtain a pure product. In contrast, industrial distillations are most often designed to produce mixtures having a desired boiling range rather than pure products.

Industrial operations commonly employ bubble-cap fractionating columns (seldom seen in laboratories), although packed columns are sometimes used.

Perhaps the most distinctive feature of large scale industrial distillations is that they usually operate on a continuous basis in which the preheated crude mixture is preheated in a furnace and fed into the fractionating column at some intermediate point. A reboiler unit maintains the bottom temperature at a constant value.

The higher-boiling components then move down to a level at which they vaporize, while the lighter (lower-boiling) material moves upward to condense at an appropriate point.

#### Petroleum

Petroleum is a complex mixture of many types of organic molecules, mostly hydrocarbons, that were formed by the effects of heat and pressure on plant materials (mostly algae) that grew in regions that the earth's tectonic movements buried over periods of millions of years. This mixture of liquid and gases migrates up through porous rock until it s trapped by an impermeable layer of sedimentary rock. The molecular composition of crude oil (the liquid fraction of petroleum) is highly variable, although its overall elemental makeup generally reflects that of typical plants.

 element amount carbon hydrogen nitrogen oxygen sulfur metals 83-87% 10-14% 0.1-2% 0.1-1.5% 0.5-6% <1000 ppm

The principal molecular constituents of crude oil are

alkanes
Also known as paraffins, these are saturated linear- or branched-chain molecules having the general formula CnH2n+2 in which n is mostly between 5 and 40.
unsaturated aliphatic
Linear- or branched chain molecules containing one or more double or triple bonds (alkenes or alkynes).
Cycloalkanes
Also known as naphthenes these are saturated hydrocarbons CnH2n containing one or more ring structures.
Aromatic hydrocarbons
These contain one or more fused benzene rings CnHn, often with hydrocarbon side-chains.

#### Distillation

The first major step of refining is to fractionate the crude oil into various boiling ranges:

The word gasoline predates its use as a motor fuel; it was first used as a topical medicine to rid people of head lice, and to remove grease spots and stains from clothing.

boiling range fraction name further processing
<30° C butane and propane gas processing
30 - 210° straight-run gasoline blending into motor gasoline
100 - 200° naphtha reforming into gasoline components
150 - 250° kerosene jet fuel blending
160 -400° light gas oil distillate fuel blending into diesel or fuel oil
315 - 540° heavy gas oil catalytic cracking: large molecules are broken up into smaller ones and recycled
>450° asphalts, bottoms may be vacuum-distilled into more fractions

#### Further processing and blending

About 16% of crude oil is diverted to the petrochemical industry where it is used to make ethylene and other feedstocks for plastics and similar products. Because the fraction of straight-run gasoline is inadequate to meet demand, some of the lighter fractions undergo reforming and the heavier ones cracking and are recycled into the gasoline stream. These processes necessitate a great amount of recycling and blending, into which must be built a considerable amount of flexibility in order to meet seasonal needs (more volatile gasolines and heating fuel oil in winter, more total gasoline volumes in the summer.)

### Contributors

12:43, 5 Feb 2016

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This material is based upon work supported by the National Science Foundation under Grant Numbers 1246120, 1525057, and 1413739.