Ways to express concentration

molarity vs molalityconcentration formulasdilution equationM1V1 = M2V2mole fractionnormality

Molarity, molality, mass percent, mole fraction, normality and the dilution equation — six answers to “how much solute is in there?”

Molarity (C = n/V)

C = \frac{n}{V}

Defines molar concentration as moles of solute per volume of solution.

Molality (b = n/m)

b = \frac{n}{m_{\text{solvent}}}

Defines molality as moles of solute per kilogram of solvent.

Mass Percent of a Solution

c = \frac{m_{\text{solute}}}{m_{\text{solution}}} \times 100\%

Expresses a solution's concentration as the solute's share of the total solution mass in percent.

Mole Fraction

x_1 = \frac{n_1}{n_1 + n_2}

Gives the fraction of all moles in a two-component mixture contributed by the solute.

Normality from Molarity

N = M \times n_{\text{eq}}

Converts molarity into normality by multiplying by the number of reactive equivalents each mole of solute supplies.

Dilution Equation (C1V1 = C2V2)

C_1 V_1 = C_2 V_2

States that concentration times volume is conserved when a solution is diluted, since the moles of solute do not change.

How they fit together

They differ in one place only: what sits in the denominator. Molarity divides by the volume of solution, molality by the mass of solvent, mass percent by the mass of solution, and mole fraction by the total moles of everything present. Normality is molarity multiplied by how many reactive equivalents each mole carries, which is why a 1 M sulfuric acid solution is 2 N in an acid-base titration.

The choice is decided by temperature. Volume expands when a solution is heated, so molarity drifts with temperature while molality, mass percent and mole fraction do not — that is exactly why the colligative-property equations are written in molality and never in molarity. Use molarity for bench work at room temperature and for anything titrated by volume; switch to molality the moment the solution is going to be boiled or frozen. The dilution equation is the one that assumes nothing: moles of solute are conserved when you add solvent, so C₁V₁ = C₂V₂ works in any concentration unit as long as both sides use the same one.