The following reaction`:` occurs in the dry cell, called flash light battery, which is used to power radios, clocks, and flashlights `:`
`2MnO_(2)(s)+8overset(o+)(N)H_(4)+Zn(s) rarr 2Mn^(3+)+8NH_(3)+Zn^(2+)+4H_(2)O`
`a.` Write the anode and cathode reactions.
`b.` Calculate `E^(c-)._(cell)` of the dry cell if the electrode potential of cathode `(E^(c-)._(reduction ))` varies between `0.49V` and `0.74V` and that of anode `E^(c-)._(reduction) ` is `-0.76V`.

Explanation

The electrode reactions are as follows`:`
Anode reaction `:`
`Zn(s)rarr Zn^(2+)(1.0M) + cancel(2e^(-))(o x i dation)E^(c-)._(reduction)=-0.76V`
Cathode reaction `:`
`8 overset(o+)(N)H_(4)(aq)+2MnO_(2)(s)+cancel(2e^(-))rarr2Mn^(3+)(aq)+8NH_(3)(g)+4H_(2)O(l)(` Reduction `)`
Cell reaction `:`
`ulbar(Zn(s)+8overset(o+)(N)H_(4)(aq)+2MnO_(2)rarr2Mn^(3+)(aq)+8NH_(3)(g)+Zn^(2+)+4H_(2)O(l))`
`(E^(c-)._(reduction))_(cathode)` varied between `0.49` to `0.74V`.
For `(E^(c-)._(reduction ))_(cathode)=0.49V,`
.E^(c-)._(cell)=(E^(c-)._(reduction))_(cathode)`-(E^(c-)._(reduction))_(anode)`
`=0.49-(-0.76)=1.25V`
For `(E^(c-)._(reduction))_(cathode)=0.74V`,
`E^(c-)._(cell)=0.74-(-0.76)=1.50V`
`E^(c-)._(cell)` varies between `1.25V` and `1.50 `.