Two beakers of copper(II) sulfate solution sat at the front of the room, one pale blue and one nearly navy. Same compound, same solvent, same temperature. Everybody could see the difference and nobody could put a number on it, which is the problem this page solves.
Water and Solutions explained whether something dissolves. Concentration is how much, and it is the point at which solutions stop being descriptive chemistry and start feeding into the calculations from Stoichiometry.
Concentration is a ratio, and both numbers matter
The concentration a chemist reaches for first is molar concentration: amount of solute in moles, divided by volume of solution in litres.
Its units are mol/L, and it is written in square brackets when you are naming a species — mol/L means the chloride ion concentration is 0.20 mol/L.
Two traps live in that one small equation.
The volume is litres, not millilitres. Every piece of glassware in the room is calibrated in millilitres and every concentration is per litre, so a division by 1000 has to happen somewhere and it is the most frequently forgotten step in the unit.
It is volume of solution, not volume of solvent. Dissolving something changes the volume — sometimes up, occasionally down. This is why a standard solution is made in a volumetric flask: you dissolve the solid in less water than you need, then top up to the etched line, so the final solution is exactly the stated volume. Measuring out 250 mL of water and then adding solid to it gives you a solution of unknown volume and therefore unknown concentration. That is the whole reason Preparing a Standard Solution is done the way it is done.
A worked example. Dissolve 5.85 g of sodium chloride and make it up to 250.0 mL:
Other units, and when each one is used
Molar concentration is the one that goes into equations. It is not the one on most labels, because most labels are not written for people doing stoichiometry.
| Unit | What it means | Where you meet it |
|---|---|---|
| mol/L | moles of solute per litre of solution | anything feeding a balanced equation; titration work |
| g/L or g/100 mL | grams of solute per litre, or per 100 mL, of solution | solubility tables and curves |
| % (m/v) | grams per 100 mL of solution, as a percentage | saline, disinfectants, medical solutions |
| % (v/v) | millilitres per 100 mL of solution | mixtures of liquids — alcohol content |
| ppm | one part per million by mass | trace metals, chlorine in tap water |
| ppb | one part per billion by mass | contaminants measurable at very low levels |
Parts per million deserves a note, because it is the unit almost every environmental measurement is reported in and it looks more mysterious than it is. One part per million is one gram of solute in one million grams of solution. For dilute aqueous solutions, one litre of solution has a mass of very nearly one kilogram, which is milligrams — so 1 ppm is 1 mg/L. That equivalence is a convenience of water’s density and it does not transfer to other solvents.
The reason to care is that guideline limits for metals and other contaminants in drinking water are published in milligrams per litre. Being out by a factor of a thousand between mg/L and g/L is not a rounding error; it is the difference between safe and not, and it is exactly the kind of unit reasoning The Water Report will ask you to be careful with.
Dilution conserves moles
Add water to a solution and the concentration falls. Nothing else changes: no solute is created and none is destroyed, so the number of moles of solute is the same before and after. That single sentence is the entire derivation.
Since and is unchanged,
Use 0.400 mol/L stock to make 100.0 mL of a more dilute solution: take 10.0 mL of the stock and add water to the 100.0 mL mark. The concentration is
Note that the volumes appear on both sides, so as long as you use the same unit throughout, millilitres are fine here. Dilution is the one place in this unit where you do not have to convert.
Add acid to water, never water to acid
Diluting a concentrated acid releases a substantial amount of heat. Pour acid slowly into a large volume of water and that heat is spread through the water, which has a high heat capacity, and the mixture warms gently. Pour water into concentrated acid and the heat is released in the small volume of the first drop, which can boil instantly and spit concentrated acid out of the container and up at your face.
Add acid to water. Stir. Use the dilute reagents supplied, never concentrated stock, and never return unused solution to the stock bottle — see Lab Safety and WHMIS.
Concentration in a stoichiometry problem
Nothing about the road in Stoichiometry changes. Concentration is simply a third way onto it, alongside mass and — later — gas volume.
Three doors into the same room. Once you have moles, everything works the way it always did: mole ratio from the coefficients, then back out through whichever door the question wants.
This matters immediately, because the two techniques the rest of the unit is built on are both stoichiometry with at the front: finding out how much precipitate two solutions will produce, in Precipitation and Net Ionic Equations, and finding an unknown concentration by reacting it with a known one, in Titrating an Acid.
Get the conversions fluent in Concentration Practice first — the chemistry in this unit is straightforward and almost every lost mark is a factor of 1000.
Curriculum connection
E2.2
solve problems related to the concentration of solutions by performing calculations involving moles, and express the results in various units (e.g., moles per litre, grams per 100 mL, parts per million or parts per billion, mass, volume per cent) [AI, C]
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