Measuring Solution Concentration

In chemistry, we must define how 'crowded' a solution is. Molarity (M) is the most common unit, defined as the moles of solute per liter of solution. However, Molarity has a flaw: liquids expand when heated, changing the volume and thus the concentration. To solve this, we use Molality (m), which is moles of solute per kilogram of solvent. Since mass does not change with temperature, molality is the gold standard for experiments involving temperature shifts, such as boiling point elevation.

When dealing with very small amounts of solute, like pollutants in a lake, we use Parts Per Million (ppm). This represents 1 gram of solute for every million grams of solution. For theoretical chemistry, we use the **Mole Fraction ($\chi$)**, which is the ratio of the moles of one component to the total moles of all components. It is a unitless number between 0 and 1.

When ionic compounds dissolve, they dissociate into their constituent ions. A $1.0$ M solution of $NaCl$ provides $1.0$ M of $Na^+$ and $1.0$ M of $Cl^-$. However, a $1.0$ M solution of $CaCl_2$ provides $1.0$ M of $Ca^{2+}$ but $2.0$ M of $Cl^-$ because there are two chloride ions for every one formula unit of calcium chloride. Always look at the subscripts in the chemical formula to determine the 'effective' concentration of ions in the solution.