Question

In ice-cream making, the ingredients are kept below 0.0 degrees C in an ice-salt bath. (a) Assuming that NaCl dissolves completely and forms an ideal solution, what mass of it is needed to lower the melting point of 5.5 kg of ice to - 5.0 degrees C? (b) Given the same assumptions as in part (a), what mass of CaCl2 is needed?

Answer 1

NaCl dissolves completely forming 2 ions Na+ and CL-, hence the vont hoff factor for NaCl will be equal to 2

5 = m * 1.86 * 2

m = molality = 1.344

Number of moles = molality * weight of ice = 1.344 * 5 = 6.72 moles

Molar mass of NaCl = 23 + 35.5 = 58.5 gm/mol

Mass of NaCl required = number of moles * molar mass = 6.72 * 58.5 = 393.12 gms

CaCl2 dissolves completely forming 3 ions 1 Ca+ and 2 Cl-, hence the vont hoff factor for CaCl2 will be equal to 3

5 = m * 1.86 * 3

m = molality = 0.896

Number of moles = molality * weight of ice = 0.896 * 5 = 4.48 moles

Molar mass of CaCl2 = 40 + 2 * 35.5 = 111 gm/mol

Mass of NaCl required = number of moles * molar mass = 4.48 * 111 = 497.28 gms