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Molarity M = n (moles) / V (liters)
Molality m = n (moles) / kg (solvent)
% w/v = (mass solute g / volume solution mL) × 100
ppm to M = ppm (mg/L) / (molar mass g/mol × 1000)
Dilution: C₁V₁ = C₂V₂
n = 5.85/58.44 = 0.100 mol | M = 0.100/0.500 = 0.200 M
% w/v = (5.85/500)×100 = 1.17% w/v | ppm = 5.85g/0.500L = 11,700 mg/L = 11,700 ppm
How to Calculate Solution Concentration
Solution concentration describes how much solute is dissolved in a given amount of solvent or solution. There are several different ways to express concentration, each suited to different applications — from industrial chemistry and environmental analysis to clinical medicine and food science.
The most common unit in laboratory chemistry is molarity (M), which expresses the number of moles of solute per liter of solution. It is ideal for reaction stoichiometry and titrations because moles can be directly related to the balanced equation. Molality (m) expresses moles of solute per kilogram of solvent and is preferred when temperature changes are involved, since it is independent of volume expansion.
Concentration Units Comparison
| Unit | Formula | Uses | Temperature Dependent? |
|---|---|---|---|
| Molarity (M) | mol / L solution | Lab chemistry, titrations | Yes (volume changes) |
| Molality (m) | mol / kg solvent | Colligative properties | No (mass-based) |
| % w/v | (g/mL) × 100 | Medicine, biology | Slightly |
| % w/w | (g solute/g solution) × 100 | Industrial, food | No |
| ppm | mg / L (for dilute aq.) | Environmental, water quality | Slightly |
| ppb | µg / L | Trace analysis, toxicology | Slightly |
| Normality (N) | eq / L | Titration, acid-base | Yes |
The Dilution Formula: C1V1 = C2V2
One of the most practical concentration calculations is dilution. The dilution formula C₁V₁ = C₂V₂ states that the number of moles of solute is conserved during dilution. If you start with a concentrated stock solution and add solvent, the moles don't change — only the volume does.
Example: How much water must be added to dilute 25 mL of 12 M HCl to 1.0 M? V₂ = (C₁ × V₁) / C₂ = (12 × 25) / 1.0 = 300 mL total volume. So add 275 mL of water to 25 mL of concentrated HCl.
For dilute aqueous solutions (density ≈ 1 g/mL):
ppm to M: divide ppm by (molar mass × 1000)
M to ppm: multiply M by molar mass × 1000
% w/v to M: divide (% × 10) by molar mass
M to % w/v: multiply M by molar mass × 0.1
Molarity vs Molality: When Does It Matter?
For most practical calculations at room temperature, molarity and molality give similar results because water has a density close to 1 kg/L, making 1 L of dilute aqueous solution weigh approximately 1 kg. However, at high concentrations, elevated temperatures, or with non-aqueous solvents, they diverge significantly. Colligative properties — boiling point elevation, freezing point depression, osmotic pressure — must be calculated with molality because these phenomena depend on the ratio of solute to solvent particles, not solution volume.
ppm and ppb in Environmental Analysis
Parts per million (ppm) and parts per billion (ppb) are the standard units for trace concentrations in environmental monitoring, drinking water analysis, and toxicology. For dilute aqueous solutions (density ≈ 1 g/mL), 1 ppm = 1 mg/L and 1 ppb = 1 μg/L. EPA drinking water standards are typically set in ppm or ppb — for example, the maximum contaminant level for lead in drinking water is 0.015 ppm (15 ppb).