What mass of salt (NaCl) should you add to 1.00 L of water in an ice-cream maker to make a solu

What mass of salt (NaCl) should you add to 1.00 L of water...

What mass of salt (NaCl) should you add to $1.00 \mathrm{~L}$ of water in an ice-cream maker to make a solution that freezes at $-10.0^{\circ} \mathrm{C} ?$ Assume complete dissociation of the $\mathrm{NaCl}$ and density of $1.00 \mathrm{~g} / \mathrm{mL}$ for water.

Key Concepts

Van't Hoff Factor

The Van't Hoff factor is used to account for the effect of solute dissociation in solution. It indicates the number of particles a solute produces when it dissolves and is crucial for accurately calculating the impact on colligative properties like freezing point depression.

Molality

Molality is a concentration unit defined as the number of moles of solute per kilogram of solvent. It is particularly useful in calculations involving temperature changes, such as freezing point depression, because it remains constant regardless of temperature fluctuations.

Colligative Properties

These are properties of solutions that depend on the ratio of solute particles to solvent molecules, such as vapor pressure lowering, boiling point elevation, freezing point depression, and osmotic pressure. They are important in studying how solutes affect the behavior of solvents.

Freezing Point Depression

This is the lowering of a solvent's freezing point due to the presence of a solute. It is a colligative property, which means that the effect depends on the number of dissolved particles rather than their identity.

Transcript

00:01 This problem, we're going to have to do a little algebra to solve for the amount of sodium chloride needed to lower the freezing point.

00:12 So we actually know what the freezing point is.

00:15 They actually tell us a change.

00:17 So we dealt in front of us.

00:18 The change in the freezing point they give us is 10 degrees celsius.

00:24 And i just turned into a positive number, even though it is a negative number.

00:27 We know that the constant or the freezing point is 1 .86 degrees celsius per malau.

00:45 Malau is something we actually don't know, since we don't know, the amount of the solute or the amount of the sodium or the sodium chloride needed.

00:58 So we're going to leave this as m for now.

01:02 And they tell us complete disassociation now.

01:05 When nacl gets dropped into water, basically gets converted into its ionic states, na plus, cl minus.

01:17 And then water pretty much surrounds all of them, keeping them separate.

01:25 So you have all this nacl running around in solution.

01:31 Because of that, because it dissociated completely, there are two of them.

01:37 We use that number two.

01:40 So first things first, we need to figure out what we can figure out for the malau.

01:45 They give us a few things about it.

01:48 Just to recall, malau is moles of the solute over the kilograms of solution.

01:59 Sorry, kilograms of the solvent, not the solution.

02:07 Well, we don't know the moles, so we let's x.

02:14 We do know the kilograms.

02:16 We knew something about the solvent.

02:18 So we know there's one liter of the solvent.

02:22 And we can do a few conversions from this.

02:25 We know that for every one liter is about one millimeter.

02:38 And what you may not know, then we can convert this, they give us a density.

02:43 So for every one gram, there's one militre...

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