When sodium chloride dissolves in water, the substance that dissolves, sodium chloride, is the solute, the liquid it dissolves in, water, is the solvent, and the mixture is a solution. A solution in water is called an aqueous solution.
Dissolving does not change the total mass. If 10.0 g of sodium chloride is dissolved in 90.0 g of water, the solution has a mass of 100.0 g, as a balance shows when the empty beaker is first set to zero.
Volumes do not simply add up, because the dissolved ions pull water molecules closely around them. This matters when a concentration is given per litre of solution.
The percentage by mass of a solution is the mass of solute divided by the mass of the whole solution, multiplied by 100. It says how many grams of solute there are in 100 g of solution.
For 10.0 g of sodium chloride in 90.0 g of water, the percentage by mass is 10.0 g ÷ 100.0 g × 100 = 10.0 %. Dividing by the mass of water alone, 90.0 g, would give the wrong value of 11.1 %.
Seawater contains about 3.5 % dissolved salts by mass, so 1 kg of seawater holds about 35 g of salts.
Molar concentration is the amount of solute in moles divided by the volume of the solution in litres, and its unit is mol/L. A solution containing 0.10 mol of solute in every 1.0 L of solution is 0.10 mol/L.
The volume is that of the solution, not of the solvent. When 1.00 mol of sodium chloride, 58.5 g, is dissolved in 1.00 kg of water, the solution has a volume of about 1.02 L, so its concentration is about 0.98 mol/L.
To make exactly 1.00 mol/L, the sodium chloride is dissolved in less water, and water is then added until the whole solution reaches 1.00 L.
A solution of exact concentration is made in a volumetric flask, which holds a stated volume when filled to the mark on its narrow neck. For 100 mL of 0.100 mol/L sodium chloride solution, 0.0100 mol is needed, which is 0.585 g.
The weighed solid is first dissolved in a little water in a beaker. The solution is poured into the flask, and the beaker is rinsed with a little water, with the rinsings added to the flask so that no solute is lost.
Water is then added until the bottom of the curved surface of the liquid sits on the mark. The flask is stoppered and turned upside down several times to mix the solution.
Multiplying a molar concentration by a volume in litres gives the amount of solute. The volume must first be changed from millilitres to litres: 25.0 mL is 0.0250 L.
So 25.0 mL of 0.100 mol/L hydrochloric acid contains 0.100 mol/L × 0.0250 L = 2.50 × \mathrm{10^{-3}} mol of hydrogen chloride.
To make 250 mL of 0.200 mol/L sodium hydroxide solution, 0.200 mol/L × 0.250 L = 0.0500 mol of sodium hydroxide is needed, which is 0.0500 mol × 40.0 g/mol = 2.00 g.