Compute the freezing point of this mixture (in °C).?

May 2021 2 90 Report

Compute the freezing point of this mixture (in °C).?

Homemade ice-cream is frozen by churning it in a bucket suspended in an ice-water-salt mixture. A typical mix calls for 2.50 kg of salt (NaCl) and 6.25 kg of ice.

Science & Mathematics / Chemistry

Arcturus C

Verified answer

Use the formula for freezing point depression: ΔTf = Kf * mB where Kf is the constant for water (1.86 (kg*K)/mol) and mB is the molality of the solute (mol/kg).

NaCl has a molar mass of 58.44 g/mol or 0.05844 kg/mol.

2.50 kg of NaCl therefore contains 44.779 moles of NaCl.

However, remember NaCl is dissociated in water, making Na+ and Cl- ions. Therefore, there are 44.779*2 = 89.56 moles of solute in your 6.25 kg of solvent. So the molality (moles of solute per kg of solvent) is 89.56/6.25 = 14.33 mB.

14.33*1.86 = 26.65 K.

The freezing point thus depressed by 26.65 K = 26.65 deg C. 0 - 26.65 = -26.65 deg C.