Concentrations of Solutions

Conservation of Concentrations

Provided the number of particles of the substance in solution is not changed (i.e. no solute or solvent is added or removed) then the concentration of a solution will remain constant across volumes. For example, if a $25text{ mL}$ sample of a $100text{ mL}$ sodium hydroxide solution with a $0.5 text{ g/dm}^3$ was taken, the concentration of this sample would also be $0.5text{ g/dm}^3$. This is because the ratio of sodium chloride molecules in the both solutions is the same. 

Concentration Calculations

Concentrations are calculated using the following formula:

$text{Concentration}$$=$$frac{text{Mass of Solute in Solution (g)}}{text{Volume of Solvent (dm)}}$

This gives us $text{g/dm}^3$ as the unit for concentration. The unit of volume used, the decimeter $left(text{dm}right)$ may be one that seems unfamiliar. The decimeter is an extremely common unit in chemistry. $1 text{ dm}^3$ is equal to $1000 text{ cm}^3$. To convert from $text{cm}^3$ to $text{dm}^3$ we divide the former by $1000$: 

$text{Volume in dm}^3=frac{text{Volume in cm}^3}{1000}$

When talking about solutions, there are four important definitions to know:

1. Solute: The solid substance which is dissolved in a solution

2. Solvent: The liquid in which a substance is dissolved to form a solution

3. Soluble: A compound that can be dissolved in a given solution

4. Insoluble: A solution that can’t be dissolved in a given solution

To illustrate this, take solid copper sulfate dissolved in water to form a solution.  The solid copper sulfate has been dissolved and so this is the solute. The water is the liquid used to dissolve the copper sulfate and so this is the solvent. 

Water is the most common solvent used to create solutions of ionic compounds. When solutions are created using water as the solvent, these solutions are said to be aqueous. Covalent compounds are often dissolved in organic solvents such as hexane.

Molar Concentrations

Though concentrations can be measured in $text{g/dm}^3$, it is more common in chemistry to measure them in $text{mol/dm}^3$. When reporting the concentrations of solutions in scientific papers, it is almost always $text{mol/dm}^3$ that is used. Calculating molar concentrations of solutions works in much the same was as the mass concentration given above:

$text{Concentration of Solution}$$=$$frac{text{Moles of Solute}}{text{Volume of Solvent}}$

Often the amount of solute will not be given in moles however. It will typically still be given in grams. Before calculating molar concentrations, the mass of the solute must be converted to moles. The molar concentration of a substance will often be smaller from the mass concentration, as the number of moles of solute is typically smaller than the mass of the solute.