Chapter 7: Solutions and concentrations

A solution consists of at least two components: the solvent, which is the component in the largest quantity (water for aqueous solutions); and the solute (the component dissolved in the solvent). A true solution is a homogenous mixture of the solute(s) and solvent where the solute molecules are dispersed within the solvent.

Concentration refers to the amount of solute dissolved per unit volume of the solvent. That is, concentration quantitatively describes the ratio of solute to solvent. There are numerous ways to express concentration but most often you will encounter concentration expressed in one of the following ways.

  • Molarity: expressed as M or mol l1 and probably most used in chemistry and biochemistry. Molarity refers to the molar concentration, that is, the number of moles per litre. This is a particularly useful measure of concentration for determining the stoichiometry (relative amount of reactant and product) for a chemical reaction.
  • Percentage composition: non-SI units that typically express the weight-to-volume percent (w/v % – percent of solute mass to solvent volume) or volume-to-volume percent (v/v % – percentage volume of solute to volume of solvent). These are commonly used for concentrated solutions.
  • Parts per million or parts per billion: expressed as ppm or ppb. These are often used for very dilute solutions.
  • Mass per volume: commonly used for drug solutions but also used in biochemistry to describe protein or nucleic acid solutions (expressed as g l1 but the prefixes will vary depending on the concentration; e.g. µg ml1).


Molarity and the mole

The mole is the SI unit used to measure the amount of a substance. The technical definition is:
  • the amount of substance which contains as many elementary entities are there are atoms in 0.012 kg of carbon-12 (12C).
The number of particles in a mole is known as Avogadro’s number[1] and is approximately equal to 6.02 × 1023.
To determine the number of moles of a substance, you need to know its mass and molecular weight.
The molecular weight of a substance is the mass of 1 mol of a substance in g mol–1.
Molecular weight or molecular mass is often interchangeably used to mean the mass of a single molecule in daltons (Da), which is the mass of molecules relative to 1/12th the mass of a carbon-12 atom. Note that although they are numerically identical, they are actually different units.
To determine the number of moles of a substance you need to divide the mass of the substance by its molecular weight:
 \displaystyle \text{mol} = \frac{\text{mass (g)}}{\text{molecular weight}}

  1. Amedeo Avogadro was the first person to clearly differentiate molecules and atoms, but the concept of the mole was only introduced after his death.

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