The depression in freezing point of `0.01 m` aqueous `CH_(3)CooH` solution is `0.02046^(@)`, `1 m` urea solution freezes at `-1.86^(@)C`. Assuming molality equal to molarity, `pH` of `CH_(3)COOH` solution is

Options

A. 2
B. 3
C. `3.2`
D. `4.2`

Answer

B

Explanation

For urea, `DeltaT_(f)=K_(f)xxm` or `K_(f)=(DeltaT_(f))/(m)=(1.86)/(1)=1.86`
Now for `CH_(3)COOH`
`DeltaT_(f)=iK_(f)m`
so `i=(0.02046)/(1.86xx0.01)=1.1`
Now `i=1+alpha
so `alpha=1.1-1=0.1`
Now `CH_(3)COOHhArrCH_(3)COO^(-)+H^(+)`
`{:(C,0,0),(C-Calpha,Calpha,Calpha):}`
`[H^(+)]=Calpha=0.01xx0.1=0.001`
so `pH=3`.