When `2.5 mL` of `2//5M` weak monoacidic base `(K_(b) = 1 xx 10^(-12) at 25^(@)C)` is titrated with `2//15 M HCI` in water at `25^(@)C` the concentration of `H^(o+)` at equivalence point is `(K_(w) = 1 xx 10^(-14) at 25^(@)C)`

Options

A. `3.7 xx10^(-13)M`
B. `3.2 xx10^(-7)M`
C. `3.2 xx10^(-2)M`
D. `2.7 xx10^(-2)M`

Answer

D

Explanation

`BOH +HCl to BCl +H_(2)O`
`{:(B^(+),+,H_(2)O, hArr,BOH,+,H^(+)),(c(1-h),,,,ch,,ch):}`
Volume of HCl used ` = (2.5 xx2/5)/(2//15) = 7.5 ` ml
Concentration of Salt , ` c = (2.5 xx2/5)/(10) = 0.1 M `
` (CH^(2))/(1-h) = (K_(w))/(K_(b))`
On Solving , h = 0.27 (hence h cannot be ignored with respect to 1 )
`[H^(+)] = Ch = 0.1 xx 0.27 = 2.7 xx10^(-2) M `