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 F3.  PHYSICAL QUANTITIES, S.I. UNIT SYMBOLS & MANIPULATION OF UNITS 

 3.1  PHYSICAL QUANTITIES & THE BASE S.I. UNIT FOR ‘AMOUNT OF SUBSTANCE’ 

A physical quantity is a physical property of a body, phenomenon, or substance that can be quantified by measurement.

The value of a physical quantity is defined as equal to the product of a number and a unit:

value of a physical quantity = number x unit

e.g., mass = 5.2 x kilogram

m = 5.2 kg

or

Manipulations of equations involving physical quantities and units follow the laws of indices.

At the outset, it is important for one to absolutely clear about the distinction, in a given context, between the:

  • recognized S.I. symbol used for the unit(s)

e.g., kg

  • name of the corresponding S.I. unit(s)

  • quantity symbol(s) in common use

  • name of the physical quantity being used

kilogram

m    (N.B. these are italicized)

mass

Nowhere is the need for clarity greater than when dealing with calculations involving the physical quantity amount of substance which possesses the unit mole, recognized S.I. unit symbol mol whose
quantity symbol is  n.

All too frequently otherwise respectable text books, dedicated calcualtions books, exam papers, exam syllabuses, websites and the like, muddle these distinctions, thus making the task of the reader far more challenging than it ought to be.  Let us be absolutely clear: mole is the unit for the physical quantity called
amount of substance; it is not a physical quantity.  And so commonly seen statements like

2022_solution_concentration_amount_ncV_v

are generally INCORRECT.  Of the four statements above, the first three are nonsensical while the last is archaic and usually wrong, although it might appear legitimately as an axis label.  Use of the term ‘number of moles’, causes problems when included in an ‘equation’ referring to the amount of substance because the relationship is very likely to be dimensionally inhomogeneous.

In addition, use of the unit for amount of substance should specify the substance involved by referring to its molecular formula or else formula unit.  So, we might be talking about potassium fluoride, KF, or perhaps the dangerous gas carbon monoxide, CO.  

All of these above could be written as 

or more succinctly

amount of KF = 0.20.mol

n(KF) = 0.20 mol

amount of CO = 0.20.mol

n(CO) = 0.20 mol

In fact, use of the loose, historical term ‘number of moles’ (from German ‘Molzahl’) which, by definition, can have no unit, was superseded by the physical quantity amount of substance, following the approval of IUPAC and IUPAP in 1969, close on half-a-century ago.

See  The International System of Units (SI) 9th edition 2019 V2.01 (December 2022)

In order to minimize confusion, where ‘amount of substance’ is being shortened to ‘amount’, it has been suggested that the term ‘chemical amount’ may be preferable.  However, each of these must be recognized as equivalent:  amount of substance; amount; chemical amount.  And it should be clear as to which substance any statement refers to, hence n(B) = 0.20 mol, an original instruction of the SI.

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