A 50.0 -mL solution is initially 1.55% MgCl2 by mass and has a density of 1.05 g / mL . What is

step 1 All right, question 124. A 50 milliliter solution is initially 1 .55 by mass of magnesium chlori

A 50.0 -mL solution is initially 1.55% MgCl2 by mass and has...

Key Concepts

Freezing Point Depression

Freezing point depression is a colligative property where the addition of a solute to a solvent lowers the freezing point of the resulting solution compared to that of the pure solvent. This phenomenon is attributable to the disruption of the solvent’s crystal lattice formation by the solute particles.

Colligative Properties

Colligative properties depend only on the number of solute particles relative to the solvent and not on the nature of the solute itself. They include freezing point depression, boiling point elevation, osmotic pressure, and vapor pressure lowering, illustrating how solute concentration influences the thermodynamic properties of solutions.

Molality

Molality is a concentration unit defined as the number of moles of solute per kilogram of solvent. It is especially useful in colligative property calculations because it is independent of temperature, making it a stable measure when assessing changes in physical properties such as freezing point.

Van't Hoff Factor

The van't Hoff factor (i) represents the number of particles into which a solute dissociates in solution. In freezing point depression calculations, it accounts for the effective increase in solute particles, thereby amplifying the colligative effect on the freezing point.

Transcript

00:01 All right, question 124.

00:03 A 50 milliliter solution is initially 1 .55 by mass of magnesium chloride.

00:10 And the solution has a density of 1 .05 gram per millimeter.

00:16 The question is asking us, after you add another 1 .35 grams of the solute, what is the new freezing point of the solution? so we'll start by writing down some data that we know.

00:30 The volume of the solution is equal to 50 milliliter.

00:36 And we know the mass percent of magnesium chloride is 1 .55 percent by mass.

00:48 So this also means that 1 .55 grams of magnesium chloride is present in 100 grams of solvent.

01:01 In our case it's the water.

01:04 So now the mass of the solvent can be converted to volume by using the density equal to 1 .05 gram per milliliter.

01:16 So we have the volume equal to mass divided by density equal to 100 gram divided by 1 .05 gram per milliliter and we get 95 .2 milliliter.

01:36 So 1 .55 gram is in 95 .2 milliliter.

01:42 So now we want to find the amount or the mass of magnesium chloride instead of 95 .2 militer, what's in 50 militer? so we have 1 .55 gram divided by 95 .2 militer times 50 militer.

02:11 So 1 .55 divided by 95 .2 means that each milliliter contains how much gram.

02:20 And then multiplied by 50, we will get 0 .814 gram.

02:27 So this is the mass of magnesium chloride in 50 milliliter of solvent.

02:44 So next step, we have 1 .3 35 gram of magnesium chloride is added to the solution.

03:02 So now the total mass present in this 50 milliliter of solution is 0 .814 is the previous amount and is added by 1 .35.

03:22 So we get the total mass of magnesium chloride equal to 2 .16 grams.

03:29 So the total mass of magnesium chloride in 50 milliliter solution is 2 .16 gram.

03:47 All right now, since the mass of 15 militer solution is calculated by mass equal to volume times density, so that's 50 milliliter times 1 .05 gram per milliliter, we get 52 .5 gram.

04:10 So the mass of 50 milliliter of solvent is 52 .5 grams.

04:16 So the amount of solute present in 1 ,000 gram of solution.

04:34 This can be calculated in 2 .16 gram is in 52 .5 gram of solution.

04:45 So in the case of 1 ,000 gram, we will get a number of 41 .14...

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