Neutralization and Titrations
A quality-control lab needs to know exactly how much acetic acid is in a bottle of vinegar, or how much active sodium hydroxide is left in a jar of drain cleaner. Nobody has to look at individual molecules. You make the sample react, drop by drop, with a solution whose concentration is known exactly, and you record how much it takes. That technique is called a titration.
What happens in a titration
A pH meter in lemon juice reads about 2.4, but that number only counts the H⁺ ions already free. It does not tell you how much citric acid is in the juice in total. How can you force every acid molecule in a sample to react so you can measure it?
Try the simulation. Change the concentrations and watch where the pH jumps.
For a monoprotic strong acid and a strong base that react 1:1, the moles are equal at the equivalence point:
If the acid or base is not 1:1, write the balanced equation and use the mole ratio. For example, $\mathrm{Ba(OH)_2 + 2\,HCl \rightarrow BaCl_2 + 2\,H_2O}$ means $n_{\mathrm{HCl}} = 2\,n_{\mathrm{Ba(OH)_2}}$.
In the lab, $40.0\,\text{mL}$ of an aqueous solution of barium hydroxide, $\mathrm{Ba(OH)2}$, of concentration $0.050\,\text{M}$ is neutralized, using as titrant an…
In the lab, $40.0\,\text{mL}$ of an aqueous solution of barium hydroxide, $\mathrm{Ba(OH)_2}$, of concentration $0.050\,\text{M}$ is neutralized, using as titrant an aqueous solution of hydrochloric acid, $\mathrm{HCl}$, of concentration $0.125\,\text{M}$ at a temperature of $25\,^\circ\text{C}$.
- a) Write the balanced chemical equation for the neutralization reaction that takes place.
- b) Calculate the volume of $\mathrm{HCl}$ solution, in milliliters, that must be added to reach exactly the stoichiometric equivalence point.
In a chemical quality control lab, $50.0\,\text{mL}$ of an aqueous solution of nitric acid, $\mathrm{HNO_3}$, $0.0400\,\text{M}$ is titrated by the controlled addition…
In a chemical quality control lab, $50.0\,\text{mL}$ 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.
- 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.
- 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.
Equivalence point and indicators
You cannot see the equivalence point directly, so you add a few drops of an indicator, a substance whose color depends on pH.
Phenolphthalein is the standard indicator in most school labs: colorless in acid, pink in base. For a strong acid–strong base titration, the pH rises so steeply near the equivalence point that either indicator in the figure gives nearly the same result.
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…
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 an Erlenmeyer 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 setup together with the initial burette reading and the final reading at the moment the color changes.
The initial meniscus reading is $1.20\,\text{mL}$ and the final reading at the persistent end point is $24.60\,\text{mL}$.
- a) Determine the net volume of $\mathrm{NaOH}$ solution used in the titration and calculate the absolute uncertainty associated with this volume measurement.
- b) Calculate the molar concentration of the $\mathrm{HCl}$ solution analyzed, 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.
Weak acids and weak bases
Neutralize $25.0\ \text{mL}$ of $0.10\ \text{M}$ HCl with $25.0\ \text{mL}$ of $0.10\ \text{M}$ NaOH and the pH at the end is $7.00$. Repeat it with acetic acid of the same concentration and the pH at equivalence is about $8.8$. Why doesn't complete neutralization always give a neutral solution?
The pH starts low, climbs slowly, then jumps steeply at the equivalence point. Because the equivalence point is above 7, you pick an indicator that changes color in the basic range, such as phenolphthalein. For a weak base titrated with a strong acid, the equivalence point is below 7, so methyl red works better.
Using titrations: percent by mass and back titrations
Once you know the volume and molarity of titrant used, the plan is always the same: titrant moles → mole ratio → analyte moles → molarity, mass, or percent by mass of the original product.
The key step is a subtraction: moles of analyte reacted = total moles of reagent added − moles of reagent left over (found by the back titration).
The acetic acid content, $\mathrm{CH_3COOH}$, of a commercial vinegar of density $1.01\,\text{g/mL}$ is analyzed. To do so, $10.0\,\text{mL}$ of the vinegar is taken…
The acetic acid content, $\mathrm{CH_3COOH}$, of a commercial vinegar of density $1.01\,\text{g/mL}$ is analyzed. 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 deionized 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: $\mathrm{C}=12.0$; $\mathrm{H}=1.0$; $\mathrm{O}=16.0$.
- a) Write the balanced equation for the neutralization reaction.
- 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…
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 color change.
Data: Atomic masses: $\mathrm{Ca}=40.1$; $\mathrm{C}=12.0$; $\mathrm{O}=16.0$.
- a) Calculate the amount of $\mathrm{HCl}$, in moles, that reacted with the $\mathrm{CaCO_3}$.
- 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.
Lab safety: concentrated acids and bases
In a teaching laboratory there are leftovers of concentrated sulfuric acid, $\mathrm{H_2SO_4}$, and of concentrated sodium hydroxide solution, $\mathrm{NaOH}$, both…
In a teaching laboratory there are leftovers of concentrated sulfuric acid, $\mathrm{H_2SO_4}$, and of concentrated sodium hydroxide solution, $\mathrm{NaOH}$, both labeled 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 lab manager for disposal in accordance with the school's procedure. Justify why any neutralization should be a controlled operation and not an improvised mixture of concentrated solutions.
Back to the start: the vinegar is $5.88\%$ acetic acid by mass ($0.990\ \text{M}$ before dilution). For the old jar of drain cleaner, you would titrate a known mass dissolved in water with standard HCl to find how much active NaOH is left.