queston in description

Question

An ice cream maker workss on the principle that salt water freezes at a much colder temperature than pure water. Rock salt ( NaCI) is mixed with crushed ice to produce a slurry that cools the milk and cream. If you want a water-salt Mixture to freeze at 0 F. How many grams of rock salt must you add to 0.347 kilograms of water to make this solution?

 

I need helping working this out 

Answer 1

First, it is easiest to convert ºF to ºC.

5/9(F-32) = 5/9(0-32) = 5/9(-32) = - 17.8ºC 

Now, for the colligative property equation for freezing point depression:

∆T = imK

∆T = change in temperature = -17.7ºC

i = van't Hoff Factor = 2 for NaCl (1Na⁺ and 1 Cl^-)

m = molality = moles NaCl/kg water = ?

K = freezing constant for H2O = -1.86ºC/m

Solving for m:  m = -17.7/(2)(-.186) = 4.78 moles/kg

Solving for moles of NaCl:  4.78 moles/Kg = x moles/0.347 kg and x = 1.66 moles NaCl

Solving for grams of NaCl:  1.66 moles x 58.4 g/mole = 96.8 g NaCl needed