The Chemistry Maths Book, Second Edition

20 Chapter 1Numbers, variables, and units

14

SI (Système International d’Unités) is the international standard for the construction and use of units

(see the NIST website at http://www.physics.nist.gov)..) In addition, IUPAC (International Union of Pure and Applied

Chemistry) provides the standard on chemical nomenclature and terminology, and on the measurement and

evaluation of data (see http://www.iupac.org)..)

that defines the dimensions of the quantity and provides a scale for the specification

of the magnitude of an arbitrary length; it is a unitof length. In general, a physical

quantity is the product of a number and a unit. All physical quantities can be

expressed in terms of the seven ‘base’ quantities whose names and symbols are listed

in the first two columns of Table 1.1.

Table 1.1 Base physical quantities and SI units

Physical quantity Symbol Dimension Name of SI unit Symbol for

SI unit

length l L metre m

mass m M kilogram kg

time t T second s

electric current I I ampere A

temperature T Z kelvin K

amount of substance n N mole mol

luminous intensity I

v

J candela cd

The symbols in column 3 define the dimensions of the base physical quantities, and

the dimensions of all other quantities (derived quantities) can be expressed in terms

of them. For example, velocity (or more precisely, speed) is distance travelled in unit

time,l 2 t 1 = 1 lt

− 1

, and has dimensions of length divided by time,LT

− 1

. The dimensions

of a physical quantity are independent of the system of units used to describe its value.

Every system of units must, however, conform with the dimensions.

A variety of systems of units are in use, many tailored to the needs of particular

disciplines in the sciences. The recommended system for the physical sciences, and

for chemistry in particular, is the International System of Units (SI)

14

which is based

on the seven base units whose names and symbols are listed in columns 4 and 5 in

Table 1.1. Every physical quantity has an SI unit determined by its dimensionality. The

SI units of length and time are the metre, m, and the second, s; the corresponding

SI unit of velocity is metre per second,m 2 s 1 = 1 m s

− 1

(see Example 1.16(i)). In addition

to the base units, a number of quantities that are particularly important in the

physical sciences have been given SI names and symbols. Some of these are listed in

Table 1.2.

We note that some physical quantities have no dimensions. This is the case for a

quantity that is the ratio of two others with the same dimensions; examples are

relative density, relative molar mass, and mole fraction. A less obvious example is

(plane) angle which is defined as the ratio of two lengths (see Section 3.2).