## SAT Subject Test Chemistry

__PART 2__

__REVIEW OF MAJOR TOPICS__

__CHAPTER 7__

__Liquids, Solids, and Phase Changes__

__DILUTION__

In dilution problems, the expression of molarity gives the quantity of solute per volume of solution. The amount of solute dissolved in a given volume of solution is equal to the product of the concentration times the volume. Hence, 0.5 liter of 2 M solution contains

*M* ×*V* = amount of solute (in moles)

Notice that volume units must be identical.

If you dilute a solution with water, the amount or number of moles of solute present remains the same, but the concentration changes. You can use the expression:

*Before* *After**M*_{1}*V*_{1} = *M*_{2}*V*_{2}

This expression is useful in solving problems involving dilution.

**TIP **

Use this equation for dilution problems:*M*_{1}*V*_{1} = *M*_{2}*V*_{2}

1 = solution before

2 = solution after

**EXAMPLE:** If you wish to make 1 liter of solution that is 6 M into 3 M solution, how much water must be added?

*M*_{1}*V*_{1} = *M*_{2}*V*_{2}

6 M × 1 L = 3 M × *x* L

Solving this expression:*x* L = 2 L. This is the total volume of the solution after dilution and means that 1 liter of water had to be added to the original volume of 1 liter to get a total of 2 liters for the dilute solution volume.

An important use of the molarity concept is in the solution of **titration** problems, which are covered in Chapter 11, along with pH expressions of concentration for acids.