###### Titration and Back Titration Calculations

Chemistry (Year 12) - Volumetric Analysis

Siobhan O'Halloran

# Titration Calculations

Titrations typically involve the reaction of an acid and base. One will have a known concentration, while the other will have an unknown concentration. Using the information gained while conducting a titration, calculations can help to determine the value of the unknown concentration.

Step 1: Determine the stoichiometric ratio between the acid and base being titrated by setting up the neutralisation equation. This is the balanced equation between the acid and base to form an ionic salt and water. For example:

Step 2: Determine the number of moles of the solution with the known concentration (i.e. the standard solution). Use the equation n = cV, where c is the concentration of the standard solution, and V is the average titre volume.

Step 3: Determine the number of moles of the solution with the unknown concentration (i.e. the analyte). This can be determined by multiplying the moles of the standard solution (calculated in Step 2) by the molar ratio between the acid and base.

Step 4: Determine the unknown concentration. Use the equation c = n/V, where n is the moles of the analyte calculated in Step 3, and V is the volume of the analyte solution pipetted into the concical flask.

# Dilution Factor

If there is a large difference in the concentration of the acid and base involved in the titration, this may result in either very small or very large volumes of titre solutions being required to reach neutralisation. Therefore, dilution may be conducted before beginning the titration to ensure more reasonable titre volumes.

A dilution factor can be calculated to determine the affect of the dilution on the titration, as this is the factor by which the concentration of a dilution solutoin has decreased.

If dilution is carried out on the analyte solution (solution with an unknown concentration), calculations from Step 1-3 remain the same, however, the final concentration determined in Step 4 will be the concentration of the diluted solution. Therefore, to find the original concentration, an extra step is added: multiply the concentration of the diluted solution by the dilution factor.

# Back Titrations

Back titrations involve 2 processes. Firstly, an analyte with an unknown concentration is added to an excess amount of an acid or base (with a known concentration). Secondly, the excess acid or base (containing the reacted analyte) is titrated against another acid or base with a known concentration.

Step 1: Write out the balanced equations for the reaction of the analyte and excess solution, and for the titration of the excess acid or base with another acid or base.

Step 2: Determine moles of excess acid or base (n(excess)) using the titration reaction. The moles of the acid or base with a known concentration can be determined using n = cV, where c is the known concentration, and V is the average titre. This value can then be multiplied by the molar ratio to determine the moles of excess acid or base left over from the analyte reaction.

Step 3: Determine total number of moles (n(total)) with n = cV, using the known concentration and volume of the excess acid or base. Then, using the equation below, determine the number of moles of the analyte which initially reacted (n(initially reacted)).

Step 4: Determine the moles of the analyte dissolved by multiplying the n(initially reacted) by the molar ratio of the equation.

# Titration worked example | Elucidate Video

In the above video, Henry works through a titration question and explains the necessary steps required to arrive at the answer.