Question

One useful method for recycling scrap aluminum converts some of it to common alum [potassium aluminum sulfate dodecahydrate, KAl(SO4)212 H2O], an important dyefixative and food preservative. 4 significant figures.

(a) How many moles of potassium ions are in 356 g alum?

(b) What is the mass % S in alum (to 3 significant figures)?

(c) What is the maximum amount of alum (in metric tons) that can be prepared from 24.3 metric tons of scrap aluminum (1 metric ton = 1000 kg)?

Answer 1

a) to calculate the mols of potassium ions, calculate the molar mass of alum which is 474.22
Take the grams of alum /(molar mass of alum) to calculate how many moles you have. (256/474.22)=.5398338324
From the chemical formula there will be 1 mole of potassium ions in 1 mole of alum. You can see this because the subscript for potassium is 1. So sincethere is .5398338324 moles of product there will be that many moles of potassium ions. So your answer with significant figures taken into account will be.5398 moles potassium ions

b) Assume you have 1 mole of the compound which is 474.22. Calculate how many grams of sulphur will be present There are two sulfurs, so it will be 64.14.Now to calculate the mass percent take (64.14/474.22)=.1352536797x100

Accounting for sig figs the answer will be .135 or 13.5%

c) To calculate this take the moles that are in 24.3 metric tons of aluminum and that will be the maximum amount of alum that can be generated because 1mole of aluminum provides 1 mole of alum. Assume that the scrap aluminum is pure aluminum. Calculate the amount of moles of aluminum in 24.3 metric tons.900667.1609 then multiply that by the molar mass of alum 474.22. This will give you the grams of alum produced. Then divide by 1000. Divide by 1000 againand this will give you the answer of 427.1 metric tons of alum