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

Answer

C

Explanation

`{:(B^(+)+,H_2O hArr, BOH+, H^(+)),(c(1-h),,ch,ch):}`
For titration
`N_1V_1=N_2V_2`
`2/15xxV_1=2.5xx2/5`
`therefore V_1` = Volume of HCl used, V=7.5 mL
In resulting solution ,
Conc. Of salt =[BCl]=`(2//5xx2.5)/10`=0.1
`K_w/K_b=(ch^2)/(1-h)` or `h=sqrt(K_w/(K_bxxc))`
`sqrt(10^(-14))/(10^(-12)xx0.1) rArr h=sqrt(1/10)`
`[H^+]=ch=0.1 xxsqrt(1/10)=3.2xx10^(-2)` M