a) An ice cream recipe calls for 2 cups (400 g) sugar (sucrose, C12H22O11) to sw

Question

a) An ice cream recipe calls for 2 cups (400 g) sugar (sucrose, C12H22O11) to sweeten 1.8 L of whole milk The density of milk is 1.04 g/mL. Assuming all other ingredients do not change the freezing point of the mixture, how cold must the ice cream freezer be, in order to freeze the ice cream?

b) For an old fashioned ice cream freezer, a rule of thumb says that you should use a 5-to-1 ratio of ice to salt, NaCl (so 5 kg of ice would need 1 kg of salt) to make the freezing mixture. What is the minimum temperature the freezer will reach?

Explanation / Answer

m = 400 g and n = 2

total mass = 800 g of sucrose

V = 1.8 L milk

D = 1.04 g/mL = 1.04 kg per liter

find Tfreezing mix

dTf = -Kf*m

m = mol os solute / kg solvent

kg of solvent = 1.8*1.04 = 1.872 kg of solvent

mol solute = mass/MW = (800)/342.2965 = 2.33715 mol of Sucrose

m = mass / MW / kg solvent = (2.33715)/(1.872) = 1.248 molal

dTf = -1.86*1.248 = -2.32128 ªC

so

Freezer must be at leas -2.32128 C lower to be ice

b)

5-1 ratio of ice to salt

to make freezing mix

find Tfreez

dTf = -K*m*i

i = 2 ions

molality = mol of solute / kg solvent

mol of solute = 1000/58 = 17.241 mol of NaCl

kg of solvent = 5 kg of ice

so

molal = 17.241/5 = 3.4482 molal

so

dTf 0 -1.86*3.4482*2 = -12.827304 C

Tf = -12.83 C at least

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