Science, Tech, Math › Science Freezing Point Depression Example Problem Calculate the Freezing Point Depression Temperature Share Flipboard Email Print Freezing Point Depression: Water will form ice at a lower temperature when a solute is added to the water. nikamata/Getty Images Science Chemistry Basics Chemical Laws Molecules Periodic Table Projects & Experiments Scientific Method Biochemistry Physical Chemistry Medical Chemistry Chemistry In Everyday Life Famous Chemists Activities for Kids Abbreviations & Acronyms Biology Physics Geology Astronomy Weather & Climate By Todd Helmenstine Todd Helmenstine is a science writer and illustrator who has taught physics and math at the college level. He holds bachelor's degrees in both physics and mathematics. our editorial process Todd Helmenstine Updated October 05, 2018 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 doesn't 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 Raoult's Law and the Clausius-Clapeyron Equation to write an equation called Blagden's 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.