Fundamentals of Electrochemistry - W.H. Freeman

1504T_ch14_270-297 1/23/06 11:35 Page 272
A current of 0.227 A is 227 mA.
To find the current, we convert moles of electrons per second into coulombs per second:
Current charge
time
coulombs
second
0.227 C/s 0.227 A
moles e
second
coulombs
mole
mol
a2.356 106 b a9.649 C 104
s mol b
In Figure 14-1, we encountered a Pt electrode, which conducts electrons into or out of a
chemical species in the redox reaction. Platinum is a common inert electrode. It does not participate
in the redox chemistry except as a conductor of electrons.
It costs energy to move like charges toward
one another. Energy is released when opposite
charges move toward each other.
Electric current is analogous
to volume of water per second
flowing out of a hose.
High
pressure
Low
pressure
1 V 1 J/C
Electric potential is analogous to the
hydrostatic pressure pushing water through
a hose. High pressure gives high flow.
Figure 14-2 Analogy between the flow of
water through a hose and the flow of
electricity through a wire.
Section 6-2 gave a brief discussion of G.
Voltage, Work, and Free Energy
The difference in electric potential, E, between two points is the work needed (or that can be
done) when moving an electric charge from one point to the other. Potential difference is
measured in volts (V). The greater the potential difference between two points, the stronger
will be the “push” on a charged particle traveling between those points.
A good analogy for understanding current and potential is to think of water flowing
through a garden hose (Figure 14-2). Current is the electric charge flowing past a point in a
wire each second. Current is analogous to the volume of water flowing past a point in the
hose each second. Potential is a measure of the force pushing on the electrons. The greater
the force, the more current flows. Potential is analogous to the pressure on the water in the
hose. The greater the pressure, the faster the water flows.
When a charge, q, moves through a potential difference, E, the work done is
Relation between
work and voltage:
Joules Volts Coulombs
(14-3)
Work has the dimensions of energy, whose units are joules (J). One joule of energy is gained
or lost when 1 coulomb of charge moves between points whose potentials differ by 1 volt.
Equation 14-3 tells us that the dimensions of volts are joules per coulomb.
Example Electrical Work
How much work can be done if 2.4 mmol of electrons fall through a potential difference
of 0.27 V in the ocean-floor fuel cell at the opening of this chapter?
Solution To use Equation 14-3, we must convert moles of electrons into coulombs of
charge. The relation is simply
q nF (2.4 10 3 mol)(9.649 10 4 C/mol) 2.3 10 2 C
The work that could be done is
Work E
q
Work E q (0.27 V)(2.3 10 2 C) 62 J
In the garden hose analogy, suppose that one end of a hose is raised 1 m above the other
end and a volume of 1 L of water flows through the hose. The flowing water goes through a
mechanical device to do a certain amount of work. If one end of the hose is raised 2 m above
the other, the amount of work that can be done by the falling water is twice as great. The elevation
difference between the ends of the hose is analogous to electric potential difference
and the volume of water is analogous to electric charge. The greater the electric potential difference
between two points in a circuit, the more work can be done by the charge flowing
between those two points.
The free-energy change, G, for a chemical reaction conducted reversibly at constant
temperature and pressure equals the maximum possible electrical work that can be done by
the reaction on its surroundings:
Work done on surroundings G
(14-4)
The negative sign in Equation 14-4 indicates that the free energy of a system decreases when
the work is done on the surroundings.
272 CHAPTER 14 Fundamentals of Electrochemistry