5 Steps to a 5 AP Chemistry

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).