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

SO32- + H2O --> SO4- + 2H+ + 2e-

In SO32- sulphur has the oxidation state +4 and in SO42- 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+ + 5SO32- --> 2Mn2+ + 5SO42- + 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 SO32- reacted.

Using stoichiometric relationships we can see that 2MnO4- reacts with 5SO32-, and therefore

moles SO32- = 5/2 x moles MnO4-

                         = 1.39x10-3

Step 4) Calculate total moles of SO32-

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 SO32- 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%

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