This tutorial sheet covers units of concentration and examples of how to convert concentration units. First, we need to define some terms:

Solution - a homogeneous mixture of one or more substances (the solutes) dissolved in another substance (the solvent)
Solute - the substance that exists in a lesser quantity than the solvent(s) in a solution
Solvent - the substance that exists in a greater quantity than the solute(s) in a solution
Concentration - the measure of how much of a given substance there is mixed with another substance

There are several ways to express concentrations. It's essential to understand the units used to express concentrations since they define the concentration. Here are some common units:

Weight Percent (wt %): The mass of one component divided by the total mass of the solution times 100%.

Parts per million (ppm): a measure of concentration that is used where low levels of concentration are significant:

parts per million (ppm) may also be expressed as:

Parts per billion (ppb): a measure of concentration that is used where low levels of concentration are significant:

parts per billion (ppb) may also be expressed as:

Molarity (M): The number of moles of solute per liter of solution.

Molality (m): The number of moles of solute per kilogram of solvent.

The main advantage of using molality is that it is temperature independent because masses do not change when substances are heated or cooled. The disadvantages of using molality are that amounts of solution are measured by mass rather than by volume and that the density of the solution must be known to convert molality into molarity.

Mole fraction (X) & mole percent (%X): The number of moles of the component divided by the total number of moles in the mixture. To find the mole percent (%X), multiply the mole fraction by 100:

There will be times when you will need to convert one unit to another. For this type of problem, you may need to make an assumption. You'll know the density of the solution because it will be given to you in the problem. But, you may have to assume the concentration units you are converting to. A good rule to follow is if you are converting weight percent (wt %) to molarity, you can assume 100g of solution. If you are converting molarity to weight percent (wt %), you can assume 1L of solution.

Here's a sample concentration problem. Find the molarity, molality & mole fraction for a 37% HCl solution with a solution density of 1.19g.mL.

Assume 100g of solution. In 100g of solution, 37.0g comes from HCl (the solute) and 63.0g comes from water (the solvent).

To calculate molarity, we need to know the moles of HCl in one liter of solution. The first step is to convert the 37.0g of HCl to moles:

Now, convert the known mass of the solution, 100g, to liters:

Now that we know the moles of HCl and the volume of the solution in liters, we can calculate the molarity (M):

Let's determine molality of the HCl solution. We know the moles of solute to be 1.01 mol HCl. Now we need to determine the kilograms of solvent:

Remember that molality (m) is the number of moles of solute per kilogram of solvent, we can now easily determine molality:

Lastly, let's calculate the mole fraction of HCl. We know that the moles of HCl in the solution is 1.01 moles. Now we must determine the moles of H₂O in the solution:

Now that we know the moles of HCl (the solute) and the moles of H₂O (the solvent), we can calculate the mole fraction of HCl: