What mass of ethylene glycol (C2H6O2, molecular weight 62.1 g) must be added to 20.00 L of water to produce a solution for use in a car's radiator that freezes at -15 degrees centigrade?

(The density of water is 1 Kg L^-1. The molal freezing point depression constant for water, Kf, is 1.86 degrees centigrade Kg mol^-1)

Question

What mass of ethylene glycol (C2H6O2, molecular weight 62.1 g) must be added to 20.00 L of water to produce a solution for use in a car's radiator that freezes at -15 degrees centigrade?

(The density of water is 1 Kg L^-1. The molal freezing point depression constant for water, Kf, is 1.86 degrees centigrade Kg mol^-1)

anonymous · Answer

delta T = Kf m
delta T = 15K
Kf= 1.86
Let x be the mass of ethylene glycol, then number of moles of ehtylene glycol will be
x/62.1

Molality m = x/(62.1*20)
So,
15=1.86*x/(62.1*20)
x=15*62.1*20/1.86 = 10016.129 gram
=10 kg approx