Calculate mole fraction of ethanol and water in a sample of rectified spirit which contains 92% ethanol by mass.

Answer

`x_("Ethanol") = 0.88 ; x_("Water") =0.12`

Explanation

Mass of solution = 100 g (say)
Mass of ethanol = 95 g
Mass of water = 100 - 95 = 5 g
Molar mass of ethanol, `C_(2) H_(5) OH = 46 g mol^(-1)`
Molar mass of water
`H_(2) O = 18 g mol^(-1)`
`n_("ethanol") = (5)/( 46) mol = 2 . 065`
`n_("water") = ( 5)/( 18) ` mol = 0 . 27
`x_("ethanol") = (n _("ethanol"))/(n _("ethanol") + n_("water"))`
`= (2 . 65)/( 2 . 065 + 0 . 278 ) = ( 2 . 0 65)/( 2 . 343)`
`= ( 2 . 0 65)/( 2 . 343) = 0 . 88`
`x_("water") = 1 - x_("ethanol")`
` 1 - 0 . 88 = 0 . 12 `