12Experiment 1: Colligative Properties Determination of the Molar Mass of a Compound by Freezing Point Depression. Objective:The objective of this experiment is to determine the molar mass of an unknown solute by measuring the freezing point depression of a solution of this solute in a solvent as compared to the freezing point of the pure solvent. Background:Colligative propertiesare properties of a solvent, such as freezing point depression and boiling point elevation, which depend on the concentration of solute particles dissolved in the solvent. The decrease in freezing point, ΔTf(freezing point depression) for a near ideal solution can be described by the equation: ΔTf= kf· mEq 1 where kfis the molal freezing point depression constantof the solvent with units °C · kg solvent/mole solute. mis the molal concentration of the solute dissolved in the solvent expressed as moles of solute/kg solvent. Since the molar mass M(traditionally and often, but erroneously called the molecular weight) of a compound has units g/mole, we can solve for moles and substitute the result into the molal concentration relationship, and then into Eq 1 as is shown below. M= g/ mole Eq 2 Rearranging Eq 2 gives moles = g/MEq 3 Now substituting Eq 3 into the unit definition of molality yields m = g/(M· kg solvent) Eq 4 And substituting Eq 4 into Eq 1 gives ΔTf= (kf· g)/(M· kg solvent) Eq 5 We can rearrange Eq 5 and solve for the molar mass, mol wt, as is shown in Eq 6, below. M= (kf· g)/(ΔTf· kg solvent) Eq 6 Therefore, if we know the mass of unknown compound added to a known mass of solvent and determine the change in freezing point of the solution, relative to pure solvent, we can use Eq 6 to determine the molar mass of the unknown compound. At the freezing point of any substance, an equilibrium exists in which both liquid and solid are present. liquid ⇄solid Eq 7
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