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A copper - silver cell is set up . The ...

A copper - silver cell is set up . The copper ion concentration in it is 0.10 M. concetration of silver ion is not known . The cell potential measured 0.422 V. determine the concentration of silver ion in the cell.
Given : `E_(Ag+//Ag)^(@)=+0.80V,E_(Cu^(2+)//Cu)^(@)=+0.34V.`

Text Solution

Verified by Experts

The given cell may be represented as
`Cu_(s)|Cu ^(2+) (0.10M)\\Ag^(+) (C )|Ag_(s)`
`E_(cell)^(@) = E_("cathode")^(@)-("anode") = 0.80V - 0.34V = 0.46 V`
`E_(cell)^(@) = E_(cell)^(@)(0.0591)/(2)log([Cu^2+])/([Ag^(+)]^(2)`
or `0.422V-0.46V- (0.0591)/(2) log (0.1)/([Ag^(+)]^(2)`
`-0.038V = -0.0295 log (0.1)/([Ag^(+) ]^(2)` or , log`(0.1)/([Ag^(+)]^(2) = (-0.038)/(-0.0295) = 1.288`
or log`(0.1)/([Ag^(+)]^(2) = ("antilog")1.288 = 19.41` `therefore ([Ag^(+))]^(2)= (0.1)/(19.41) = 5.1519xx10^(-3)`
`([Ag^(+)] = 7.1 xx10^(-2) M`
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