Question

What mass of salt (nacl) should you add to 1.80 l of water in an ice cream maker to make a solution that freezes at -13.4 ∘c ? assume complete dissociation of the nacl and density of 1.00 g/ml for water?

Answer 1

We will use this formula:
Δ T = i*Kf*C
when i = vant Hoff factor = 2
Kf = Constant 1.86 °C/m
and C = Concentration of molality
ΔT =13.4 °C

So by substitution:
C = ΔT/(i*Kf)
= 13.4 / (2*1.86)
= 3.6 m

when molality = moles of solute / Kg of solvent
note molar mass of NaCl = 58.5 g /mol
∴mass of NaCl = 1.8 Kg * (3.6m NaCl / 1Kg) *(58.5 g /mol)
= 379 g