a. `25 mL` of sample of saturated solution of `PbI_(2)` requires `10mL` of a certain `AgNO_(3)(aq)` for its titration. What is the molarity of this `AgNO_(3)(aq)? K_(sp)` of `PbI_(2) = 4 xx 10^(-9)`.
b. `M(OH)x` has `K_(sp) = 27 xx 10^(-12)` and solubility in water is `10^(-3)M`. Calculate the value of `x`.

Explanation

a. For `PbI_(2), S =3sqrt((K_(sp))/(4)) =3sqrt((4xx10^(-9))/(4)) = 10^(-3)`
`{:(PbI_(2)hArr,Pb^(2+)+,2I^(Theta),,),(,S,S,,):}`
`:. [I^(Theta)] = 2S = 2 xx 10^(-3)M`
Now, for: `Ag^(o+) + I^(Theta) rarr AgI`
`mEq of Ag^(o+) = mEq of I^(Theta)`
`N xx 10 = 2 xx 10^(-3) xx 25`
`N` or `M of AgNO_(3) = 5 xx 10^(-3)`
b. `{:(M(OH)_(x)hArr,M^(+x)+,xoverset(Theta)OH,,),(,S,xS,,):}`
`K_(sp) = S xx (xS)^(x) = x^(x). S^((1+x))` (Given `S = 10^(-3))`
`27 xx 10^(-12) = x^(x). 10^((1+x)) :. x = 3`
Thus hydroxide is `M(OH)_(3)`.