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In the button cells, widely used in watc...

In the button cells, widely used in watches and other devices, the following reaction takes place
`Zn (s) + Ag_(2) O(s) + H_(2) O (l) rarrZn^(2+) (aq) + 2Ag(s) + 2OH^(-) (aq)`
Determine `E^(@)` and `Delta G^(@)` for the reaction.
(Given, `E_(Ag^(+)//Ag)^(@) = + 0.80 V, E_(Zn^(2+)//Zn)^(@) = -0.76 V ` )

Text Solution

Verified by Experts

Since, `E_(Ag^(+)//Ag)^(@) gt E_(Zn^(2+)//Zn)^(@) ` the zinc electrode is the anode. The half-cell reactions are as follows `:`
At anode `Zn rarr Zn ^(2+) + 2e^(-)`
At cathode `Ag^(+) + e^(-) rarr Ag`
Overall cell reaction is
`Zn + 2Ag^(+) rarr Zn^(2+) + 2Ag`
`E^(@) = E_("cathode") - E_("anode")`
`= 0.80 V - ( - 0.76 )V`
`= 0.80 V = 0.76V`
= 1.56 V
Number of electrons involved is 2. Therefore, `Delta G^(@)` value is given by the formula
`Delta G^(@) = - n FE^(@)`
`= - 2 xx 96500C "mol"^(-1) xx 1.56 V`
`= - 301080 J "mol"^(-1)`
`= - 301.08 kJ "mol"^(-1)`
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