Page 131 - Basic physical chemistry for the atmospheric sciences

Oxidation-reduction reactions 1 1 7

We could set up a number of electrochemical cell , each with a differ­
s
ent pair of metal electrodes in contact with solutions of their metal ions,
and measure the steady potential difference generated by each cell un­
der standard conditions (i.e. , 25°C , 1 atm and I M concentrations of the
metal ions). 5 The voltages obtained in this way are called standard cell
potentials (�en>· The greater the tendency (or driving force) for a redox
reaction to occur (with reactants and products in their standard states),
the greater will be its standard cell potential.
Exercise 6.5. An electrochemical cell has a standard cell potential of
2 . 0 V . How much electrical work can it do in 1 . 0 minute if it operates
under standard conditions and a steady current of . 0 ampere is drawn
1
from the cell? If the cell is that shown in Figure 6. 1 , how many moles
of Ag + (aq) ions are neutralized by electrons in 1 . 0 minute? [The
s
electric charge on I mole of electron , called the Faraday constant
(F), is about 96,489 coulom s . ] 6
b
Solution. When a current I (in amperes) flows through a potential
difference E (in volts) for time t (in seconds), the electrical work done
is, from elementary electrical theory, E/t (in joules). Therefore, since
the cell provides a potential difference of . 0 V (assuming no potential
2
loss at the electrodes), the electrical work done by the cell in 1 minute,
J
w
1
1
when a current of . 0 ampere flo s , is 2.0 x l . O x 6 0 = 2 0 .
o
b
Since electric charge ( i n coulombs) is given y the product f cur­
rent (in amperes) and time (in seconds), the electric charge that flows
through the circuit in time t is It = y F, where y is the number of moles
of electrons that pass in t second . Therefore, /t = 96,489y or, since
s
I = t 1 . 0 x 60 ampere-sec, y = 6.2 x 1 0 - 4 moles of electrons in 1 minute.
I n the half-cell depicted on the left side of Figure 6. 1 , the electrons
neutralize the Ag + (aq) ions in solution. Also, it can be seen from
Reaction (6. 1 ) that 1 mole of electrons reacts with 1 mole of Ag + (aq)
ion . Hence, the number of moles of Ag + (aq) ions that are neutralized
s
6
in I minute is . 2 x 1 0 - 4 •
So far we have considered only the magnitude of the standard cell
potential �e · By convention, �en is considered to have a positive
n
value if the reaction proceeds spontaneously in the forward directio .
n
Thus , Reaction (6.3)
Cu(s) + 2Ag + ( aq)� c uz + ( aq) + 2Ag(s) (6.3)
proceeds spontaneously in the forward direction (i . e . , from left to
right); therefore its standard cell potential is 0.46 V . Conversely, the
reaction