Back titration to determine the amount of an inert solid

You have read the exam question carefully and decided that the following are the key bits of information:

  • 100 cm3 of 0.1 mol/dm3 HCl is added to 0.240 g of a mixture containing Mg(OH)2 and an inert solid.
  • The resulting solution is made up to 250 cm3 with distilled water.
  • 25 cm3 of the solution is titrated with 22.1 cm3 of 0.02 mol/dm3 NaOH.
  • Calculate the mass of inert solid in the sample.
Step 1

We know that moles = concentration x volume:

HCl = 0.1 x (100 / 1000) =  0.01 mol.

n NaOH = 0.02 x (22.1 / 1000) =  4.42 x 10-4 mol.

Step 2

The balanced symbol equations aren’t given so we need work them out.

Reaction 1: 2 HCl + Mg(OH)2 –> MgCl2 + 2 H2O 

Reaction 2: HCl + NaOH –> NaCl + H2O 

Step 3

The balanced symbol equation for Reaction 2 tells us that HCl and NaOH react in a 1:1 ratio so the HCl moles at the start of Reaction 2 was:

n HCl = 1 x 4.42 x 10-4 = 4.42 x 10-4 mol

Step 4

The total is 10x bigger than the sample (i.e., 250 / 25) so we can work out the HCl moles at the end of Reaction 1.

n HCl = 10 x 4.42 x 10-4 = 4.42 x 10-3 mol

(NB: The original sample volume of 100 cm3 is not relevant to the calculation here; this is because the dilution from 100 cm3 to 250 cm3 does not change the number of moles)

Step 5

We know that there was 0..01 mol HCl at the start and 4.42 x 10-3 mol HCl at the end of Reaction 1. By subtraction, we can work out the HCl moles used up in Reaction 1:

0.01  – 4.42 x 10-3 = 5.58 x 10-3 mol

Step 6

From Reaction 1, we know that HCl and Mg(OH)2 react in a 2:1 ratio, so:

n Mg(OH)2 = 0.5 x 5.58 x 10-3 = 2.79 x 10-3 mol

Step 7

Now that we have the moles of Mg(OH)2 we can work out the mass of Mg(OH)2 using its Mr (58.3):

m Mg(OH)2 = 58.3 x 2.79 x 10-3 = 0.163 g

Step 8

The mass of the inert solid is then found by subtracting the mass of Mg(OH)2 from the total mass:

0.240 – 0.163 = 0.077 g