Molarity (M), one of the most common units of concentration used by the chemist, is defined as the number of moles of solute per liter of solution. It has as its unit the capital letter "M" and is read as "molar".
A solution labeled as 1.0 M NaOH, has the equivalent of 1.0 moles of NaoH dissolved in 1.0 liters of solution. Notice that the volume is liter of solution and not liter of water.
A 1.0 M NaOH solution would be made by measuring out the mass of 1.0 moles of NaOH which is 40.0 grams of NaOH. The solid NaOH would be placed in a liter volumetric flask, and then distilled water would be added in small amounts with vigorous swirling of the flask to get the NaOH to dissolve. Since the dissolving process for NaOH is quite exothermic, the flask should be lowered into cool water as the water is gradually added to the line on the flask.
One doesn't always have to make up a liter of solution, but can make up the equilivance of that amount. Suppose you only want 500 mL of the 1.0 M NaOH solution. Then you put 20.0 g (0.5 mol) of NaOH in a 500 mL volumetric flask, and add distilled water to the line on the flask. You now have half a mole of NaOH in half a liter of solution which is equivalent to one mole of NaOH in a liter of solution.
Molality (m), another unit of concentration used by chemists, is defined as the number of moles of solute per kilogram of solvent. It has as its unit the lower case letter "m" and is read as "molal".
It is primarily used when one is dealing with colligative properties of solutions such as freezing point lowering of sovents by solutes. A 1.0 molal solution of NaCl sould be made by measuring out 1.0 Kg of distilled water and then dissolving 58.5 g (1.0 mole) of NaCl in the water.
Parts per million
Parts per million (ppm), is a unit of concentration often used when dealing with very small amounts of metal ions and other solutes in water, air or soil.
A solution with a concentration of 1 ppm of Pb2+ is equal to 1 mg lead(II) ion per liter of water, or 1 μg of lead(II) ion per mL of water. A Cu2+ solution reported to be 20 ppm would be equilavent to 20 mg of Cu2+ per liter of water or 20 μg/1.0 mL