To `500cm^(3)` of water, `3.0 xx 10^(-3) kg` acetic acid is added. If `23%` of acetic acid is dissociated, what will be the depression in freezing point? `K_(f)` and density of water are `1.86 K kg mol^(-1)` and `0.997 g cm^(-3)` respectively.

Explanation

`{:(,CH_(3)COOHhArrCH_(3)COO^(-)+H^(+),),("Initial"," 1 mole 0 0 ",),("After disso. "," 1 - 0.23 0.23 0.23"," Total = 1.23 moles"):}`
`therefore " van't Hoff factor, i = 1.23"`
Mass of water (solvent) `=500xx0.997=498.5g`
No. of moles of acetic acid `=(3xx10^(-3)xx10^(3))/(60)=0.05`
`therefore" Molality of the solution "=(0.05)/(498.5)xx1000=0.1`
`DeltaT_(f)=iK_(f)m=1.23xx1.86xx0.1=0.228K`