Brass is a substitutional alloy consisting of a solution of...

Brass is a substitutional alloy consisting of a solution of copper and zinc. A particular sample of red brass consisting of 80.0$\%$ Cu and 20.0$\%$ Zn by mass has a density of 8750 $\mathrm{kg} / \mathrm{m}^{3} .$ (a) What is the molality of $\mathrm{Zn}$ in the solid solution? (b) What is the molarity of $\mathrm{Zn}$ in the solution?

Transcript

00:01 In this problem, we're given an alloy that's 80 % copper, 20 % zinc, and it's density, and we're asked to find the molality of zinc.

00:10 Students struggle with this kind of problem because they feel like they don't know how much they're working with, and what you have to realize is that these are concentrations.

00:18 It doesn't matter if you have one cubic centimeter of this alloy or a whole ton of this alloy.

00:25 The concentrations are all going to be the same.

00:27 So let's, for the sake of simplicity, and you can pick any amount that you want, but for the sake of simplicity, let's assume that we have one cubic meter, that's the three, of the alloy.

00:47 If we have one cubic meter of the alloy, then we know that we have 8 ,750 kilograms, right? because that's its density.

01:00 So i found that using the density.

01:02 So if that's my total mass, then i can find how much mass corresponds to the copper and how much mass corresponds to the zinc.

01:16 Now remember that for molality, what i need is moles of solute.

01:21 In this case, copper is the solute, and the solvent is the zinc because there's more zinc.

01:35 Sorry, i have that backwards.

01:39 I have that backwards.

01:41 The copper, the copper is the solvent.

01:52 That's what i was trying to say.

01:57 The copper is the solvent, and the zinc is the solute.

02:04 So if we know that the total mass is 8750, then that's in kilograms.

02:18 Then we know that 20 % of that is zinc, so i'm going to write that as a decimal.

02:26 That means that the mass that is zinc is equal to 17 ,050 kilograms.

02:33 Now, i need moles of zinc, and i have molar mass and grams per mole, so i'm going to change this kilograms to grams, multiply by 1 ,000.

02:43 It's an outrageously large mass, but remember that we're trying to pick numbers that are easy to work with.

02:48 So 1 ,750 multiplied by, that's how many grams we have.

02:57 We're going to divide by the molar mass of zinc if we look up our periodic table.

03:01 That's 65 .38 grams of zinc for every one mole of zinc.

03:08 This is zinc.

03:09 And what we find is we have 26 ,770 moles of zinc.

03:18 I know that looks outrageous...

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