Physical Chemistry , 1st ed.

8.3 Energy and Work

How are these ideas related to energy, the principal quantity of thermody-

namics? Let us consider work. We usually define work in terms of pressure-

volume work. This is not the only kind of work that can be defined. For work

involving charges, the definition is different. The infinitesimal amount of elec-

trical work,dwelect, is defined as the infinitesimal change in amount of charge,

dQ, moving through some electric potential :

dwelectdQ (8.8)

Since electric potential has units of V and charge has units of C, equation 8.7

shows that the unit for work using equation 8.8 is joules. Now that we are con-

sidering a new kind of work, we must remember to include this as part of the

total change in internal energy under the first law of thermodynamics. That is,

the infinitesimal change in the internal energy is now

dUdwpV dq dwelect

This is not a changein the definition of internal energy. It is simply including

another type of work. There are actually many contributions to work, and so

far we have considered only pressure-volume work. Other types of non-pV

work include not just electrical (that is, potential-charge), but also surface

tension–area, gravitational-mass, centrifugal-mass, and others. However, we

will consider only electrical work in this chapter.

Electrical work is performed by the movement of electrons, which are the

charged particles that move around in the course of chemical reactions. (The

proton has exactly the opposite charge, but in normal chemical reactions, it re-

mains confined to the nucleus.) One of the properties of a single electron is that

it has a specific charge, about 1.602   10

19 C. This value is symbolized by the

letter e. (For an electron, the charge is symbolized as e, and for the oppositely

charged proton, the charge is e.) In molar quantities,eNA(NAAvog adro’s

number) equals about 96,485 C/mol. This quantity is called Faraday’s constant

(in honor of Michael Faraday) and is symbolized by F. Ions that have a positive

charge of ztherefore represent zFof positive charge per mole of ions, and

ions having a negative charge of zrepresent zFof negative charge per mole.

The infinitesimal change in charge dQis related to the infinitesimal change

in moles of ions,dn(where nis the number of moles of ions). Using the ex-

pressions from the previous paragraph, we can say that

dQzFdn

Substituting this expression for dQinto equation 8.8, the infinitesimal amount

of work is

dwelectzFdn (8.9)

For multiple ions, the amount of work required to change the number of

charged species labeled with an isubscript is

dwelect

0

i

(^) iziFdni (8.10)
In a system where there is a transfer of charge, the number of species hav-
ing any particular charge is changing, so in equation 8.10,dniis not zero. If we
want to consider the infinitesimal change in G, we have to modify the natural
variable equation for G, given by equation 4.48:
dG
S dT V dp (^) 
0
i
idni
210 CHAPTER 8 Electrochemistry and Ionic Solutions