Concentration Expressions/Definitions

Many reactions, and experiments are performed in solution. When doing quantitative experiments we must know the exact amount of reagents involved in the reaction. We can express the relative amount of a solute in a solution by expressing the concentration of the reagent as a ratio of an amount of solute to the amount of solvent. In your earlier experience in chemistry the concentration expression you are familiar with is molarity.

Molarity is defined as

molarity is a ratio of the mol of solute to the volume of solution.

There are three additional concentration definitions that we will discuss: weight %, mol fraction and molality. These new terms are defined as;

To see how we use these definitions we prepared a solution in class by mixing 10.0 g CuSO₄ with 90.0 g of H₂O.

I. Weight Percent CuSO₄

Substituting the amounts into the weight % expression and solving,

So the solution is 10.0% CuSO₄. The weight % water is 100 - 10.0 = 90.0%

II. Mol fraction CuSO₄

First we need to determine the number of mol of solute and solvent;

Substituting the amounts into the mol fraction and solving,

The mol fraction of H₂O is obtained by subtracting the mol fraction of CuSO₄ from 1.00.

III. Molality of CuSO₄

We know the mol of CuSO₄ from the mol fraction calculation and the mass of H₂O.

0.0627 mol CuSO₄

90.0 g of H₂O

Substituting,

IV. Molarity of CuSO₄

Determining the molarity of the solution requires additional information. Initially we were given the mass of CuSO₄ and the mass of H₂O. Adding the masses together to gives 100 g of solution however, we can not say that the volume is 100 mLs of solution. To obtain the volume of the solution we must know the density of the solution. Since the solution is 10% CuSO₄ we cannot assume the density of the solution is the same as the density of water. When we mixed the 10.0 g of CuSO₄ with 90.0 g of water the final volume of the solution was about 90.2 mLs.

So the mol of CuSO₄ and the volume of solution are;

0.0627 mol CuSO₄

90.2 mL of solution

Substituting,

The four concentration expressions we will use are weight%, mol fraction, molality and molarity. You must know these definitions. I will not include them on the Useful Information page of the next exam. You must feel comfortable using each of these concentrations and converting between them.

Let's consider a few problems to practice using these expression and converting between them.

Problem I:

Calculate the molality and mol fraction of HCl for a solution which has a mass percent of 37.1 %.

Show Me! (Help me by showing me some steps to solve this problem.)

Answer (This is the answer)

Problem II:

If the density of the HCl solution is 1.18 g/mL, calculate the molarity of the solution.

Problem III:

The density of a solution of Pb(NO₃)₂ prepared by adding enough water to 24.0 g of solid Pb(NO₃)₂ and diluting to a final volume of 100 mLs is 1.20 g mL^-1. Calculate the weight%, mol fraction, molality and molarity of Pb(NO₃)₂ in the solution.

Problem IV:

A solution of HF is 40.9 m. The density of the solution is 1.14 g cm^-3. Calculate the molarity of the solution.