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 given acid is triprotic, as it donates 3 protons per mole of acid. This conclusion is based on the calculated mole ratio between the acid and NaOH of approximately 0.332, which is close to 1/3.

Step-by-step solution

Calculate the moles of NaOH used in the titration

We are given the concentration of NaOH solution (0.108 M) and the volume of the solution used during the titration (30.5 mL). The moles of NaOH can be calculated using the following formula: Moles of NaOH = Concentration × Volume (in Liters) Keep in mind that we need to convert the volume from mL to L by dividing the value by 1,000. Moles of NaOH = 0.108 M × (30.5 mL / 1000) = 0.003294 \(mol\)

Calculate the moles of the acid in the sample

We are given the mass of acid sample (0.210 g) and the molar mass of the acid (192 g/mol). Moles of Acid = (Mass of Acid) / (Molar Mass of Acid) Moles of Acid = 0.210 g / 192 g/mol = 0.001094 \(mol\)

Determine the acid's proticity

Now we need to find the ratio between the moles of acid and moles of NaOH to determine the number of protons the acid donates per mole: Mole Ratio = Moles of Acid / Moles of NaOH = 0.001094 / 0.003294 Mole Ratio ≈ 0.332 Now let's compare the mole ratio value to the possible proton numbers for monoprotic, diprotic, and triprotic acids: - If the acid is monoprotic, the mole ratio would be close to 1:1 (1 proton per mole acid). - If the acid is diprotic, the mole ratio would be close to 1:2 (2 protons per mole acid). - If the acid is triprotic, the mole ratio would be close to 1:3 (3 protons per mole acid). Based on our calculated mole ratio of approximately 0.332, which is very close to 1/3, we can conclude that the given acid is: Triprotic (donates 3 protons per mole of acid).

Key concepts

Molecular Mass

Understanding molecular mass is vital in chemistry, especially in titration problems. Molecular mass, measured in grams per mole ( ext{g/mol}), represents the mass of one mole of a substance. In this exercise, the molecular mass of the acid is given as 192 ext{g/mol}. To find the moles of a sample, you divide the sample's mass by its molecular mass.
This gives the number of molecules in that sample.
For the acid in question, with a sample mass of 0.210 g, we find the moles by using:

• Moles of Acid = \( \frac{0.210 ext{ g}}{192 ext{ g/mol}} = 0.001094 ext{ mol} \)

Knowing molecular mass allows you to relate the sample's mass to the number of molecules, which is essential for analyzing reactions.

Molar Ratio

The molar ratio in a chemical reaction tells us the proportion of reactants that react with each other. It's crucial for determining the stoichiometry of the reaction. For titration, we often look at the ratio between the acid and the base used.
In this problem, the moles of NaOH are calculated using its concentration and volume:

• Moles of NaOH = \( 0.108 ext{ M} \times \frac{30.5 ext{ mL}}{1000} = 0.003294 ext{ mol} \)

Next, we determine the molar ratio by dividing the moles of acid by the moles of NaOH:

• Mole Ratio = \( \frac{0.001094}{0.003294} \approx 0.332 \)

This ratio helps determine how many moles of a reactant are needed to completely react with another.

Proticity

Proticity refers to the number of protons an acid can donate. In this context, it identifies whether an acid is monoprotic, diprotic, or triprotic.
To determine proticity, compare the mole ratio of acid to base:

• Monoprotic: ratio of approximately 1:1
• Diprotic: ratio of approximately 1:2
• Triprotic: ratio of approximately 1:3

In this exercise, the mole ratio is approximately 0.332, closely aligning with 1:3, indicating that the acid is triprotic. This means the acid can donate three protons per molecule.

Phenolphthalein Endpoint

In acid-base titrations, we use indicators to identify when the reaction has reached its endpoint. Phenolphthalein is a common indicator that changes color at different pH levels, typically turning pink in basic solutions.
The phenolphthalein endpoint represents the point at which the amount of base added completely neutralizes the acid in the solution.
This visual cue helps determine when to stop the titration. In this exercise, reaching the phenolphthalein endpoint signifies that stoichiometric amounts of acid and base have reacted, allowing us to accurately calculate the proticity of the acid.