EXPRESSIONS OF CONCENTRATION - Liquids, Solids, and Phase Changes - REVIEW OF MAJOR TOPICS - SAT Subject Test Chemistry

SAT Subject Test Chemistry




Liquids, Solids, and Phase Changes


There are general terms and very specific terms used to express the concentration of a solution. The general terms and their definitions are:


= small amount of solute is dispersed in the solvent.


= large amount of solute is dissolved in the solvent.


= the solution is holding all the solute possible at that temperature. This is not a static condition; that is, some solute particles are exchanging places with some of the undissolved particles, but the total solute in solution remains the same. This is an example of equilibrium.


= more solute can go into solution at that temperature. The solvent has further capacity to hold more solute.


= sometimes a saturated solution at a higher temperature can be carefully cooled so that the solute does not get a chance to come out of solution. At a lower temperature, then, the solution will be holding more solute in solution than it should for saturation and is said to be supersaturated. As soon as the solute particles are jarred or a “seed” particle is added to the solution to act as a nucleus, they rapidly come out of solution so that the solution reverts to the saturated state.

It is interesting to note that the words saturated and concentrated are NOT synonymous. In fact, it is possible to have a saturated dilute solution when the solute is only slightly soluble and a small amount of it makes the solution saturated, but the concentration of the solution is still dilute.

Specific Terms of Concentration

The more specific terms used to describe concentration are mathematically calculated.

1. PERCENTAGE CONCENTRATION is based on the percent of solute in the solution by mass. The general formula is:


How many grams of NaCl are needed to prepare 200. grams of a 10% salt solution?

10% of 200. grams = 20.0 grams of salt

You could also solve the problem using the above formula and solving for the unknown quantity.


Know how to calculate molarity (M).

The next two expressions depend on the fact that, if the formula mass of a substance is expressed in grams, it is called a gram-formula mass (gfm), molar mass, or 1 mole. Gram-molecular mass can be used in place of gram-formula mass when the substance is really of molecular composition, and not ionic like NaCl or NaOH. The definitions and examples are:

2. MOLARITY (abbreviated M) is defined as the number of moles of a substance dissolved in 1 liter of solution.

A 1 molar H2SO4 solution has 98. grams of H2SO4 (its molar mass) in 1 liter of the solution.

This can be expressed as a formula:

If the molarity (M) and the volume of a solution are known, the mass of the solute can be determined. First, use the above equation and solve for the number of moles of solute. Then, multiply this number by the molar mass.


How many grams of NaOH are dissolved in 200. milliliters of solution if its concentration is 1.50 M?

Solving for number of moles gives:

No. of moles of solute = M × volume in liters of solution

No. of moles of NaOH = 1.50 M × volume in liters of solution

 No. of moles of NaOH

The molar mass of NaOH = 23 + 16 + 1.0 = 40 g of NaOH

3. MOLALITY (abbreviated m) is defined as the number of moles of the solute dissolved in 1,000 grams of solvent.

EXAMPLE: A 1 molal solution of H2SO4 has 98 grams of H2SO4 dissolved in 1,000. grams of water. This, you will notice, gives a total volume greater than 1 liter, whereas the molar solution had 98 grams in 1 liter of solution.

EXAMPLE: Suppose that 0.25 mole of sugar is dissolved in 500. grams of water. What is the molality of this solution?

If 0.25 mole is in 500. grams of H2O, then 0.50 mole is in 1,000 grams of H2O. Thus:

m = 0.50


Know how to determine the mole fraction.

4. MOLE FRACTION is another way of indicating the concentration of a component in a solution. It is simply the number of moles of that component divided by the total moles of all the components. The mole fraction of component i is written as Xi . For a solution consisting of nA moles of component A, nB moles of component B, nC moles of component C, and so on, then the mole fraction of component A is given by:

As an example, if a mixture is obtained by dissolving 10 moles of NaCl in 90 moles of water, the mole fraction of NaCl in that mixture is 10 (moles of NaCl) divided by (10 + 90) or 100 moles, giving an answer of 0.1, the mole fraction of NaCl.