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

Answer

`5.077g`

Explanation

`Mw_(2)(C_(6)H_(8)O_(6))=12xx6+1xx8+6xx16=72+87+96`
`=176gmol^(-1)`
`Mw_(1)(CHM_(3)COOH)=60g mol^(-1)`
`DeltaT_(f)=1.5^(@)K_(f)=3.9K kg mol^(-1)`
`W_(1)(CHM_(3)COOH)=75g, W_(2)=?`
Applying the formula,
`DeltaT_(f)=K_(f)xxm=K_(f)xx(W_(2)xx1000)/(Mw_(2)xxW_(1))`
`1.5K=3.9K kg mol^(-1)xx(W_(2)xx1000)/(176g mol^(-1)xx75g)`
`:. W_(2)=(1.5xx176g mol^(-1)xx75g)/(3.9xxK kgmol^(-1)xx1000)`
`=5.0769~~5.077g `