Answer to Question #322434 in General Chemistry for Psychopomp

Question

Salt is often used to melt ice and snow on roads in the winter and the temperature right now is -4.500°C. How much NaCl (complete dissociation) would be necessary to melt 1000kg of ice by bringing down the freezing temperature to -4.500°C?

Answer 1

Solution:

The lowering (depression) of the freezing point of the solvent can be represented using the following equation: 

Δt = i × K_f × m

where:

Δt = the change in freezing point

i = the van't Hoff factor

K_f = the freezing point depression constant

m = the molality of the solute

 

The normal freezing point of pure water is 0.0°C

Therefore, Δt = 0.0°C − (−4.500°C) = 4.500°C

i = 2 (for NaCl)

K_f = 1.86°C kg mol¯¹ (for water)

 

Thus,

m = Δt / (i × K_f)

Molality of NaCl solution = (4.500°C) / (2 × 1.86°C kg mol¯¹) = 1.2097 mol kg¯¹

Molality = Moles of solute / Kilograms of solvent

Therefore,

Moles of NaCl = Molality of NaCl solution × Kilograms of water

Moles of NaCl = 1.2097 mol kg¯¹ × 1000 kg = 1209.7 mol

 

The molar mass of NaCl is 58.44 g/mol

Therefore,

Mass of NaCl = (1209.7 mol NaCl) × (58.44 g NaCl / 1 mol NaCl) = 70695 g NaCl = 70.695 kg NaCl

Mass of NaCl = 70.695 kg

Answer: 70.695 kilograms of NaCl