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The sp cond of a saturated solution of A...

The sp cond of a saturated solution of `AgCI` at `25^(@)C` after substractin the sp conductances of conductivity of water is `2.28 xx 10^(-6) mho cm^(-1)`. Find the solubility product of `AgCI` at `25^(@)C(lambda_(AgCI)6(oo) = 138.3 mho cm^(2))`

Text Solution

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For equilibrium,
`AgCl = Ag^(+) + Cl^(-)`
`K_(sp) [Ag^(+)][Cl^(-)]`
If the solubility of AgCl in water is, say, x moles/litre or x eq./L,
`K_(sp) = x.x = x^(2)`
`therefore` volume containing 1 eq. of AgCl `= (1000)/(x)`
`Lambda_(AgCl) = "sp. cond. xx V`
`= 2.28 xx 10^(-6) xx (100)/(x)`.
Since AgCl is sparingly soluble in water, `Lambda_(AgCl) = Lambda_(AgCl)^(@) = 138.3`
`therefore 2.28 xx 10^(-6) xx (1000)/(x) = 138.3`
or `x = 1.644 xx 10^(-5)` eq./litre or mole/litre
`K_(sp) = x^(2) = (1.644 xx 10^(-5))^(2)`
`= 2.70 xx 10^(-10) ("mole/litre")^(2)`
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