Question

At -18.6 °C, a common temperature for household freezers, what is the maximum mass of sucralose (C₁₂H₁₉Cl₃O₈) in grams you can add to 2.00 kg of pure water and still have the solution freeze?

Assume that sucralose is a molecular solid and does not ionize when it dissolves in water.

`K_f` = 1.86 °C/m.

Answer 1

Answer : The maximum mass of sucralose is, 7952.8 grams.

Explanation : Given,

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

Mass of water (solvent) = 2.00 kg

Molar mass of sucralose = 397.64 g/mole

Formula used :

`\Delta T_f=i* K_f* m\\\\T^o-T_s=i* K_f*\frac{\text{Mass of sucralose}}{\text{Molar mass of sucralose}* \text{Mass of water in Kg}}`

where,

`\Delta T_f` = change in freezing point

`\Delta T_s` = freezing point of solution =
`-18.6^oC`

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

i = Van't Hoff factor = 1 (for sucralose 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-(-18.6)^oC)=1* (1.86^oC/m)* \frac{\text{Mass of sucralose}}{397.64g/mol* 2.00kg}`

`\text{Mass of sucralose}=7952.8g`

Therefore, the maximum mass of sucralose is, 7952.8 grams.