How do I calculate the percentage by mass of a metal within an impure substance?

For this question we will look at Sodium Sulphite (Na₂SO₃) and its titration against Potassium Permanganate (KMnO₄). This requires acidic conditions.

In this example we need to know several things:

That 1.5g of the impure substance was dissolved and made up to a 100cm³ solution.

That 25cm³ of this solution was titrated against 35.1cm³ of 0.015

moldm^-3 KMnO₄^-.

Step 1) First we need to balance the equation for the reaction of Na₂SO₃ with KMnO₄.

Use ionic half equations first to work out the change in oxidation state.

Mn0₄^- + 2H⁺ + 5e^- --> Mn²⁺ + H₂O  

In Mn0₄^- manganese has the oxidation state +7 (due to oxygen being -2) and in Mn²⁺ it has the oxidation state +2. Hydrogen and oxygen do not change oxidation state. This means the oxidation state has changed by -5 overall, so there must be 5e^- on the left hand side to balance this.

In the other half equation we see that

SO₃^2- + H₂O --> SO₄^- + 2H⁺ + 2e^-

In SO₃^2- sulphur has the oxidation state +4 and in SO₄^2- has the oxidation state +6. Hydrogen and oxygen again do not change. This means the oxidation state has change by +2 overall, so there must be 2e^- on the right hand side to balance this.

From these two equations we can make the full ionic equation, which is written as

2MnO₄^- + 6H⁺ + 5SO₃^2- --> 2Mn²⁺ + 5SO₄^2- + 3H₂O

Step 2) Calculate the moles of MnO₄^- used.

Conc = moles/volume and therefore moles= conc x volume

moles = 0.015 x 0.0371   be careful to convert units from cm³ to dm³ here

             = 5.565x10^-4

Step 3) Calculate the moles of SO₃^2- reacted.

Using stoichiometric relationships we can see that 2MnO₄^- reacts with 5SO₃^2-, and therefore

moles SO₃^2- = 5/2 x moles MnO₄^-

                         = 1.39x10^-3

Step 4) Calculate total moles of SO₃^2-

In the information at the beginning of the question it says that the original mass of substance was dissolved in 100cm3, but only 25cm3 was used in the titration. Therefore, to get the total moles we need to multiply by 4.

Total moles = 5.565x10-3

Step 5) Calculate mass of Na present

As there are two atoms of Na per Na₂SO₃ then the moles of SO₃^2- must be doubled to find the total mass of Na.

Mass = moles x molecular mass

           = 2 x 5.565x10-3 x 23.0

           = 0.25599

Step 6) Calculate the percentage by mass

Percentage = mass of Na/total mass x 100

                       = 0.25599/1.5 x 100

                       = 17.1%