The Foundations of Chemistry

Solution

(a) EcellE^0 cell

0.0

n

592

log Q

Substituting and solving for Q,

0.522 V0.763 V

0.0

2

592

log Q



0.05

2

92 V

log Q(0.7630.522) V0.241 V

log Q

(2

0

)(

.0

0

5

.2

9

4

2

1

V

V)

8.14

Q 10 8.14 1.4 108

(b) We write the expression for Qfrom the balanced overall equation, and solve for [H].

Q

[Z

[

n

H

2 



]

]

P

2

H 2



[H]^2 

[Zn^2

Q

]PH

^2 (1

1

.

.

0

4

0



)(1

1

.0

0

0

8

)

7.1 10 ^9

[H] 8.4 10 ^5 M

(c) pHlog [H]log (8.4 10 ^5 ) 4.08

You should now work Exercises 81 and 82.

882 CHAPTER 21: Electrochemistry

E

nrichment

Concentration Cells

As we have seen, different concentrations of ions in a half-cell result in different half-cell

potentials. We can use this idea to construct a concentration cell,in which both half-cells

are composed of the same species, but in different ion concentrations. Suppose we set up

such a cell using the Cu^2 /Cu half-cell that we introduced in Section 21-9. We put copper

electrodes into two aqueous solutions, one that is 0.10 MCuSO 4 and another that is

1.00 MCuSO 4. To complete the cell construction, we connect the two electrodes with a

wire and join the two solutions with a salt bridge as usual (Figure 21-14). Now the relevant

reduction half-reaction in either half-cell is

Cu^2  2 e88nCu E^0 0.337 V

Thus the Cu^2 ions in the more concentrated half-cell can be considered as the reactant,

and those in the more dilute cell as the product.

Cu^2 (1.00 M)88nCu^2 (0.10 M)

The overall cell potential can be calculated by applying the Nernst equation to the overall

cell reaction. We must first find E^0 , the standard cell potential at standard concentrations;

because the same electrode and the same type of ions are involved in both half-cells, this

E^0 is always zero. Thus,

Microelectrodes have been
developed to measure concentrations
in very small volumes of solution.