Titration calculations
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The actual mathematics required for a titration calculation is straightforward arithmetic and simple proportion. However, there are several points that students need to understand and be able to string together. Therefore, titration calculations can be broken down into small steps that help students to develop understanding.
Consider what is meant by each step in the following sequence:
Review the experimental results.
Irregular titres are ruled out and concordant titres are used to take the average (or 'mean') titre.
Express volumes, typically cm3, in dm3 or litres.
Typical data from experiments is expressed in cm3. Divide by 1000 to get the value in dm3.
Use the formula, number of moles = concentration x volume.
Use this formula to work out the number of moles of acid or base, where you know the concentration and the volume.
Write a balanced chemical equation.
It's necessary to write a balanced equation for the reaction of the acid and alkali to check the ratio of acid to alkali. Often it is 1:1.
How many moles?
The number of moles of acid or alkali has been calculated from the known volume and known concentration already. The ratio of acid to alkali in the reaction has been established from the balanced equation. Therefore, the number of moles of the solution of unknown concentration can be written.
Rearrange the formula.
Because number of moles = concentration x volume, it follows that concentration = number of moles/volume.
Calculate the unknown concentration.
Use the rearranged formula and the known number of moles and volume to calculate the concentration.
An example of a student's results for an acid and alkali titration has been written on the board shown. The first calculation steps have been written:
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Check through the steps that the student has written. Is this correct?
Yes, so far as it goes. The number of moles of NaOH = 0.0025 and the ratio of NaOH to HCl is 1:1.
Complete the final steps to find the concentration of the hydrochloric acid.
Because the no. of moles NaOH = no. of moles HCl, the number of moles HCl = 0.0025 moles. Rearranging the mathematical equation gives concentration = no. moles / volume.
Concentration of HCl = 0.0025 / 0.0125 = 0.20 mol dm–3
If a diprotic acid such as H2SO4 was used in a similar titration, what difference would this make to the calculation?
The balanced equation, 2NaOH + H2SO4 2H2O + Na2SO4, shows that the ratio of NaOH to H2SO4 is 2:1. Therefore, the number of moles of alkali is twice the number of moles of acid, and this ratio must be taken into account when calculating the number of moles of H2SO4 that must neutralise the NaOH in the flask.
Further practice with titration calculations of volumes, concentrations and number of moles can be freely accessed from the RSC's Problem solving tutor, including the 'storyboarding' of titration calculations.