Calculate the mass of ascorbic acid (Vitamin `C, C_(6)H_(8)O_(6)`) to be dissolved in 75 g g of acetic acid to lower its melting point by `1.5^(@)C, [K_(f)=3.9" K kg mol"^(-1)]`.

Explanation

Mass of acetic acid, `w_(1)=75 g`
Molar mass of ascoric acid `(C_(6)H_(8)O_(6))`,
`M_(2)=6xx12+8xx1+6xx16=176g mol^(-1)`
Lowering of melting point, `Delta T_(f)=1.5 K`
We know that :
`K_(f)=3.9" K kg mol"^(-1)`
`Delta T_(f)=(K_(f)xx w_(2)xx1000)/(M_(2)xx w_(1))`
`w_(2)=(Delta t_(f)xx M_(2)xx w_(1))/(K_(f)xx1000)=(1.5xx176xx75)/(3.9xx1000)`
= 5.08 gram
= 5.08 g (approx)
Hence, 5.08 g of ascorbic acid is needed to be dissolved.