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The standard reduction potential for two...

The standard reduction potential for two reactions are given below
`AgCl(s)+e^(-)rarrAg(s)+Cl^(-)(aq) ,E^(@)=0.22V`
`Ag^(+)(aq)+e^(-)rarrAg(s),E^(@)=0.80V`
The solubility product of AgCl under standard conditions of temperature is given by

A

`1.6 xx 10^(-5)`

B

`1.5 xx 10^(-8)`

C

`3.2 xx 10^(-10)`

D

`1.5 xx 10^(-10)`

Text Solution

Verified by Experts

The correct Answer is:
D
Subtracting eqn. (ii) from eqn (i)
`AgCl (s) hArr Ag^(+) (aq) + Cl^(-) (aq) E^(@) = -0.58 V`
`E = E^(Theta) - (0.059)/(1) "log" ([Ag^(+)][Cl^(-)])/([AgCl(s)])`
At equilibrium , E = 0 and `[Ag Cl (s) ] = 1`
`E^(@) = 0.059 log [Ag^+] [Cl^-]`
`0.059 log K_(sp)`
`therefore 0.059 log K_(sp) = -0.58`
`log K_(sp) = -9.831`
`therefore K_(sp) = 1.48 xx 10^(-10)`
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