370 8 The Thermodynamics of Electrochemical Systemsthe half-reaction equations. This is the proper procedure in
the case that the electrons cancel out of the final equation.
However, this is not the case in adding equations as in the
following case.
Calculate the value ofE◦for the half-reactionFe^3 ++ 3 e−−→Fe(s)from theE◦values of the half-reactionsFe^2 ++ 2 e−−→Fe(s)Fe^3 ++e−−→Fe^2 +
Explain why theE◦values must be multiplied by the
number of electrons in the half-reaction equation before
adding. (Hint: Think about adding the∆G◦values.)
Comment on the consistency of the data in Table A.13. The
measurement of theseE◦values has apparently been very
difficult.8.12 a.Write the cell symbol for an electrochemical cell with a
chlorine electrode at the left and a silver–silver chloride
electrode at the right and a solution of HCl. The
chlorine electrode is similar to a hydrogen electrode,
with a platinum electrode surface and a means of
bringing Cl 2 gas to the electrode.
b.Find the value ofE◦for this cell.
c.Find the value ofEfor this cell if the pressure of the
chlorine gas is 755.0 torr and the activity of the Cl−is
0.100 on the molality scale. In which direction do
electrons flow spontaneously if the cell acts as a
galvanic cell?
8.13 A cell has a silver electrode at the left, in contact with a
solution containing Ag+ions, and a silver–silver chloride
electrode at the right, in contact with a solution containing
Cl−ions.
a.Write the cell symbol for the cell. Is a salt bridge
needed? If a salt bridge is needed, can the usual
electrolyte be used? Explain. Propose another
electrolyte if one is needed.
b.Write the two half-reaction equations and the cell
equation.
c.FindE◦for the cell at 298.15 K.
d.Find the cell voltage at 298.15 K if the Ag+activity is
0.250 and the Cl−activity is 0.199. Is the cell reaction
spontaneous as written?
8.14 The lead storage battery used in automobiles has an anode
made of lead, a cathode containing lead oxide, PbO 2 , and
an electrolyte solution of sulfuric acid. Solid lead sulfate,
PbSO 4 , is formed.
a.Write the cell reaction of the lead storage battery.
b.FindE◦for a six-cell lead storage battery at 25◦C.
c.FindEfor a six-cell lead storage battery at 25◦C if each
cell contains aqueous sulfuric acid with 24.4% sulfuric
acid by weight and density 1.2023 g cm−^3. The mean
ionic activity coefficient of sulfuric acid under these
conditions is equal to 0.150.
d.The voltage regulator in most automobiles is set to
charge the battery, which has six cells, at about 13.5 V.
Calculate the activity of sulfuric acid necessary to make
the reversible voltage equal to 13.5 V. Do you think that
the battery could have this reversible voltage?
8.15 Find the reversible cell voltage at 298.15 K of a
concentration cell in which both half-cells have calomel
electrodes and HCl solutions. In one solution the molality
is equal to 2.50 mol kg−^1 and in the other solution the
molality is equal to 0.100 mol kg−^1. Carry out the
calculation once assuming that activity coefficients are
equal to unity, and once using activity coefficient values
from Figure 6.10.
8.16 Consider the cell with a hydrogen electrode on the left, a
silver–silver chloride electrode on the right, and a solution
of HCl.
a.Write the cell symbol, the electrode half-reaction
equations, the cell reaction equations, and find the value
ofE◦at 298.15 K. Is a salt bridge not needed? Why or
why not?
b.When the molality of a solution of HCl is
0.500 mol kg−^1 , the mean ionic activity coefficient,γ±,
is equal to 0.757 at 298.15 K. Find the cell
voltage at 298.15 K for a cell with a 0.500 mol kg−^1
solution of HCl and a partial pressure of H 2 equal
to 738 torr.
c.Find the pressure of H 2 gas that would be at
equilibrium with the solution of part b at 298.15 K.
8.17 The cell reaction of the lead storage battery isPb(s)+PbO 2 (s)+2H 2 SO 4 (aq)−→2PbSO 4 (s)+2H 2 O(l)a.Find the value ofE◦at 25◦C.
b.Find the value of∆H◦at 25◦C.
c.Find the value ofE◦at− 18 ◦C (approximately 0◦F).