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

Options

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

Answer

D

Explanation

Let 'v' ml of HCl is used reach equivalence point
`2.5xx 2/5= Vxx2/15 implies V=7.5ml`
Number of moles of salt formed =1m mole
Final total volume =2.5 + 7.5 = 10ml
Final conc. of salt`=1/10 = 0.1M`
`K_(h)=K_(w)/K_(b)=10^(-14)/10^(-12) = 10^(-2) implies K_(h)=(Ch^(2))/(1-h)` (we cannot assume (1-h) approx. 1)
Solve quadratic to find 'h', here, h=0.27
`[H^(+)] = Ch=0.1xx0.27=2.7xx10^(-2)M`