`30 mL` of `CH_(3)OH (d = 0.8 g//cm^(3))` is mixed with `60 mL` of `C_(2)H_(5)OH(d = 0.92 g//cm^(2))` at `25^(@)C` to form a solution of density `0.88 g//cm^(3)`. Select the correct option(s) :

Options

A. Molarity and molarity of resulting solution are `6.33 M` and `13.59 m` respectively.
B. The molar friction of solute and molarity are `0.38` and `13.59 m` respectively.
C. Molarity and percentage change in volume are `13.5 M` and zero repectively.
D. Mole fraction of solvent and molality are `0.62` and `13.59 m` respectively.

Answer

B, D

Explanation

`CH_(3)OH` is solute (less amount)
Mass of `CH_(3)OH = 30 xx 0.8 = 24 g`
Mass of `C_(2)H_(5)OH = 60 xx 0.92 = 55.2 g`
Mass of solution `= 79.2 g`
Volume of solution `= (79.2)/(0.88) = 90 mL`
Moarity `= (n_(CH_(3)CH))/(V(L)) = (24//32)/(90) xx 1000 = 8.33 M`
Molarity `= (24//32)/(55.2) xx 1000 = 13.59 m`
Mole fraction of solute `= ((24)/(32))/((24)/(32) + (55.2)/(46)) = 0.38`
Mole fraction of solvent `= 1 - 0.38 = 0.62`