# Units of Concentration for Solutions

With most of our familiar solutions, water is the solvent and the solution is called an aqueous solution. Milk, juices, soft drinks, alcoholic drinks, and sports beverages are all aqueous solutions. Ponds, lakes, and oceans are all aqueous solutions in which the solutes are dissolved solids, gases, and various organic compounds. The main component of blood is water, so blood is an aqueous solution.

Gasoline is a homogeneous mixture of many different compounds in which water is not the solvent—in fact, one usually takes care that gasoline is not contaminated with water. Paints are solutions in which water may or may not be the solvent. In oil-based paints oil is the solvent.

Air is also a solution. In air, the gas present in greatest quantity is nitrogen, so N2 is the solvent. All other gases—mostly oxygen (O2), argon (Ar), carbon dioxide (CO2), and water vaporare the solutes.

The concentration of a solution is meant to express how much solute is present compared to the amount of solvent. There are several different units of concentration used in science; each one is preferred in particular applications.

The units of concentration we will use are the following:

1.      Percent by weight (or mass)

2.     Percent by volume

3.     Molarity

4.     Mole fraction

5.     Molality

## Percent by Weight

A glucose solution administered intravenously to a hospital patient is usually labeled as the percent glucose by weight.

For example, the solution could be 10 percent glucose in water; every 100 g of total solution contains 10 grams of glucose and 90 grams of water. Such solutions are simple to prepare and the concentration as a percent by weight does not change if, for example, the temperature changes. In certain types of chemical calculations, however, concentrations of solutes need to be included and percent by weight is not very convenient for calculations. So, we might label a solution that way, but probably not if the solution is going to be further diluted or used in a chemical reaction.

## Percent by Volume

Percent by volume is the most common unit of concentration used for mixtures of gases. It is also true that the percent by relative numbers of molecules in a mixture of gases has the same value as the percent by volume of those gases. Therefore, when we say that the atmosphere is 78 percent N2 by volume, we mean that in a sample of 100 liters of air we can think of 78 liters of the sample as being N2. However, we can also say that for every 100 molecules of air, 78 of the molecules are N2.

Because concentrations as relative numbers of particles are so common in mixtures of gases, related units are the following:

1.      Parts per million, or ppm

2.     Parts per billion, or ppb

3.     Parts per trillion, or ppt

Thus, we could also describe the concentration of N2 in the atmosphere as 780 thousand parts per million. It is more common, however, to use ppm for gases that are present in very small quantities. For example, the concentration of carbon monoxide (CO) in a polluted atmosphere might be 10–20 ppm, or 10–20 molecules of CO for every million air molecules total.

## Molarity

The molarity of a solution (symbolized M) is defined as the number of moles of solute present per liter of total solution. For example, if 2.00 moles of table salt are dissolved in enough water to make one liter of solution, then the molarity of the solution is 2.00 M, pronounced “2.00 molar.” Molarity is probably the most common unit of concentration used in chemistry, especially when working with aqueous solutions.

There are, however, disadvantages to using molarity. First of all, the volume of a liquid solution changes with temperature—usually liquids expand as temperature increases and contract as temperature decreases. Molarity, therefore, changes as temperature changes. Fortunately, the volume change can usually be neglected except in the most precise work.

Second, notice that molarity is defined in terms of volume of total solution, not just volume of solvent.

In the example above, if you want the final volume to be 1.00 liter, you cannot just add 2.00 moles of table salt (117 grams of salt) to 1.00 liter of water. When solutions are prepared, some expansion or contraction, however slight, will occur, so the final volume is not exactly 1.00 liter. To prepare the solution, therefore, it is best to dissolve the table salt completely in a slightly smaller volume of water—80–90 mL for example—and then dilute the resultant solution to a final volume of 1.00 liter.

Because the use of molarity simplifies many calculations, especially in thermodynamics and kinetics, the advantages of using molarity outweigh the disadvantages.

## Mole Fraction

Suppose a solution has two components, which we will label A and B. The mole fraction (symbolized by the Greek letter chi, χ) of component A is defined as the number of moles of A present divided by the total number of moles present:

XA = number of moles of component A ./ total number of moles

Notice that mole fraction is dimensionless—moles in the denominator cancel moles in the numerator. We may speak of the mole fraction of either the solute or the solvent, or, in the case of several solutes, the mole fraction of each solute.

The use of mole fraction has several advantages. One advantage is that the number of moles of a component of a solution is determined by the mass of that component. Mass does not change with temperature, so mole fractions avoid any problems of being temperature dependent. Another advantage is that the masses of the various components do not change when the components are mixed together, so preparing a solution of known mole fraction is relatively simple—just weigh each component and then mix them all together.

## Molality

The molality of a solution (symbolized m, and not to be confused with molarity, symbolized with a capital M) is defined as the number of moles of solute per kilogram of solvent.

Molality has the same advantage as mole fraction in that it is temperature independent.

A solution with a specified molality is also easy to prepare because all we have to do is weigh out a certain amount of solute and a certain amount of solvent and then mix the two together.

## Conclusion

A lot of new vocabulary was introduced in this article. Most of it may have been new to you and may seem like a lot to remember. With time, however, you should become more familiar with these terms.

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