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Ways of expressing concentrations of solutions. Solute, solvent. Molarity, Formality, Normality, Molality, Mole fraction. Dilution problems.

Def. Solution. A homogeneous mixture formed by dissolving one or more substances, whether solid, liquid, or gaseous, in another substance.

Solute and solvent. In a solution the dissolved substance is called the solute and the substance in which the solute is dissolved is called the solvent. In a solution consisting of the mixture of two liquids, the liquid present in the larger amount is generally regarded as the solvent.

Ways of expressing concentrations of solutions in physical units:

1. By weight of solute per unit volume of solution.

Example. 10 g of NaCl per liter of solution.

2. By percentage composition i.e. the number of grams of solute per 100 grams of solution.

Example. A 10% NaCl solution contains 10 grams of NaCl per 100 grams of solution. Ten grams of NaCl are mixed with 90 grams or milliliters of water to form 100 grams of solution.

3. By weight of solute per weight of solvent.

Example. 6 g of NaCl per 100 g of water.

Ways of expressing concentrations of solutions in chemical units:

1. Molarity. The molarity of a solution is the number of moles of the solute contained in one liter of the solution.


2. Formality. The formality of a solution is the number of gram-formula weights of the solute contained in one liter of the solution.


3. Normality. The normality of a solution is the number of gram-equivalent weights of the solute contained in one liter of the solution.



where a milligram-equivalent is 1/1000 of a gram-equivalent weight.

4. Molality. The molality of a solution is the number of moles of the solute per kilogram of solvent.

Syn. Weight molarity


5. Mole fraction. The mole fraction of one component in a solution is defined as the number of moles of that component divided by the total number of moles of all components in the solution. The sum of the mole fractions of all components of a solution is 1. In a two-component solution consisting of solute plus solvent, the mole fraction of the solute is


and the mole fraction of solvent is


In general,


Dilution problems. Volume-referenced measures of concentration are those in which concentration is expressed as x units of solute per unit volume. For example, moles per liter (molarity), gram-formula weights per liter (formality), gram-equivalent weights per liter (normality), and grams per liter are volume-referenced measures.

If concentration is expressed as x units of solute per unit volume, then the total amount of solute in solution is given by

1)        Amount of solute = volume × concentration

Example. A NaCl solution has a concentration of 7 g per liter. Then the amount of solute in 5 liters is given by

            Amount of solute = 5×7 = 35 g

When a solution is diluted, the volume is increased and the concentration is decreased, but the total amount of solute in the solution remains the same. Thus if v1 and c1 are the volume and concentration of the solution before dilution and v2 and c2 are the volume and concentration of the solution after dilution, then

2)        v1 × c1 = v2 × c2

In a dilution problem, if any three of these variables are known, the other can be calculated.

Problem. A solution of AgNO3 has a concentration of 40 mg per ml. How much must this solution be diluted to yield a concentration of 10 g per ml?

Solution. Using 2) above

            v1 × c1 = v2 × c2

            1 ml × 40 mg/ml = v2 × 10 mg/ml

            v2 = 40/10 = 4 ml

Thus each ml of the given solution must be diluted to a volume of 4 ml.


 Schaum, Beckman, Rosenberg. College Chemistry. (Schaum)

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