Page 344 - Physical chemistry understanding our chemical world

ACTIVITY 311

The activity of a solid The activity of a pure solid in its standard
Unit and unity here
state is unity, so the activity of pure copper or of zinc metal elec-
trodes is one. We write this as a (Cu) or a (Zn) = 1. both mean ‘one’, so
unit activity means
The activity of an impure solid is more complicated. Such an
a = 1.
‘impure’ system might be represented by a solid metal with a dirty
surface, or it might represent a mixture of two metals, either as an alloy or an amalgam
with a metal ‘dissolved’ in mercury.
For example, consider the bi-metallic alloy known as bronze,
which contains tin (30 mol%) and copper (70 mol%). There are An ‘alloy’ is a mixture
two activities in this alloy system, one each for tin and copper. The of metals, and is not a
activity of each metal is obtained as its respective mole fraction x, compound.
so x (Sn) = a (Sn) = 0.3, and a (Cu) = 0.7.

Worked Example 7.10 A tooth filling is made of a silver amalgam that comprises
37 mol% silver. What is the activity of the mercury, a (Hg) ?

The activity of the mercury a (Hg) is the same as its mole fraction, Thesum of themole
x (Hg) . By definition fractions x must always
x (Hg) + x (Ag) = 1 add up to one because
‘the sum of the con-
so stituents adds up to
x (Hg) = 1 − x (Ag) = 0.63 the whole’.

The activity is therefore
x (Hg) = a (Hg) = 0.63

The activity of a gas The activity of a pure gas is its pressure
Reminder:the value of
O
O
(in multiples of p ), so a (H 2 ) = p (H 2 ) ÷ p . The activity of pure p O is 10 Pa.
5
O
hydrogen gas a (H 2 ) at p is therefore unity.
In fact, for safety reasons it is not particularly common to employ
pure gases during electrochemical procedures, so mixtures are pre- In a mixture of gases,
ferred. As an example, the hydrogen gas at the heart of the standard we call the inert gas a
hydrogen electrode (SHE) is generally mixed with elemental nitro- base or bath gas.
gen, with no more than 10 per cent of H 2 by pressure. We call the
other gas a base or bath gas. Conversely, we might also say that hydrogen dilutes
the nitrogen, and so is a diluent.
In such cases, we can again approximate the activity to the mole fraction x.

Worked Example 7.11 Hydrogen gas is mixed with a nitrogen ‘bath gas’. The overall
pressure is p . If the mole fraction of the hydrogen is expressed as 10 per cent, what is
O
its activity?
By definition, x (X) = partial pressure,p (X) ,so

a (H 2 ) = p (H 2 ) ÷ p (total) = 0.1