A solution of urea boils at `100.18^(@)C` at the atmospheric pressure. If `K_(f)` and `K_(b)` for water are `1.86` and `0.512K kg mol^(-1)` respectively, the above solution will freeze at,

Options

A. `-6.54^(@) C`
B. `6.54^(@)C`
C. `0.654^(@)C`
D. `-0.654^(@)C`

Answer

D

Explanation

For water (same solution)
`(Delta T_(f))/(Delta T_(b)) = K_(f)/K_(b)`
`:. Delta T_(f) = (0.512 xx 0.18^(@)C)/1.86 = 0.654`
`[(Delta T_(b) = T_(b) - T^(@))=100.18^(@)-100^(@) = 0.18^(@) C]`
`:. Delta T_(f) = T^(@) - T_(f)`
`:. T_(f) = T^(@) - Delta T_(f)`
`T_(f) = O^(@) C - 0.654^(@)C = -0.654^(@)C`