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 a m urea solution, `DeltaT_(f)=K_(f)m` gives
`K_(f)=1.86^(@)C//m`
For acetic acid, `DeltaT_(f)=iK_(f)m`
`0.2046=ixx1.86xx0.01 or I = 1.1`
`{:(,CH_(3)COOH,hArr,CH_(3)COO^(-),+,H^(+)),("Initial","C mol L"^(-1),,,,),("After disso.",C-Calpha,,Calpha,,Calpha","):}`
`" Total "=C+C alpha=C(1+alpha)`
`therefore" "i=(C(1+alpha))/(C)=1+alpha or alpha=i-1=0.1`
`[H^(+)]=Calpha=(0.01)(0.1)=10^(-3M`
Hence, `pH=3`