The freezing point of solution containing 10 mL of non-volatile and non-electrolyte liquid "A" in 500 g of water is `-0.413^@C`. If `K_f` of water is 1.86 K kg `mol^(-1)` and the molecular weight of `A=60 g mol^(-1)` , what is the density of the solution in g `mL^(-1)` ?
(Assume `Delta_(mix)` V=0)

Options

A. 1.13
B. 1.3
C. `0.90`
D. `0.993`

Answer

D

Explanation

Given,
Volume of solute = 10 mL
`Delta T_(f)=0-(-0.413)=0.413^(@)C`
w (solvent) = 500 g
`K_(f)` (water) `=1.86" K kg mol"^(-1) (= w_(A))`
Molecular weight of (A) or `M_(B)=60` g
Let mass of solute `(A) =w_(B)`
`:. Delta T_(f)=K_(f)xx w_(B)/M_(B)xx1000/w_(A)`
`0.413 =1.86xxw_(B)/60xx1000/500`
`:. w_(B)=(0.413xx60xx500)/(1.86xx1000)`
Mass of solute `=6.66 g`
Also,
`:'` Density (d) of solution `=("Total mass")/("Total volume")`
`=(6.66+500)/(500+10)=506.66/10=0.993 ("g mL"^(-1))`
Density (d) of solution `=0.993"g mL"^(-1)`
Hence, option (d) is the correct answer.