Question

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

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 :  

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

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

$0^oC-T_s=2\times (1.86^oC/m)\times \frac{100g}{58.5g/mol\times 0.500kg}$

$T_s=-12.7^oC$

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