The extent of the reaction of aqueous HCl with aqueous NaOH can be stated as 0.2 moles HCl reacted out of 0.5 moles HCl originally present in the same way that extent of travel on a trip to the seashore can be stated in terms of 200 km travelled out of 500 km required. Although the amount of substance reacted is the most fundamental unit for the extent of a chemical reaction, it is usually inconvenient to measure amount of substance directly. More convenient methods can be used if the reaction occurs either uniformly on a surface or uniformly throughout a volume, as most reactions do. For reactions which take place on a uniform surface, such as an electrode reaction or a reaction taking place at the surface of a solid or liquid, the reaction occurs uniformly across the surface and so the more easily measured moles per unit area can be used in place of total moles present. We will not take up surface reactions in any detail now, but you will encounter them in any future studies in electrochemistry, chemical engineering, and biochemistry.
Many chemical reactions take place uniformly throughout a volume.
All reactions which take place in a homogeneous medium, including gas mixtures and liquid solutions, fall into this category. Since the reaction occurs uniformly throughout the volume, the extent of the reaction is measured in moles per unit volume rather than in total moles present. This is the molar concentration M, which we indicate with square brackets. Partial pressures are usually used to give the extents and rates of gas-phase reactions.