Concentration

The most common concentration unit in chemistry is molar concentration (also called molarity), symbol $c$, measured in moles of solute per litre of solution (mol/L, sometimes written M). Why count moles instead of grams? Because chemical reactions happen particle by particle. One mole of NaCl (58.44 g) and one mole of glucose (180.16 g) contain the same number of formula units even though their masses are very different, so a 1.0 mol/L solution of either holds the same number of solute formula units per litre. That is exactly what you need when a solution is used in a balanced equation.

• Concentration in g/L — mass of solute (in grams) per litre of solution. Useful when you care about mass rather than moles.
• Parts per million (ppm) — used for very dilute (trace) concentrations, such as contaminants in drinking water. $1\text{ ppm}=1\text{ mg solute per L of solution}$ (for dilute aqueous solutions, where 1 L ≈ 1 kg, this is equivalent to 1 mg solute per kg of solution).
• Percent concentration (% w/v, also written % m/v) — grams of solute per 100 mL of solution, expressed as a percent. E.g. a 5% w/v solution has 5 g of solute per 100 mL of solution.
• Percent concentration (% v/v) — mL of solute per 100 mL of solution, used when both solute and solvent are liquids (e.g. rubbing alcohol is often 70% v/v isopropanol).
• Percent by mass (% w/w) — grams of solute per 100 g of solution. Concentrated reagents are often labelled this way (concentrated hydrochloric acid is about 37% w/w HCl).

When a solute is present in tiny amounts, mol/L gives awkward numbers — Canada's limit for lead in drinking water, written in mol/L, is about 0.000 000 024 mol/L. Parts per million compares the mass of solute with the mass of the whole solution, scaled up by a million: $\text{ppm}=\frac{m_{\text{solute}}}{m_{\text{solution}}}\times 10^6\text{.}$ One ppm is like a single drop of dye stirred into about 50 L of water. Because 1 L of dilute aqueous solution has a mass of about 1 kg, or 1 000 000 mg, each milligram of solute per litre is one part per million — so for drinking water, mg/L and ppm are interchangeable. For even smaller amounts, parts per billion (ppb) scales by $10^9$ instead: 1 ppm = 1000 ppb, and 1 ppb ≈ 1 µg/L. Health Canada sets a maximum acceptable concentration (MAC) for each harmful substance in drinking water, and treatment plants test regularly to stay below it.

All these units describe the same solution in different ways, and molar mass is the bridge between the mole-based and mass-based ones. To turn a molar concentration into a mass concentration, multiply by molar mass: 0.100 mol/L NaCl × 58.44 g/mol = 5.84 g/L. Dividing g/L by 10 gives grams per 100 mL, so the same solution is 0.584% w/v. Multiplying g/L by 1000 gives mg/L — 5840 mg/L, or about 5840 ppm. To go the other way, divide by molar mass. The table shows how to recognise which unit a situation calls for.

A standard solution is one whose exact concentration is known precisely. To make one in the lab: (1) accurately weigh out the required mass of solid solute; (2) dissolve it completely in a small amount of solvent inside a volumetric flask; (3) once dissolved, carefully add more solvent until the liquid level reaches the calibration line etched on the neck of the flask (this fixes the TOTAL volume of solution, not just the water added); (4) stopper and invert/mix thoroughly to ensure uniform concentration throughout. Each detail has a reason. Rinse the weighing boat into the flask so no solute is left behind. Dissolve BEFORE filling to the line, because dissolving can change the volume slightly. Use distilled water so no extra ions sneak in. Read the bottom of the meniscus at eye level, and add the last few millilitres dropwise — once you overshoot the line, the solution is too dilute and must be remade.