Question

What mass of salt (NaCl) should you add to 1.98 L of water in an ice cream maker to make a solution that freezes at -15.0 ∘C ? Assume complete dissociation of the NaCl and density of 1.00 g/mL for water.

Answer 1

Tf = To - Tf = 0 - (-15) = 15 oC

i value for NaCl = 2 (NaCl has 2 ions)

Kf of water = 1.86 oC / m

Tf = i x Kf x m

15 = 2 x 1.86 x m

m = 4.032 m

molality = 4.032 m

mass of water solvent = volume x density

= 1.98 x 10^3 x 1

= 1980 g

= 1.98 kg

molality = moles of NaCl / mass of water

4.032 = moles of NaCl / 1.98

moles of NaCl = 4.032 x 1.98

moles of NaCl = 7.984

mass / molar mass = 7.984

mass = 7.984 x 58.5

mass = 467 g

mass of salt NaCl = 467 g