# Unit 8: When Chemicals Meet Water—The Properties of Solutions

## Section 6: Solutions and the Gases above Them—Raoult's Law

Before learning about Raoult's Law and what that tells us about solutions, we need to introduce and review a few terms. Raoult's Law is all about the relationship between a solution and how it affects the gases above the solution. So, we need to refer back to partial pressure of gases and review what a vapor pressure is.

In Unit 1, partial pressures were introduced as part of the history of John Dalton, the founder of modern atomic theory. He discovered that if we have a mixture of gases, then each of the gases exerts a part of the total pressure, relative to its amount in the mixture. This rule is known as Dalton's Law of Partial Pressures, named for its discoverer. The partial pressure of oxygen (O2) in air is 0.20 atm and that of nitrogen (N2) is 0.78 atm. There are also trace amounts of argon (Ar), carbon dioxide (CO2), and other gases, but their partial pressures are very small. Together, they will add up to the 1.00 atm of normal atmospheric pressure at sea level. This is because 20% of the molecules in air are oxygen molecules, and 78% of the molecules in air are nitrogen molecules.

##### Vapor Pressure

Imagine we fill a jar halfway with water, and seal it. (Figure 8-9) Some of the water will start evaporating until the air above the container has some water vapor in it. On a normal temperature day, the partial pressure from just the water vapor is about 3% of the pressure of the air in the jar. This partial pressure of the vapor of a liquid is called the "vapor pressure." Any liquid placed in a jar will produce a vapor pressure in this way, but the vapor pressures will vary for different substances.

FIgure 8-9. The Vapor Pressure of a Substance

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### FIgure 8-9. The Vapor Pressure of a Substance

An equilibrium exists between the substance in the liquid phase (in this case, water) and the same substance in the gas phase (here, water vapor).

If attractive forces between particles of a liquid are relatively strong, the liquid's evaporation rate will be low and it will have a low vapor pressure. If the forces are weak, it will evaporate more readily and have a high vapor pressure. Liquids with a high propensity to evaporate are called "volatile." If we were to open a container of a volatile liquid, like gasoline, within a minute, we could smell its vapors throughout the room. However, a liquid like baby oil, which isn't very volatile, has such a low vapor pressure that we can only smell it by putting our noses right into the container. Vapor pressure for a given liquid increases as temperature increases, because adding heat increases the kinetic energy of molecules in the liquid, making it easier for the liquid to overcome attractive forces and change to a gas. The higher the temperature, the more liquid evaporates and the higher the vapor pressure. This will be important later when we discuss the process of boiling.

So, now that we know what partial pressure and vapor pressure are, what is Raoult's Law? Raoult's Law usually applies to solutions when two different volatile liquids are mixed together into a solution. It can also be used for mixtures of multiple volatile liquids or in cases where one of the components is a solid; solids and Raoult's Law will be discussed in the next section. It turns out that each volatile liquid will have a vapor pressure above the solution, and its vapor pressure is proportional to what fraction of the solution that liquid is.

PA = XAP°A

Vapor Pressure of A above the solution = Mole Fraction of A in the solution x Standard Vapor Pressure for A

While that might sound complicated, in reality it means this: If we have two liquids that are both volatile in a solution, the vapors above them will always be richer in the more volatile component. So, if we were able to take the vapors above the solution and cool them and recondense those vapors into a new solution, that solution would have a higher percentage of the more volatile component. If we could repeat that over and over again, it would allow us, in theory, to separate a more volatile compound from the less volatile one. Doing this in multiple steps isn't practical, but it can be done easily in a laboratory or in an industry using special equipment. This process of exploiting Raoult's Law to separate two or more volatile compounds is called "distillation."

Figure 8-10. A Laboratory Distillation Apparatus and a Petrochemical Refinery

© Left: Science Media Group. Right: Wikimedia Commons, Creative Commons License 3.0. Author: Secl, 1 January 2006.

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### Figure 8-10. A Laboratory Distillation Apparatus and a Petrochemical Refinery

Raoult's Law is exploited in a lab to separate liquids from each other through the process of distillation. This is expanded on the industrial scale to separate out the components of crude oil based on their volatility using giant distillation plants. The end products of crude oil refinery include gasoline, several types of fuel (diesel and jet fuels), short chain hydrocarbons, which are used for industrial solvents, and oils and waxes, which are needed for the cosmetics industry.

Distillation is used widely in the oil industry. When crude oil is pumped out of the ground, it consists of a mixture of many different hydrocarbon molecules. At an oil refinery, it is distilled repeatedly to separate out different components according to their different vapor pressures. From crude oil, one can separate out and produce gasoline, kerosene, liquid petroleum gas (LPG), diesel fuel, waxes, and tar. Distillation is also used to prepare medicines from certain plants, produce perfumes, and purify beverages. (Figure 8-10)

## Glossary

### Partial pressure

The part of the total pressure exerted by one of the gases in a mixture of gases. Each gas exerts the pressure it would exert if it were by itself in the same volume at the same temperature as the mixture; the total pressure is the sum of these partial pressures.

### Raoult's Law

The partial pressure of a gas over a liquid mixture is equal to the vapor pressure of the pure substance multiplied by the mole fraction of that substance in the liquid mixture.

### Vapor pressure

The gas pressure, defined at a given temperature, due to the evaporation from the surface of a liquid phase.