Solutions

A system of two or more components is referred to as solution or  mixture. A solution is defined as a homogeneous system of two or more components. The term "homogeneous" means that the properties and the composition of the system are uniform at a macroscopic level. As an example water and ethanol is a solution in that at a macroscopic level we can not distinguishe between water and ethanol. On the other hand water and sand is a mixture. However, there are many cases in which the difference between solutions and mixtures is very subtle. The component of a solution (mixture) present in greatest quantity is called solvent; the others are the solutes. Normally, the quantitative composition of a solution (mixture) is given as the relative amounts of solute (concentration). 

Generally, we deal with materials containing two or more components and thus we need to conveniently express the nature of components and the amount of each components. Normally, the quantitative composition of a solution (mixture) is given as the relative amounts of solute (concentration). There are several ways to express the concentration of a solution or a mixture, each expression being convenient in a particular application.

Gram %

Grams of solute per 100 grams of solution. It is calculated as follows:

gr solute
1. gr % = -------------- x 100
gr solution

Volume %

ml of solute per 100 ml of solution. It is calculated as follows:

vol solute
2. Vol % = ------------- x 100
vol solution

Mass fraction

The mass fraction (generally indicated with x) of a component of a solution is the ratio between the mass of the component and the total mass of the solution. As an example, for a solution (or a mixture) of three components:

It should be evident that x₁ + x ₂ + x₃ = 1.

Furthermore, it is worth to note that the mass fraction is given by the number expressing the percentage by weight (gram %, see 1) divided by 100. As an example, let's consider a solution containing 3 grams of a component per 100 grams of solution. The percent concentration according to equ. 1 will be 3. If we divide the percent concentration with 100 we obtain the concentration expressed as mass fraction, i.e., x = 0.03. Now, lets calculate the grams of solute contained in 2 grams of the solution above:

0.03 is the mass fraction and 2 are the grams of solution thus, in general, the grams contained in given amount of a solution is given by the product of the mass fraction with the grams of solutions.

Molarity

Molarity is the number of moles of solute in one liter of solution. The symbol for molarity is M.

Molality

Molality is the number of moles of solute in 1 kg (1000 grams) of solvent. The symbol for molality is m

Mole fractions

The mole fraction (generally indicated with x) of a component of a solution is the ratio between the number of moles of the component and the total number of moles forming the solution. As an example, for a solution (or a mixture) of three components it is calculated as follows:

It should be evident that x₁ + x₂ + x₃ = 1. Analogously to mass fraction, the number of moles contained in a given amount of a solution is given by the product of the volume (in liters) with the molarity of the solution, i.e., N^o moles = VM.

Example. Consider 0.3 liter of a solution 1 M to which 200 ml of water are added and let's calculate the concentration of the solution after the addition of water. Since the number of moles are conserved (law of the conservation of mass) it must be V_iM_i = V_fM_f = (0.3) (1) = M_f(0.3 + 0.2) and by solving for M_f we have M_f = 0.3/0.5 = 0.6 M.