Question

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 −12.6°F? (Assume ideal behavior.)

Answer 1

Answer : The minimum mass of ethylene glycol is, 12000.2 grams.

Explanation :  Given,

Molal-freezing-point-depression constant $(K_f)$ for water = $1.86^oC/m$

Mass of water (solvent) = 14.5 kg

Molar mass of ethylene glycol = 62.07 g/mole

Formula used :  

$\Delta T_f=i\times K_f\times m\\\\T^o-T_s=i\times K_f\times\frac{\text{Mass of ethylene glycol}}{\text{Molar mass of ethylene glycol}\times \text{Mass of water in Kg}}$

where,

$\Delta T_f$ = change in freezing point

$\Delta T_s$ = freezing point of solution = $-12.6^oF=-24.8^oC$

Conversion used :

$^oF=\frac{9}{5}^oC+32$

$\Delta T^o$ = freezing point of water = $0^oC$

i = Van't Hoff factor = 1 (for non-electrolyte)

$K_f$ = freezing point constant for water = $1.86^oC/m$

m = molality

Now put all the given values in this formula, we get

$0^oC-(-24.8^oC)=1\times (1.86^oC/m)\times \frac{\text{Mass of ethylene glycol}}{62.07g/mol\times 14.5kg}$

$\text{Mass of ethylene glycol}=12000.2g$

Therefore, the minimum mass of ethylene glycol is, 12000.2 grams.