The Chemistry of Solutions

Concentration

Solutions and Concentration

In lab, we will often deal with solutions. This lesson introduces two related concepts - the concentration of a solution and the process of diluting a solution.

A solution

A solution consists of a liquid (the solvent) with a substance (the solute) dissolved in it. You are probably familiar with many solutions from your everyday life. Milk is a solution consisting of water (the solvent) with lactose and salts dissolved in it. Ocean water is another type of solution. Both of the examples given above, along with many of the solutions we work with in lab, are known as aqueous solutions because the solvent is water.

Have you ever mixed up orange juice from concentrate and added too many cans of water? I'm sure you could taste the difference between the watery orange juice and the properly prepared orange juice. The amount of solute (orange juice concentrate in the case of this example) in a solution is known as the solution's concentration. As you will find, solutions with different concentrations act differently in the lab, just as different concentrations of orange juice taste different in your kitchen. The rest of this page will be devoted to the terminology and math we use to determine the concentration of solutions.

Molarity

There are many different ways to measure concentration, including molarity, ppm, mg/L, and percent concentration. Molarity is typically used in very concentrated solutions and will be used in many of the solutions we prepare in lab. We calculate molarity using the following formula:

As you can see, the unit for molarity - "M" - is equivalent to mol/L.

How many grams of table sugar (C_{12}H_{22}O_{11}) would you need to dissolve in water to produce 0.75 liters of a 0.125 M aqueous solution of table sugar? The first step in finding the answer to this question is to calculate the number of moles of table sugar which would be needed:

Next, you have to transform the number of moles of sugar into grams of sugar. We use the technique introduced in the last lesson:

- The molecular formula of table sugar is given as C
_{12}H_{22}O_{11}.- We calculate table sugar's molar mass using the following calculations:

Element |
Number of atoms per water molecule |
Atomic weight |
Contribution to molar mass of the molecule |

Carbon |
12 |
12.01 g/mol |
144.12 g/mol |

Hydrogen |
22 |
1.01 g/mol |
22.22 g/mol |

Oxygen |
11 |
16.00 g/mol |
176.00 g/mol |

Total |
342.34 g/mol |

- Finally, we convert from 0.094 moles of sugar to grams of sugar:

342.34 g/mol × 0.094 mol = 32.17996 g = 32 g

So the answer is that we must dissolve 32 grams of table sugar in enough water to make up 0.75 L of solution. This will result in a 0.125 M solution.

ppm

While molarity is used for solutions with relatively large concentrations of solute, we use ppm and mg/L to denote much lower concentrations. This will often be the case when you are measuring solutes in water at a treatment plant, such as the concentration of iron in the water. We will discuss ppm in this section, then move on to mg/L in the next section.

Parts per million, or ppm, is just what the name suggests - the number of parts of solute in one million parts of solution. Concentration in ppm is calculated using the following formula:

Let's consider a simple example:

You add 11 mg of sulfuric acid to 2,000 grams of water. What is the resulting concentration of sulfuric acid, in ppm?

In order to solve this problem, you first must make the units of the solute the same as the units of the solvent. So, you will convert from milligrams to grams:

Then you simply plug the numbers into the formula:

So, the concentration of sulfuric acid in the resultant solution is 5.5 ppm.

mg/L

Milligrams per liter, or mg/L, can be used to denote concentration in similar circumstances to ppm. The following formula is used to calculate concentration in mg/L:

As you can see, the primary difference between the two calculations is that ppm is a mass per mass calculation while mg/L is a mass per volume calculation. Due to the special characteristics of water, the concentration of an aqueous solution is the same when calculated in mg/L as it is when calculated in ppm. So, the 5.5 ppm sulfuric acid aqueous solution discussed in the last section has a concentration of 5.5 mg/L.

Let's consider the following example problem:

You dissolve 1 mg of salt in water to produce 2 liters of solution. What is the concentration of salt in the solution?

You could choose to calculate the concentration as either ppm or mg/L, but mg/L is the better choice since you are given the amount of solution in liters. We would calculate the answer as follows:

You can state the concentration as either 0.5 mg/L or 0.5 ppm.

Percent

The final unit we use to measure concentration is percent. Percent concentration is calculated using the following formula:

Notice that I have given no units for the amounts of solute and solution. That is because you can either calculate weight per weight (w/w) percent concentration or volume per volume (v/v) percent concentration. Since these two methods can give you different answers, you should always note which method you used.

How does percent concentration relate to concentration in ppm? In order to figure out the answer, let's consider the same solution we considered in the section on ppm:

An aqueous solution contains 0.011 g of sulfuric acid and 2,000 grams of water. The concentration was found to be 5.5 ppm.

We would calculate the percent concentration as follows:

The w/w percent concentration is 0.00055%. You will notice that this is the same as the ppm concentration divided by 10,000. W/w concentrations always show this relationship to ppm concentrations since the calculations are identical except for multiplying by one hundred in percent concentration and by one million in ppm concentration.

A concentration of 0.00055% is less understandable than a concentration of 5.5 ppm. As a result, percent concentration is usually used in situations more like that in which molarity is used, when the solute makes up a larger percentage of the solution.

Converting Between Types of Concentration

Next, you will be called on to convert between different types of concentration. For example, if you had a 35.7 ppm solution, what would this be in percent concentration? If you had a 0.2 M solution, could you convert this to mg/L?

We've already mentioned a few conversion factors previously. In aqueous solutions, the following conversion factors are in effect:

1 mg/L = 1 ppm

1,000,000 ppm = 100%

1,000,000 mg/L = 100%

Converting to molarity is a little more complicated. You must use the following formula to convert from mg/L (or ppm) to molarity in an aqueous solution:

We'll give you some practice with making conversions on the next page.