Question

If pK_b for CN⁻ at 25°C is 4.7, the pH of 0.5 M aqueous NaCN solution is ______.

Options

• 12

• 10

• 11.5

• 11

Answer 1

If pK_b for CN⁻ at 25°C is 4.7, the pH of 0.5 M aqueous NaCN solution is 11.5.

Explanation:

\[\ce{CN^- + H2O -> HCN + OH^-}\]; pK_b = 4.7 ∴ pK_a = 9.3

[OH⁻] = ch = `"c" sqrt(("K"_"H")/"c") = sqrt("K"_"H"."c") = sqrt(("K"_"w")/"K"_"a" . "c")`

= `sqrt((10^-14 xx 0.5)/(10^(-9.3)))`

[OH⁻] = `sqrt(10^-4.7 xx 0.5)`

∴ pH = 11.5