How to Calculate Freezing Point Depression

How to Calculate Freezing Point Depression This example problem demonstrates how to calculate freezing point depression using solution of salt in water. Quick Review of Freezing Point Depression Freezing point depression is one of the colligative properties of matter, which means it is affected by the number of particles, not the chemical identity of the particles or their mass. When a solute is added to a solvent, its freezing point is lowered from the original value of the pure solvent. It doesnt matter whether the solute is a liquid, gas, or solid. For example, freezing point depression occurs when either salt or alcohol are added to water. In fact, the solvent can be any phase, too. Freezing point depression also occurs in solid-solid mixtures. Freezing point depression is calculated using Raoults Law and the Clausius-Clapeyron Equation to write an equation called Blagdens Law. In an ideal solution, freezing point depression only depends on solute concentration. Freezing Point Depression Problem 31.65 g of sodium chloride is added to 220.0 mL of water at 34  °C. How will this affect the  freezing point of the water?Assume the  sodium chloride completely dissociates in the water.Given: density of water at 35  °C 0.994 g/mLKf water 1.86  °C kg/molSolution:To find the  temperature change elevation of a solvent by a solute, use the freezing point depression equation:ΔT iKfmwhereΔT Change in temperature in  °Ci van t Hoff factorKf molal freezing point depression constant or cryoscopic constant in  °C kg/molm molality of the solute in mol solute/kg solvent.Step 1 Calculate the molality of the NaClmolality (m) of NaCl moles of NaCl/kg waterFrom the periodic table, find the atomic masses of the elements:atomic mass Na 22.99atomic mass Cl 35.45moles of NaCl 31.65 g x 1 mol/(22.99 35.45)moles of NaCl 31.65 g x 1 mol/58.44 gmoles of NaCl 0.542 molkg water density x volumekg water 0.994 g/mL x 220 mL x 1 kg/1000 gkg water 0.219 kgmNaCl moles of NaCl/kg watermNaCl 0.542 mol/0.219 kgmNaCl 2.477 mol/kgStep 2 Determine the van t Hoff factorThe van t Hoff factor, i, is a constant associated with the amount of dissociation of the solute in the solvent. For substances which do not dissociate in water, such as sugar, i 1. For solutes that completely dissociate into  two ions, i 2. For this example, NaCl completely dissociates into the two ions, Na and Cl-. Therefore, i 2 for this example.Step 3 Find ΔTΔT iKfmΔT 2 x 1.86  °C kg/mol x 2.477 mol/kgΔT 9.21  °CAnswer:Adding 31.65 g of NaCl to 220.0 mL of water will lower the freezing point by 9.21  °C.