Galvanic Cell

Question

!!E_1,E_2!! and !!E_3!! are the emfs values of the three galvanic cells respectively,

!!i) Zn|Zn^(2+)(1M)|| Cu^(2+)(0.1M)|Cu!!

!!ii) Zn|Zn^(2+)(1M)|| Cu^(2+)(0.01M)|Cu!!

!!iii) Zn|Zn^(2+)(0.01M)|| Cu^(2+)(0.1M)|Cu!!

Find the correct order from the following:

(a) !!E_3< E_1< E_2!!

(b) !!E_3 >E_1 >E_2!!

(c) !!E_1< E_2< E_3!!

(d) !!E_3< E_2< E_1!!

Solution

By using Nernst equation:

!!E = E_0- 0.0592/n log ([Zn^(2+)]/[Cu^(2+)])!!

All will have same !!E_0!!.

For cell (i), we get

!!E_1 = E_0- 0.0592/n log(1/0.1)!!

!!=> E_1 = E_0 - 0.0592/n log 10....(1)!!

For cell (ii), we get

!!E_2 = E_0- 0.0592/n log(1/0.01)!!

!!=> E_2 = E_0 - 0.0592/n (2log 10)....(2)!!

For cell (iii), we get

!!E_3 = E_0- 0.0592/n log(0.01/0.1)!!

!!=> E_3 = E_0 + 0.0592/n log 10....(3)!!

Comparing equation (1),(2) and (3), we get

!!E_3 > E_1 > E_2!!

Therefore option (B) is correct.

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