What is the minimum mass?

2019-03-04 10:53 pm
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?

回答 (2)

2019-03-04 11:17 pm
✔ 最佳答案
Normal boiling point of water = 32.0°F
ΔTf = [32.0 - (-18.8)] °F = 50.8 °F = 50.8 °F × (5 °C / 9 °F) = 28.22 °C
i = 1
Kf = 1.86 °C kg/mol
m = ? mol/kg

ΔTf = i Kf m
28.22 °C = 1 × (1.86 °C kg / mol) × m
Molality, m = 28.22/1.86 mol/kg

Molar mass of C₂H₆O₂ (ethylene glycol) = (12.0×2 + 1.0×6 + 16.0×2) g/mol = 62.0 g/mol
Minimum mass of C₂H₆O₂ needed = (28.22/1.86 mol/kg) × (14.5 kg) × (62.0 g/mol) = 13600 g = 13.6 kg
2019-03-04 11:16 pm
Convert farenheit temperture to celcius gives -28.1 C

Since water freezes at 0C, and since Kf for water = -1.86 C/m, calculate the molality of the needed solution:

-28.1 C = -1.86 C/m (m)
m = 15.1 m

So, for each kilogram of water, you would need 15.1 moles ethylene glycol. For 14.5 kg water, then,

15.1 mol / kg X 14.5 kg = 219 mol ethylene glycol

Mass ethylene glycol = 219 mol X 62.07 g/mol = 1.36X10^4 g = 13.6 kg ethylene glycol


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