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 xx 10^(-13)M`
B. `3.2 xx 10^(-7) M`
C. `3.2 xx 10^(-2)M`
D. `2.7 xx 10^(-2)M`

Answer

C

Explanation

`underset("Base")(N_(1)V_(1))=underset("Acid")(N_(2)V_(2))`
`2.5 xx (2)/(5)=(2)/(15)xx V_(2)` or `V_(2)=(15)/(2)mL =7.5 mL`
`BOH +HCl rarr BCl +H_(2)O`
2.5 mL of 2 M base contain base
`=(2.5 xx 2)/(5)=1 m` mol
`:. `salt of BCl formed `=1 m `mL
volume of solution `=2.5 mL +7.5 mol =10mL`
`:. `conc. of salt (BCl) in solution `=(1)/(10)M=0.1 M`
For the salt of weak base and the strong acid
`[H^(+)]=sqrt((K_(w)C)/(K_(b)))=(10^(-14)xx0.1)/(10^(-12))=3.2 xx 10^(-2)M`