For example, if liquid titanium(IV) chloride (acidified with HCl) is electrolyzed by a
current of 1.000 amp for 2.000 h, how many grams of titanium will be produced?
Answer:
Calculation of E°cellalso allows for the calculation of two other useful quantities—the
Gibbs free energy (ΔG°) and the equilibrium constant (K).
The Gibbs free energy is the best single thermodynamic indicator of whether a reaction
will be spontaneous (review the Thermodynamics chapter). The Gibbs free energy for a
reaction can be calculated from the E°of the reaction using the following equation:
where Fis Faraday’s constant of 96,500 C/mol e−=96,500 J/V.
ΔGnFE°=− °cell
TiCl l Ti s Cl g n ot n eces s a ry
Ti e Ti
42
4
2
4
()→+() ( )( )
+−+→necessary
h s
h
C
s
()
(.2 000 )^3600 1 000.
⎛
⎝
⎜
⎞
⎠
⎟
⎛
⎝
⎜
⎞
⎠⎠
⎟
⎛
⎝
⎜
⎞
⎠
⎟
⎛
⎝
⎜
⎞
⎠
⎟
−
−
1
96485
1
4
mole e 4
C
mole Ti
mole e
7790
0 8936
.
.
gTi
mol Ti
gTi
⎛
⎝
⎜
⎞
⎠
⎟
=
248 Step 4. Review the Knowledge You Need to Score High
0.48 V
Voltmeter
Salt bridge Salt bridge
e− e− e− e−
Sn
Sn Sn2+
Cu2+
2e− 2e−
Cu
Cu
Anode
(–)
Cathode
(+)
Cu
Cu Cu2+
Sn2+
2e− 2e−
Sn
Sn
Anode
(+)
Cathode
(–)
Oxidation half-reaction
Sn(s)
Sn(s) + Cu2+(aq) Sn2+(aq) + Cu(s)
Cu2+(aq) + 2e−
Sn2+(aq) + 2e−
Cu(s)
Reduction half-reaction
Overall (cell) reaction
Oxidation half-reaction
Cu(s) Cu2+(aq) + 2e−
Cu(s) + Sn2+(aq) Cu2+(aq) + Sn(s)
Sn2+(aq) + 2e− Sn(s)
Reduction half-reaction
Overall (cell) reaction
External source
greaterthan 0.48 V
Figure 16.2 Comparison of a galvanic cell (left) and an electrolytic cell (right).