Expressing Concentration — Part 1

The most common way to express concentration of solid-in-liquid or liquid-in-liquid solutions.

$\text{w/w\%} = \frac{\text{mass of solute}}{\text{mass of solution}} \times 100$

Mass of solution = mass of solute + mass of solvent

Example: 10 g of NaOH dissolved in 90 g of water:
$\text{w/w\%} = \frac{10}{10 + 90} \times 100 = 10\%$

v/v% — used when both solute and solvent are liquids:
$\text{v/v\%} = \frac{\text{volume of solute}}{\text{volume of solution}} \times 100$
Example: 40 mL of ethanol in 100 mL of solution → 40% v/v (the standard for alcohol labelling).

w/v% — mass of solute per 100 mL of solution. Used in medicine and pharmacy:
$\text{w/v\%} = \frac{\text{mass of solute (g)}}{\text{volume of solution (mL)}} \times 100$
Example: Normal saline = 0.9 g NaCl per 100 mL = 0.9% w/v.

Mole fraction expresses concentration as a ratio of moles — temperature-independent and used extensively in Raoult's law calculations.

For a binary solution with solute (2) and solvent (1):
$\chi_2 = \frac{n_2}{n_1 + n_2}, \quad \chi_1 = \frac{n_1}{n_1 + n_2}$

Key property: $\chi_1 + \chi_2 = 1$ (mole fractions of all components always sum to 1)

Mole fraction has no units. It ranges from 0 to 1.