1 Numbers, variables, and units
1.1 Concepts
Chemistry, in common with the other physical sciences, comprises
(i)experiment: the observation of physical phenomena and the measurement of
physical quantities, and
(ii)theory: the interpretation of the results of experiment, the correlation of one set
of measurements with other sets of measurements, the discovery and application
of rules to rationalize and interpret these correlations.
Both experiment and theory involve the manipulation of numbers and of the symbols
that are used to represent numbers and physical quantities. Equations containing
these symbols provide relations amongst physical quantities. Examples of such
equations are
- the equation of state of the ideal gas
pV=nRT (1.1)
- Bragg’s Law in the theory of crystal structure
nλ 1 = 2 d 1 sin 1 θ (1.2)
- the Arrhenius equation for the temperature dependence of rate of reaction
(1.3)
- the Nernst equation for the emf of an electrochemical cell
(1.4)
When an equation involves physical quantities, the expressions on the two sides of the
equal sign
1must be of the same kind as well as the same magnitude.
EE
RT
nF
=− Q
oln
kAe
ERT=
−a/1The sign for equality was introduced by Robert Recorde (c.1510–1558) in his The whetstone of witte(London,
1557); ‘I will sette as I doe often in woorke use, a paire of paralleles, or Gemowe (twin) lines of one lengthe, thus:
, bicause noe.2. thynges can be moare equalle.’