Answer to Question #75832 in General Chemistry for Ernst Cariño

Question

What volume of ethylene glycol, an anti-freezing agent, C2H6O2 (p=1.12g/ml) must be added to 20.0ml of water in a car radiator to produce a solution that freezes at -10.0C?

Answer 1

Answer: 5.95 ml

delta Tf = Kf × m

where delta Tf = depression in freezing point

since pure water freezes at 0 degree C but this solution is freezing at -10.0 ...so delta Tf = 10.0

Kf = 1.86 deg /m

m = molality of solute = n of moles of solute/amount of solvent in kg

n of moles of C2H6O2 (solute) = given weight of C2H6O2/molecular mass = w/M

M for C2H6O2 = 62 g/mole

so n of moles = w/62

volume of water = 20 ml

density of water = mass of water/volume of water

so mass of water = density of water × volume of water

so mass of water = 1 × 20 = 20 g

mass of water in kg (solvent) = 0.02 kg

so molality = w/62 / 0.02 = w/1.24

delta Tf = Kf × m

10 = 1.86 × w/1.24

w = 10 × 1.24 /1.86 = 6.67 g
V = m/p
V = 6.67/1.12 = 5.95 ml