Question

At –13.0 °C (a common temperature for household freezers), what is the maximum mass of aspartame (C14H18N2O5) you can add to 1.50 kg of pure water and still have the solution freeze? Assume that aspartame is a molecular solid and does not ionize when it dissolves in water. Kf values are given here.

Answer 1

for the solution to get frozen at -13 deg.c

deltaTf = Kf b i, i= Van't hoff factor= 1 since the solud does not ionize, kf= 1.86 deg.c.kg/mole

for freezing to take place, the temperature has to be 0 deg.c, which gives rise to depression in freezing point of 13 deg.c

deltaTf= 13 deg.c = 1.86*m*1

m= 13/1.86= 7 mol/kg

but mass of water= 1.5 kg, so moles of the solid required= 7*1.5= 10.5 moles

molar mass of aspartame (C14H18N2O5) = 12*14+18+2*24+5*16= 294

moles of solid= 294*10.5= 3087 gm= 3.087 kg