0.5 molal aqueous solution of a weak acid (HX) is 20% ionised. If `K_(f)` of water is 1.86 K kg `"mol"^(-1)` , the lowering in freezing point of the solution is :

Options

A. 0.56 K
B. 1.12 K
C. `-0.56` K
D. `-1.12` K

Answer

B

Explanation

`{:(,"HX",hArr,H^(+),+,X^(-)),("Initial moles",1,,0,,0):}`
If `alpha` is the degree of dissociation, then moles after dissociation.
`{:(1-alpha,,,alpha,,alpha):}`
Total moles after dissociation `=1-alpha+alpha+alpha=1+alpha`
`i=(1+alpha)/(1)=(1+0.2)/(1)=1.20`
`DeltaT_(f)=iK_(f)`
`=1.20xx1.86xx0.5=1.12K`