The balanced chemical equation is 2AlBr₃ + 3K₂SO₄ → 6KBr + Al₂(SO₄)₃
Law of Conservation of Matter
When we look closely at the given reaction which is
AlBr₃ + K₂SO₄ → KBr + Al₂(SO₄)₃
Aluminuim is not balance, potassium is not balanced, bromine is also not balanced as well as oxygen and sulphur.
To do that, let's pick the reactant side
2AlBr₃ + 3K₂SO₄
Adding two moles to the aluminuim bromide will give us 2 atoms of aluminuim and 6 atoms of bromine while 3 moles to potassium sulphate will give us 6 atoms of potassium, 3 atoms of sulphur and 12 atoms of oxygen.
To ensure that law of conservation of matter is maintained here, our product should be
6KBr + Al₂(SO₄)₃
This shows that there's no loss of matter.
The overall balanced chemical equation is
2AlBr₃ + 3K₂SO₄ → 6KBr + Al₂(SO₄)₃
At the end of this, we can see that
2 moles of aluminuim at the reactant is reflected at the product
6 moles of bromine at the reactant is reflected at the product
6 moles of potassium at the reactant is reflected at the product
3 moles of sulphur at the reactant is reflected at the product
12 moles of oxygen at the reactant is reflected at the product
From the explanation above, the balanced equation is
2AlBr₃ + 3K₂SO₄ → 6KBr + Al₂(SO₄)₃