Solution Concentration: Molarity, Dilution, and Related Units

Molarity vs molality, mass percent, ppm, and how to use C₁V₁ = C₂V₂ for dilution calculations.

Solution stoichiometry and lab prep depend on clear concentration units. The most common volumetric unit is molarity.

Molarity

M = \frac{\text{moles of solute}}{\text{liters of solution}}

Example: 0.500 mol NaCl in 0.250 L of solution → $M = 2.00$ mol/L (2.00 M).

Molarity depends on temperature because volume expands or contracts with $T$.

Molality uses solvent mass, so it is independent of temperature:

m = \frac{\text{moles of solute}}{\text{kg of solvent}}

Mole fraction of component $i$:

x_i = \frac{n_i}{n_{\mathrm{total}}}

When you dilute a stock solution without adding or removing solute:

C_1 V_1 = C_2 V_2

$C_1$, $V_1$ — stock concentration and volume used
$C_2$, $V_2$ — desired concentration and final volume

Prepare 500 mL of 0.100 M HCl from 12.0 M stock.

$V_1 = C_2 V_2 / C_1 = (0.100)(0.500)/(12.0) = 0.00417$ L = 4.17 mL of stock, diluted to 500 mL.

For dilute aqueous solutions, ppm ≈ mg solute per liter; ppb ≈ μg/L. Use exact mass ratios when density is not ≈ 1 g/mL.

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