The acid ionization constant for
`Zn^(2+)+H_(2)O hArr (OH^(+)) + H^(+)`
is `1.0 xx 10^(-9) ` .Calculate the pH of `0.0010` M solution of `ZnCl_(2)` . Also calculate basic dissociation constant of `Zn(OH)^(+)`

Explanation

`Zn^(2+) +H_(2)O hArr Zn(OH)^(+) + H^(+) `
` :. [H^(+)] = C.h =Csqrt((K_(H))/(C)) = sqrt((K_(H))/(C))`
` = sqrt((K_(w))/(K_(b).C))" " [("where "K_(b) " is basic dissociation constant "),("of " Zn(OH) "i.e ., " Zn(OH)^(+) hArr Zn^(2+) +OH^(-))]`
We know `Zn^(2+)` and `Zn(OH)^(+)` are conjugate acid and base .
` :. K_(a) xx K_(b) = 10^(-14)`
or `K_(b) = (10^(14))/(10^(-9)) = 10^(-5)`
Now , `[H^(+)] = sqrt((10^(-14))/(10^(-5)xx0.001)) = sqrt(10^(-12)) = 10^(-6)`
pH = 6