Читать книгу Electroanalytical Chemistry - Gary A. Mabbott - Страница 17

If charge is moved, the amount of work done is proportional to the difference in voltage. Because the voltage difference, ΔV, is the energy spent per unit charge, the total work done in moving the charge, Q, is

(1.12)

This is analogous to carrying a piano up a flight of stairs. The potential energy difference is fixed by the height of the stairs. To move two pianos requires twice the amount of work.

There are a couple of other conventions worth mentioning here. In electrochemical contexts, E is used instead of ΔV to represent the electrochemical potential energy difference. It is also common to equate electrical work and the Gibb's free energy change, ΔG. The relationship between potential and ΔG is usually expressed in terms of the energy per mole of reactant:

(1.13)

where n is the number of moles of electrons/mol of reactant, F is Faraday's constant in coulombs/mol of electrons, and E is the potential difference in volts or joules/coulomb. A dimension analysis indicates that ΔG in Eq. (1.13) has the units of joules per mole of reactant. To find the total energy spent/released, or the total work done, one needs to multiply Eq. (1.13) by N, the number of moles of reactant being converted. Also, note that it is a matter of convention that favorable electrochemical processes are assigned positive potentials. Thus, the sign in Eq. (1.13) yields a negative ΔG for a positive value of E for a favorable process.

Another convention is to define the direction of a current as the direction that the positive charges move. This is the case, despite the fact that electrons are usually the major charge carriers and are moving in the opposite direction. That means that a current flows from a point of a higher potential to a point of lower potential; the electrons move in the opposite direction.