Answer :
Answer : The maximum mass of sucralose is, 7952.8 grams.
Explanation : Given,
Molal-freezing-point-depression constant [tex](K_f)[/tex] for water = [tex]1.86^oC/m[/tex]
Mass of water (solvent) = 2.00 kg
Molar mass of sucralose = 397.64 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 sucralose}}{\text{Molar mass of sucralose}\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]-18.6^oC[/tex]
[tex]\Delta T^o[/tex] = freezing point of water = [tex]0^oC[/tex]
i = Van't Hoff factor = 1 (for sucralose 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-(-18.6)^oC)=1\times (1.86^oC/m)\times \frac{\text{Mass of sucralose}}{397.64g/mol\times 2.00kg}[/tex]
[tex]\text{Mass of sucralose}=7952.8g[/tex]
Therefore, the maximum mass of sucralose is, 7952.8 grams.