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Titration!

There is a question which I don't fully understand:-

A student carried out a titration to find the concentration of phosphoric acid in a solution.

50cm3 of phosphoric acid solution was neutralised by 28cm3 of a sodium hydroxide solution of concentration 0.50 mol dm-3.

The equation for this reaction is:

3NaOH(aq) + H3PO4(aq) -> Na3PO4(aq) + 3H2O(l)

(a) Calculate the number of moles used.

(b) Calculate the concentration of phosphoric acid in moles per cubic decimetre (mol dm-3)

This is what I would do:-

(a) Moles = Concentration x Volume
Moles = 0.50 x (28 / 1000) - This would convert the volume into dm3 from cm3.
Moles = 0.50 x 0.028
Moles = 0.014 -> Which is correct.

(b) Concentration = Moles / Volume
Concentration = 0.014 / (50 / 1000)
Concentration = 0.28 -> Which is wrong.

The correct working is as follows (for part (b)):-

0.33 moles H3PO4 reacts with 1 Mole NaOH
Moles H3PO4 in 50cm3 = 0.014 x 0.33
Therefore moles H3PO4 in 1 dm3 = (0.014 x 0.33 x 1000) / 50
= 0.09

I don't get it.
Reply 1
The equation tells you that NaOH and H3PO4 react in a 3:1 ratio.

So for every 1 mole of H3PO4 you need 3 moles of NaOH.
i.e. moles H3PO4 = one third = 0.33 moles NaOH.

You have found the conc of NaOH = 0.28 mol dm-3
This means there are 0.28 moles of NaOH in 1000cm

If 0.28 moles of NaOH react then moles of H3PO4 that react must be one third of the moles of NaOH.

i.e. 0.28 divided by 3 = 0.9 moles

0.9 moles of H3PO4 react with 0.28 moles NaOH per 1000cm

hope that helps
the number of moles you have found out in part a) needs to be divided by 3 because its a 3:1 ratio. now use this new number of moles in the equation conc=number of moles/volume

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