Now that we have put a coefficient of 3 in front of caso4 and a coefficient of 3 in front of cacl2, what coefficient should go in front of alcl3 to balance both the cl atoms and the al atoms?
3caso4 + ? alcl3 --> 3cacl2 + al2(so4)3

The coefficient of AlCl₃ should be 2

Explanation:

In the given reaction, calcium sulphate (CaSO₄) reacts with aluminium chloride (AlCl₃) to give calcium chloride (CaCl₂) and aluminium sulphate (Al₂(SO₄)₃)

In a balanced chemical equation, quantity of elements on the left side or reactant side should be equal to the quantity of elements on the right side or product side of the chemical reaction, according to the law of conservation of mass.

On reactant side, there are 3 calcium atoms, 3 sulphur atoms and 12 oxygen atoms in 3CaSO₄ and 1 aluminium atom and 3 chlorine atoms in AlCl₃.

Whereas, on the product side, there are 3 calcium atoms, 6 chlorine atoms in 3CaCl₂ and 2 aluminium atoms, 3 sulphur atoms, and 12 oxygen atoms in Al₂(SO₄)₃.

So, all the other atoms except aluminium (Al) and chlorine (Cl) atoms are not balanced in the given chemical equation.

Therefore, in order to balance the number of aluminium (Al) and chlorine (Cl) atoms, AlCl₃ is given the coefficient 2.

Now, there are 2 Al atoms, 6 Cl atoms, on the reactant as well as the product side of the chemical equation.

Therefore, the balanced chemical reaction is:

3CaSO₄ + 2AlCl₃ → 3CaCl₂ + Al₂(SO₄)₃