Volume percent?

Question

What is the volume percent of ethanol in a solution that is 24.3% by mass ethanol (d = 0.789 g/mL) in an aqueous solution with d = 0.963 g/mL?

Answer 1

Let M = mass of solution

    V = volume of solution

    D = density of solution

    m = mass of ethanol

    v = volume of ethanol

    d = density of ethanol

v/V = volume % of ethanol in solution

m/M = mass % of ethanol in solution

0.243 = m/M

D = M/V

d = m/v

D/d = (M/V) / (m/v) = (M/m)(v/V) = (v/V) / (m/M)

0.963/0.789 = (v/V) / (0.243)

v/V = 0.963/0.789*0.243

v/V = 0.2966 = 29.66 %