Question

At what temperature will water freeze if 100g NaCl are dissolved in 500g H2O?

water's Kf = 1.86 °C/m

Answer 1

Answer : The temperature at which water freeze will be,
`-12.7^oC`

Explanation : Given,

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

Mass of NaCl (solute) = 100 g

Mass of water (solvent) = 500 g = 0.500 kg

Molar mass of NaCl = 58.5 g/mole

Formula used :

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

where,

`\Delta T_f` = change in freezing point

`\Delta T_s` = freezing point of solution = ?

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

i = Van't Hoff factor = 2 (for NaCl 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-T_s=2* (1.86^oC/m)* (100g)/(58.5g/mol* 0.500kg)`

`T_s=-12.7^oC`

Therefore, the temperature at which water freeze will be,
`-12.7^oC`