Q. 13

Write the Nernst

Answer :


The net reation for the given cell :


Mg(s) +Cu2+(aq) Mg2+(aq) + Cu(s)


Nerst equation =
Ecell = E0cell – log kc


where , Ecell=cell emf


E0cell = standard eletrode potentialof the cell


kc = rate constant for the reaction and n = no. Of electrons transferred.


Ecell = 2.71 - 0.059 log [Mg2+(aq)] [Cu(s)] ( n=2 beacause there are 2


2 [Cu2+(aq)] [Mg(s)] electrons transferred)


=2.71 - 0.059 log (.001)


2 (.0001)


= 2.71 - 0.059 log 10


2


=2.71 – 0.0295 V ( log10 = 1 and .059/2 = .0295)


= 2.6805 V .


As the reaction proceeds[ Mg2+]in the anode compartment increases whereas [Cu2+] in the cathode compartment decreases as Cu is being deposited as metallic Cu in the electrode .


During this process, the ratio [Mg2+]/[Cu2+] steadily increases, and the cell voltage therefore steadily decreases and Eventually,


[Mg2+] = [Cu2+], so the ratio becomes = 1 and


Ecell = E°cell .


Beyond this point, [Mg2+] will continue to increase in the anode compartment, and [Cu2+] will continue to decrease in the cathode compartment. Thus the value of [Mg2+]/[Cu2+] will increase further, leading to a further decrease in Ecell .


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