What is the minimum mass of ethylene glycol (C2H6O2) that must be dissolved in 14.5 kg of water to prevent the solution from freezing at −18.6°F? (Assume ideal behavior.)
g?
Sol . As Freezing point of solution = - 18.6 °F = (-18.6 - 32) × 5/9 = - 28.11°C
Freezing point of solvent (water) = 0°C
So , Depression in freezing point = deltaTf = Freezing point of solvent - Freezing point of solution
= 0 - ( - 28.11)
= 28.11°C
Now , deltaTf = Kf × m
where kf = freezing point depression constant
m = molality of solution
For water , Kf = 1.86 °C/m
So , m = deltaTf / Kf = 28.11 / 1.86 = 15.1129 m
As Molar mass of ethylene glycol = 62.07 g/mol
Mass of water = 14.5 Kg
So,
molality of solution = Mass of ethylene glycol (in g)
/ ( Molar mass of ethylene glycol (in g/mol) × Mass of water (in Kg) )
And , Mass of ethylene glycol ( in g) = 15.1129 × 62.07 × 14.5
= 13601.8366 g
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