Question

A 0.210 -g sample of an acid (molar mass \(=192 \mathrm{g} / \mathrm{mol}\) ) is titrated with \(30.5 \mathrm{mL}\) of \(0.108 \mathrm{M} \mathrm{NaOH}\) to a phenolphthalein end point. Is the acid monoprotic, diprotic, or triprotic?

Short answer

The acid is triprotic since the number of protons that reacted with NaOH, calculated by \(\frac{\text{moles of NaOH}}{\text{moles of acid}} = \frac{0.00329 mol}{0.00109 mol} = 3.02\), is approximately 3.

Step-by-step solution

Determine the number of moles of the acid

Using the formula, \[ \text{moles} = \frac{\text{mass}}{\text{molar mass}} \] the number of moles of the acid can be calculated as follows: \[ \text{moles} = \frac{0.210 g}{192 g/mol} = 0.00109 mol \]

Determine the number of moles of NaOH

The moles of NaOH can be determined using the formula, \[ \text{moles} = \text{molarity} \times \text{volume} \] Where the volume is in liters. Thus, \[ \text{moles NaOH} = 0.108 M \times 30.5 mL = 0.108 M \times 0.0305 L = 0.00329 mol \]

Determine the protic nature of the acid

The protic nature of the acid can be determined by comparing the moles of the acid and NaOH. Since the mole ratio of acid to NaOH is either 1:1, 1:2, or 1:3 for monoprotic, diprotic, or triprotic acids respectively. The number of acid protons that reacted with NaOH can be calculated by: \[ \text{protons} = \frac{\text{moles of NaOH}}{\text{moles of acid}} = \frac{0.00329 mol}{0.00109 mol} = 3.02 \] Rounded to the nearest whole number, this yields 3. Therefore, the acid is triprotic.

Key concepts

Molarity Calculation

Molarity, often represented by the letter M, is an essential measurement in chemistry that indicates the concentration of a solution. It is defined as the number of moles of a solute (the substance being dissolved) per liter of solution. The formula for calculating molarity is easy to remember:
\[\begin{equation}M = \frac{\text{moles of solute}}{\text{liters of solution}}\end{equation}\]
In the context of the exercise, the molarity of NaOH solution is given (0.108 M), which means there are 0.108 moles of NaOH in every liter of solution. Understanding molarity is crucial when it comes to titrations, as it allows us to determine the exact amount of titrant needed to reach the equivalence point during a titration process.

Titration Stoichiometry

Titration stoichiometry involves the calculation of the quantities of reactants in a chemical reaction, specifically within the framework of a titration experiment. A titration is an analytical technique wherein a solution of known concentration (titrant) is used to determine the concentration of an unknown solution.
Stoichiometric Point: This is the part of the titration when the number of moles of the titrant equals the number of moles of substance originally in the solution. The stoichiometry of the titration will change depending on the type of reaction occurring between the acid and the base.
In the step-by-step solution, stoichiometry is used to infer the nature of the acid (whether it is monoprotic, diprotic, or triprotic) by comparing the mole ratio of the titrant, NaOH, to that of the unknown acid. The mole ratio corresponds to the number of protons the acid can donate. For instance, a diprotic acid would react with twice as many moles of NaOH as there are moles of the acid.

Proton Transfer Reactions

Proton transfer reactions, or acid-base reactions, lie at the heart of a titration process involving acids and bases. In these reactions, a proton, or hydrogen ion (H+), is transferred from the acid to the base, constituting a neutralization reaction. This reaction typically creates water (H2O) and a salt as products.
Acid Definition: An acid can be defined as a substance that donates protons (H+ ions) in a reaction. Based on the number of protons an acid can donate, it is classified as monoprotic (one proton), diprotic (two protons), or triprotic (three protons).
The reaction stoichiometry in the original exercise suggests that each mole of acid donates three protons, as indicated by the ratio of moles of NaOH to moles of the unknown acid. Therefore, because one mole of acid neutralizes three moles of NaOH, the acid in question is identified as triprotic.