Respuesta :
Answer : The minimum mass of ethylene glycol is, 12000.2 grams.
Explanation : Given,
Molal-freezing-point-depression constant [tex](K_f)[/tex] for water = [tex]1.86^oC/m[/tex]
Mass of water (solvent) = 14.5 kg
Molar mass of ethylene glycol = 62.07 g/mole
Formula used :
[tex]\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}}[/tex]
where,
[tex]\Delta T_f[/tex] = change in freezing point
[tex]\Delta T_s[/tex] = freezing point of solution = [tex]-12.6^oF=-24.8^oC[/tex]
Conversion used :
[tex]^oF=\frac{9}{5}^oC+32[/tex]
[tex]\Delta T^o[/tex] = freezing point of water = [tex]0^oC[/tex]
i = Van't Hoff factor = 1 (for non-electrolyte)
[tex]K_f[/tex] = freezing point constant for water = [tex]1.86^oC/m[/tex]
m = molality
Now put all the given values in this formula, we get
[tex]0^oC-(-24.8^oC)=1\times (1.86^oC/m)\times \frac{\text{Mass of ethylene glycol}}{62.07g/mol\times 14.5kg}[/tex]
[tex]\text{Mass of ethylene glycol}=12000.2g[/tex]
Therefore, the minimum mass of ethylene glycol is, 12000.2 grams.
