An ethylene glycol solution contains 21.2 g of ethylene glycol (C2 H6 O2) in 85.4 mL of water.

step 1 Here we have problem 78. An ethylene glycol solution contains 21 .2 grams of ethylene glycol in

An ethylene glycol solution contains 21.2 g of ethylene...

Key Concepts

Colligative Properties

Colligative properties are characteristics of solutions that depend on the number of solute particles present rather than their specific identity. They include effects such as freezing point depression, boiling point elevation, vapor pressure lowering, and osmotic pressure. These properties illustrate how dissolved substances alter the physical properties of the solvent.

Freezing Point Depression

Freezing point depression is the phenomenon where the addition of a solute lowers the freezing point of a solvent. It is quantified by the equation ?Tf = Kf · m, where ?Tf is the decrease in freezing temperature, Kf is the cryoscopic constant of the solvent, and m is the molality of the solution. This concept is fundamental in understanding why adding solutes boosts the temperature at which a solution solidifies compared to the pure solvent.

Boiling Point Elevation

Boiling point elevation refers to the increase in boiling point experienced by a solvent when a nonvolatile solute is added. This effect is described by the equation ?Tb = Kb · m, where ?Tb is the elevation in boiling temperature, Kb is the ebullioscopic constant of the solvent, and m is the molality of the solution. This concept is crucial for explaining how the presence of solutes makes it more difficult for the solvent to reach the vapor pressure necessary for boiling.

Molality

Molality is a concentration unit defined as the number of moles of solute per kilogram of solvent. It is used in colligative property calculations because it is independent of temperature and volume changes, making it a reliable measure for determining how the concentration of a solution affects its physical properties, such as freezing point depression and boiling point elevation.

Transcript

00:01 Here we have problem 78.

00:02 An ethylene glycol solution contains 21 .2 grams of ethylene glycol in 85 .4 milliliter of water.

00:14 Assume that the density for water is 1 gram per milliliter, we're going to determine the freezing point and the boiling point for the solution.

00:23 So the data we have is the mass ethylene glycol is equal to 21 .2 grams.

00:42 And the molar mass of ethylene glycol is equal to 62 .068 grams per mole.

00:59 So the moles of ethylene glycol is equal to the mass divided by molar mass, that is 21 .2 gram divided by 62 .068 grams per mole, and this is equal to 0 .342 mole.

01:24 So here we have the number of moles of ephylene glycol, 0 .342 moles.

01:32 The problem is also telling you the volume of the water is 85 .4 .4.

01:42 Millimeter and the density of water is equal to one grams per militer so we can calculate the mass of the water so mass of the water is equal to the volume of the water times the density of the water so 85 .4 militer times one gram per militer equal to 85 .4 grams and that is equal to 0 .080 854 kilogram.

02:21 So we have the moles of ethylene glycol and we have the mass of the solvent water.

02:33 Now we can calculate the molality of ethylene glycol.

02:39 So the molality is equal to the most of the solid ethylene glycol in moles divided by the mass of the solvent, water in kilogram and this is equal to 0 .342m divided by 0 .0854 kilograms.

03:12 So we get a number of 4 molar.

03:18 So the molality of the solution is equal to 4 molar.

03:23 So that is the we have the formula delta t f equal to kf times m in this equation delta t f is the depression in freezing point k f is the freezing point depression constant and the small m is the molality and for water we know that the freezing point tf is equal to 0 celsius degree.

04:38 So let's calculate the delta tf.

04:42 Delta tf is equal to kf.

04:46 So kf of water is equal to 1 .86 celsius per molar.

04:55 So this is delta tf is equal to 1 .86 celsius per mole.

05:07 Times the molality, which is 4 molar times 4.

05:13 This will give us a number of 7 .44 celsius degree.

05:19 So the depression of freezing point is 7 .44 degree...