Concentration Units

A solution is a mixture of two or more substances that is of the same composition throughout. The host substance is a solvent, and the dissolved substance is a solute. Although the most familiar solvents are liquids, like water or ethyl alcohol, the general concept of a solution includes solvents that are gases or even solids.

In a solution, the ratio of solvent to solute is not fixed, and it can vary over a wide range, unlike compounds that are composed of definite, fixed ratios of the elements that make them up.

Seawater is an example of a liquid solution with water as solvent because the dissolved sodium chloride, calcium carbonate, magnesium bromide, and other solutes are of varying concentrations. Carbonated soda water is another liquid solution, but in this case, the solute is a gas—carbon dioxide.

Air is considered to be a gaseous solution with the abundant nitrogen as the solvent and scarcer oxygen as the solute.

An example of a solid solution is electrum, the alloy of gold and silver. The ratio of the two metals is not fixed but can range from nearly pure gold to nearly pure silver. The dominant metal is deemed to be the solvent in which the minor metal is dissolved.

The abundance of a solute is its concentration, and this characteristic can be reported with an intimidating variety of terms that you must master because the accurate description of solutions is central to chemical theory and laboratory practice.

One way to measure the concentration is to measure the relative masses of the constituents, usually expressed as mass percents. Take, for example, an electrum ingot that was formed by melting 62 grams of gold and 800 grams of silver and then letting the material cool and solidify. The following is the composition of the ingot in mass percent: 

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You know, however, that gold and silver have different atomic masses (see Figure 1) and that the preceding percents do not represent relative numbers of atoms. You can calculate the number of moles of gold and silver in the electrum by dividing the masses of each metal by the corresponding atomic mass. Knowing the number of moles of each metal allows you to calculate the mole fraction of each element, that is, the fraction of atoms that are gold and the fraction that are silver.

Figure 1. Silver and gold.

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This is done by dividing the number of moles of one element by the sum of the number of moles of both gold and silver in the mixture using the following formula: 

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The mole fraction of silver is found to be 0.959. This means that 959 out of every 1,000 atoms in the mixture are silver atoms. The mole fraction of gold is 0.041, which means that 41 of every 1,000 atoms in the mixture are gold. The sum of the mole fractions of silver and gold will equal 1.00.

Although units of weight percent and mole fraction can be applied to all types of solutions, the most common concentration terms are molarity or molality. If water is the solvent, the solution is called an aqueous solution.

The molarity is the number of moles (or gram formula masses) of solute in 1 liter of solution. This unit is the most convenient one for laboratory work. A solution of calcium chloride that is 0.5 molar (abbreviated with an uppercase “M” as 0.5M) contains one‐half mole of CaCl 2 (55.49 grams) in enough water to make the total volume 1 liter.

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The other common unit for liquid solutions is molality, the number of moles of solute in 1 kilogram of solvent. Molality contrasts with molarity because it reports the amount of solute relative to the mass of the solvent, not the volume of the solution. A 2 molal solution of hydrogen fluoride, abbreviated 2 m (with a lowercase “m” for distinction from molarity), contains 2 moles of HF (40.02 grams) dissolved in 1,000 grams of H 2O.

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Molality is the preferred unit for certain types of calculations, although it is used less in laboratory work.

  • 80 grams of a simple sugar is added to 750 g of water. The sugar is glucose, with the composition C 6H 12O 6. What is the molality of glucose in the solution?
  • A solution is prepared by mixing 100 g of methyl alcohol (CH 3OH) and 100 g of water. What is the mole fraction of alcohol in the solution?