# Dilutions

Dilutions
Dr. MJ Patterson

Preparing a solution of known concentration by dilution is one of the most common laboratory procedures performed in preparing the chemistry labs at BC.  It is relatively simple and fast to prepare by dilution as compared to weighing a solid and waiting (sometimes hours) for the solid to dissolve.  However, to accurately prepare a diluted solution, you need to be able to calculate the needed volumes.  This page addresses the dilution process, and an equation to describe it.

The Dilution Process

Think about preparing orange juice from a frozen concentrate.  First, you let the concentrate thaw.  Then, you put the concentrate in a pitcher or some sort of container.  Last, you add water and mix.

We can talk about this same process using the language of chemistry.  The concentrate is a solution with a high concentration or molarity.  The solvent is water, or we can say that it is an aqueous solution.  The solute is a complex mixture of sugars, flavorings, vitamins and other chemicals squeezed from oranges.  When you dilute the concentrate, you add more solvent or water.

The Dilution Equation

In this process, the amount of solute stays constant.  Only the solvent is being added.

Since the amount of solute stays the same before and after dilution, we can write an equation to say the same thing mathematically:

(amount of solute before dilution) = (amount of solute after dilution)

Now, we just need to figure out how to specify the amount of solute.  Since we frequently characterize solutions in terms of molarity and volume, moles seem a natural way to work, since multiplying molarity times volume in liters will give the moles of solute.  In other words,

MV = moles of solute

If we use a subscript 1 to specify the concentrated solution, or the solution before dilution, we can write:

M1V1 = moles of solute before dilution

Using a subscript 2 for after dilution:

M2V2 = moles of solute before dilution

Substituting,

(amount of solute before dilution) = (amount of solute after dilution)

M1V1 = M2V2

Units

We derived the dilution equation assuming molarity for concentration and liters for volume.  However, the dilution equation is a rare entity in chemistry - it almost does not matter which units you choose to use in the equation, as long as you use the same units on both sides of the equation.  In other words, your volumes could be in liters, mL, quarts, fluid ounces, gallons or any other convenient units, just as long as you use the same ones on both sides.  Your concentration could be expressed in molarity, molality, percent volume or any other convenient unit, just as long as it is the same unit on both sides of the equation.  (For some of the concentration units, this statement is not strictly true.  However, unless you are performing analytical experiments which require a high degree of precision, it is close enough to be within experimental error.)