Step 1 - Reading the chemical equation
The exercise says alum can be synthesized from metal aluminum. As the process involves several steps with different reactions, let's just write the equation in a simplified way:
There are, of course, a lot more reagentes in the right hand side, but we don't need to know them to still solve this question. What really matters is the proportion between Al and KAl(SO₄)₂·12H₂O.
To 'read' a chemical equation properly, we must remember the bigger numbers, those that come before the formulas of each substance, represent its number of moles. Therefore, we can state that:
one mole of Al produces one mole of KAl(SO₄)₂·12H₂O
Step 2 - Converting moles to grams
Now that we have obtained a relation in moles, we can convert it to grams. In order to do so, we just need to multiply each number of moles by the respective molar mass of the substances:
We can thus rewrite the statement in step 1 as:
26.98g of Al produces 474.38g of KAl(SO₄)₂·12H₂O
This is like a 'recipe' for this reaction, and we'll use it to predict how much alum will be formed if we start with different amouns of Al.
Step 3 - Finding how much alum should be produced
Since we used 0.45g of aluminum, we should have produced:
Step 4 - Determining the percent yield
We should have produced 7.91g of alum, but only 5.47g were indeed produced. Therefore, the percent yield will be:
The yield percent for this reaction is thus 69.15%.