Molarity and Concentration

MOLES AND MOLARITY

• 1 mole of a substance contains 6.02 x 10²³ (Avogadro’s number) atoms/molecules etc.
• The number of moles of a substance is calculated by dividing the mass or weight of the substance by its molecular weight. (Remember this equation) Moles = weight in grams
               Molecular weight (mw)
• A 1 molar solution contains 1 mole of substance in 1 litre.

If you remember the above definitions, you will be able to make up any molar solutions as long as you know the molecular weight of the substance, which is usually written on the bottle the chemical is supplied in.

Examples

1.    Make up 1 litre of 1 molar (1M) NaCl. Mw NaCl = 58.5

Moles (1) per litre = weight (grams to be weighed)
                                              58.5

grams to be weighed out = 58.5 x 1 = 58.5 grams of NaCl dissolved in 1litre of water to make the solution.

2.    Make up 1 litre of 1mM NaCl

Moles (1mM or 10^-3M) per litre = grams to be weighed
                                                         58.5

amount to be weighed = 58.5 x 10^-3g = 58.5 milligrams in 1l of water

3.    To make up 500 ml of 1M NaCl

moles (1) per litre (1) = weight in grams
                                        58.5

to make up a quantity different from 1 litre, you must multiply the number of moles by the proportion of 1 litre that you require. In the above example for instance

moles(1) x 500 = weight        (remember that there are 1000 ml in a litre)
                1000   58.5

1 x 58.5 = 29.25 g weight of NaCl to add to 500 mls of water
2

4.    How many atoms of sodium are there in 1l of a 1M solution of NaCl?

Answer is equal to Avogadro’s number = 6.02 x 10²³

How many in 1l of a 1mM solution?

6.02 x 10²³ x 10^-3 = 6.02 x 10²⁰

Reiterate:

Moles =        weight
             molecular weight

a mole contains 6.02 x 10²³ particles

As long as you know the amount of a particular substance that you have and its molecular weight, you can work out its molarity and calculate how many molecules of that substance you have.

ALTERNATE WAYS OF CALCULATING CONCENTRATIONS

Percentage

Some solutions or mixtures of solvents are commonly expressed as a percent solution. This may be either percent weight per weight (w/w) or weight per volume (w/v) or volume per volume (v/v).

e.g. 70% (v/v) ethanol consists of 70 parts ethanol to 30 parts water

physiological saline consists of 0.9% (w/v) NaCl which is made by adding 0.9 grams NaCl to 100 ml of water, hence w/v percentage is determined by measuring grams per 100 ml of water.

Parts per million

This way of expressing concentration refers to the number of parts of a substance to 1 million parts of the solvent (usually water).

e.g. 5 parts per million chlorine equals 5 grams chlorine in 1 million grams water. 1 gram of water equals 1 ml hence 1 million grams (10⁶) would equal 1000 litres of water. This can also be expressed as 5 μg chlorine/ml. How?

Start with 5g/10³ litres.  Divide numerator and denominator by 1000 (10³):

= 5 mg/l                       Divide numerator and denominator by 1000 (10³) again:

= 5 μg/ml