Exercises: Neutralisation and titrations

In the laboratory, $40.0\,\text{mL}$ of an aqueous solution of barium hydroxide, $\mathrm{Ba(OH)_2}$, of concentration $0.050\,\text{M}$ is neutralised, using as titrant an aqueous solution of hydrochloric acid, $\mathrm{HCl}$, of concentration $0.125\,\text{M}$ at a temperature of $25\,^\circ\text{C}$.

1. a) Write the balanced chemical equation for the neutralisation reaction that takes place.
2. b) Calculate the volume of $\mathrm{HCl}$ solution, in millilitres, that must be added to reach exactly the stoichiometric equivalence point.

When carrying out the volumetric titration of $25.0\,\text{mL}$ of acetic acid, $\mathrm{CH_3COOH}$ (a weak acid), with a solution of sodium hydroxide, $\mathrm{NaOH}$ (a strong base), the equivalence point is theoretically reached at $\mathrm{pH} \approx 8.8$. Two acid-base indicators are available in the laboratory: methyl red (transition range of $\mathrm{pH}$ between $4.4$ and $6.2$, from red to yellow) and phenolphthalein (transition range of $\mathrm{pH}$ between $8.2$ and $10.0$, from colourless to pink).

1. a) Define and concisely distinguish the concept of equivalence point from that of end point in a volumetric titration.
2. b) Justify which of the two indicators is ideal for minimising experimental error in this titration.

In a teaching laboratory there are leftovers of concentrated sulfuric acid, $\mathrm{H_2SO_4}$, and of concentrated sodium hydroxide solution, $\mathrm{NaOH}$, both labelled as corrosive. A student proposes mixing them directly in a beaker and pouring the result down the drain. a) Identify two risks of this proposal and explain what eye, skin and clothing protection is required for supervised work with corrosive reagents. b) Suggest how to identify, separate and report these wastes to the laboratory manager for disposal in accordance with the school's procedure. Justify why any neutralisation should be a controlled operation and not an improvised mixture of concentrated solutions.

To determine the unknown concentration of an aqueous solution of hydrochloric acid, $\mathrm{HCl}$, an aliquot of $25.0\,\text{mL}$ is taken with a volumetric pipette and transferred to a conical flask, and two drops of phenolphthalein are added. A graduated burette of $50.0\,\text{mL}$ (reading uncertainty of $\pm 0.05\,\text{mL}$ per meniscus setting) is filled with a standard solution of sodium hydroxide, $\mathrm{NaOH}$, $0.100\,\text{M}$. The figure shows the experimental set-up together with the initial burette reading and the final reading at the moment the colour changes.

The initial meniscus reading is $1.20\,\text{mL}$ and the final reading at the persistent end point is $24.60\,\text{mL}$.

1. a) Determine the net volume of $\mathrm{NaOH}$ solution used in the titration and calculate the absolute uncertainty associated with this volume measurement.
2. b) Calculate the molar concentration of the $\mathrm{HCl}$ solution analysed, giving the result to the appropriate number of significant figures. Estimate the uncertainty of the volume used conservatively by adding the two maximum reading uncertainties.

The acetic acid content, $\mathrm{CH_3COOH}$, of a commercial vinegar of density $1.01\,\text{g/mL}$ is analysed. To do so, $10.0\,\text{mL}$ of the vinegar is taken with a volumetric pipette, placed in a volumetric flask of $100.0\,\text{mL}$, made up to the mark with deionised water and mixed thoroughly. An aliquot of $20.0\,\text{mL}$ of the diluted solution is then taken and titrated with an aqueous solution of $\mathrm{NaOH}$ of concentration $0.120\,\text{M}$ in the presence of phenolphthalein. Exactly $16.5\,\text{mL}$ of titrant is used to reach the end point.

Data: Relative atomic masses: $\mathrm{C}=12.0$; $\mathrm{H}=1.0$; $\mathrm{O}=16.0$.

1. a) Write the balanced equation for the neutralisation reaction.
2. b) Calculate the molar concentration of acetic acid in the original vinegar and determine its percentage by mass ($\%\,\text{m/m}$).

The aim is to quantify the calcium carbonate content, $\mathrm{CaCO_3}$, of a commercial antacid tablet of total mass $1.20\,\text{g}$. The powdered sample is reacted with $50.0\,\text{mL}$ of aqueous solution of $\mathrm{HCl}$ $0.600\,\text{M}$, producing carbon dioxide according to the process:

$\mathrm{CaCO_3\,(s) + 2\,HCl\,(aq) \rightarrow CaCl_2\,(aq) + CO_2\,(g) + H_2O\,(l)}$.

Once all the gas formed has been expelled, the excess hydrochloric acid remaining is back-titrated with a solution of $\mathrm{NaOH}$ $0.250\,\text{M}$, a volume of $44.0\,\text{mL}$ of the base being required to reach the colour change.

Data: Atomic masses: $\mathrm{Ca}=40.1$; $\mathrm{C}=12.0$; $\mathrm{O}=16.0$.

1. a) Calculate the amount of $\mathrm{HCl}$, in moles, that reacted with the $\mathrm{CaCO_3}$.
2. b) Determine the mass of $\mathrm{CaCO_3}$ present in the tablet and its percentage by mass in the medicine. Assume that the other components of the tablet do not react with the acid and that no HCl is lost during the expulsion of the gas.

$25.0\,\text{mL}$ of an aqueous solution of benzoic acid, $\mathrm{C_6H_5COOH}$ (a weak monoprotic acid), of concentration $0.0100\,\text{M}$ is titrated with a standard solution of potassium hydroxide, $\mathrm{KOH}$, $0.0100\,\text{M}$ at $25\,^\circ\text{C}$.

Data at $25\,^\circ\text{C}$: $K_\mathrm{a}(\mathrm{C_6H_5COOH}) = 6.30 \times 10^{-5}$; $K_\mathrm{w} = 1.00 \times 10^{-14}$.

1. a) Calculate the initial $\mathrm{pH}$ of the acid solution before any base is added, and calculate the $\mathrm{pH}$ after exactly $12.5\,\text{mL}$ of the $\mathrm{KOH}$ solution has been added.
2. b) Determine the volume of $\mathrm{KOH}$ solution needed to reach the equivalence point and calculate, with justification, the value of $\mathrm{pH}$ at that stoichiometric point, writing the corresponding reactions. Consider the solutions to be ideal and the volumes to be additive.

In a chemical quality control laboratory, $50.0\,\text{mL}$ of an aqueous solution of nitric acid, $\mathrm{HNO_3}$, $0.0400\,\text{M}$ is titrated by the controlled addition of a standard solution of sodium hydroxide, $\mathrm{NaOH}$, of concentration $0.0500\,\text{M}$ at $25\,^\circ\text{C}$.

Data: $K_\mathrm{w} = 1.00 \times 10^{-14}$ at $25\,^\circ\text{C}$. Volumes are assumed to be strictly additive.

1. a) Determine the $\mathrm{pH}$ of the resulting mixture after $30.0\,\text{mL}$ of the $\mathrm{NaOH}$ solution has been added. Also calculate the volume of titrant needed to reach the equivalence point and justify the value of $\mathrm{pH}$ at that point.
2. b) Calculate the new value of $\mathrm{pH}$ of the solution after adding a cumulative volume of $45.0\,\text{mL}$ of $\mathrm{NaOH}$ (in excess of the equivalence point). Consider the solutions to be ideal and the volumes to be additive.

$30.0\,\text{mL}$ of an aqueous solution of ammonia, $\mathrm{NH_3}$, of concentration $0.150\,\text{M}$ is titrated with a solution of hydrochloric acid, $\mathrm{HCl}$, $0.100\,\text{M}$ at $25\,^\circ\text{C}$.

Data at $25\,^\circ\text{C}$: $K_\mathrm{b}(\mathrm{NH_3}) = 1.80 \times 10^{-5}$; $K_\mathrm{w} = 1.00 \times 10^{-14}$.

Available indicators (name, transition range, acid form colour/basic form colour): bromocresol green ($3.8 - 5.4$, yellow/blue); methyl red ($4.4 - 6.2$, red/yellow); thymolphthalein ($9.3 - 10.5$, colourless/blue).

1. a) Calculate the volume of $\mathrm{HCl}$ solution used at the equivalence point and the $\mathrm{pH}$ of the solution at that point, justifying its acidity chemically.
2. b) Select, with justification, a suitable indicator from the three proposed and explain in detail the analytical consequence of wrongly using thymolphthalein in this titration. Consider the solutions to be ideal and the volumes to be additive.