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Calculate the potential of a half cell ...

Calculate the potential of a half cell having reaction : `Ag_2 S (s) + 2e^- iff 2Ag (S) + S^(2-) (aq)` in a solution buffered at `p^(H) =3` and which is also saturated with ` 0.1 MH_2S (aq)`
[Given : `K_(sp)(Ag_2 S ) = 2 xx 10^(-49) , K_(a1). K_(a2) = 1.1 xx 10^(-21) , E_(As^(+) // Ag)^(@) = 0.8V`]

A

`-0.19 V `

B

`0.19 `

C

` 1.18 V `

D

`-0.166 V `

Text Solution

Verified by Experts

The correct Answer is:
D
`K_a = K_(a1). K_(a_2) = ((H^(oplus))^(2)(S^(-2)))/([H_2S]) `........... (1) , `K_(sp) = [Ag^(oplus)][S^(-2)] `........ (2)
`((1))/((2)) = (K_(a))/(K_(sp))=([H^(oplus)]^(2))/([H_2S]) xx ([S^(2)])/([Ag^(ox)][S^(-2)]), (1.1 xx 10^(-21))/(2 xx 10^(-49)) = (10^(-6) xx 1)/( 0.1 xx [Ag^(oplus)]) implies (Ag^(oplus)) = 4.264 xx 10^(-17) M`
` E_(S^(-2)) . // Ag_2S // Ag =E_(Ag^(+)//Ag)^(0) to (0.859)/(1-1) , E = 0.8 - (0.0591)/(1) log""((1)/(4.264 xx 10^(-17)))`
`=0.8p + (0.0591 xx-16.37 ) = (0.8 - 0.9675 ) , E = - 0.166`
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