Question

An unknown solid acid is either citric acid or tartaric acid. To determine which acid you have, you titrate a sample of the solid with aqueous \(\mathrm{NaOH}\) and from this determine the molar mass of the unknown acid. The appropriate equations are as follows: Citric acid: \(\mathrm{H}_{3} \mathrm{C}_{6} \mathrm{H}_{5} \mathrm{O}_{7}(\mathrm{aq})+3 \mathrm{NaOH}(\mathrm{aq}) \rightarrow\) $$ 3 \mathrm{H}_{2} \mathrm{O}(\ell)+\mathrm{Na}_{3} \mathrm{C}_{6} \mathrm{H}_{5} \mathrm{O}_{7}(\mathrm{aq}) $$ Tartanic acid: \(\mathrm{H}_{2} \mathrm{C}_{4} \mathrm{H}_{4} \mathrm{O}_{6}(\mathrm{aq})+2 \mathrm{NaOH}(\mathrm{aq}) \rightarrow\) $$ 2 \mathrm{H}_{2} \mathrm{O}(\ell)+\mathrm{Na}_{2} \mathrm{C}_{4} \mathrm{H}_{4} \mathrm{O}_{6}(\mathrm{aq}) $$ A \(0.956-\mathrm{g}\) sample requires \(29.1 \mathrm{mL}\) of \(0.513 \mathrm{M} \mathrm{NaOH}\) to consume the acid completely. What is the unknown acid?

Short answer

The unknown acid is citric acid.

Step-by-step solution

Calculate Moles of NaOH

First, determine the number of moles of NaOH used in the titration. Use the formula \[ \text{moles of NaOH} = \text{molarity} \times \text{volume in liters} \]Given, the molarity is 0.513 M and the volume is 29.1 mL. Convert the volume from mL to L:\[ 29.1 \text{ mL} = 0.0291 \text{ L} \]Now, calculate the moles of NaOH:\[ \text{moles of NaOH} = 0.513 \times 0.0291 = 0.0149223 \approx 0.0149 \text{ moles} \]

Determine the Moles of the Unknown Acid

Since we do not know the acid, we will consider each potential reaction and determine how many moles of the acid would react with the moles of NaOH calculated._If citric acid:_The reaction is 1:3, so the moles of citric acid \[ = \frac{0.0149}{3} = 0.00497 \text{ moles} \]_If tartaric acid:_The reaction is 1:2, so the moles of tartaric acid \[ = \frac{0.0149}{2} = 0.00745 \text{ moles} \]

Calculate Molar Mass for Each Acid Scenario

Using the sample mass and the moles calculated, determine the molar mass._If citric acid: (Molar mass = Sample mass / moles)_\[ \text{Molar mass} = \frac{0.956}{0.00497} \approx 192.37 \text{ g/mol} \]_If tartaric acid:_\[ \text{Molar mass} = \frac{0.956}{0.00745} \approx 128.28 \text{ g/mol} \]

Compare Molar Masses to Known Values

Compare the calculated molar masses with the known values. - Citric acid has a known molar mass of approximately 192.12 g/mol. - Tartaric acid has a known molar mass of approximately 150.09 g/mol. The calculated molar mass closest to the known molar mass corresponds to citric acid.

Key concepts

Molarity

Molarity is a measure of the concentration of a solute in a solution, specifically the number of moles of solute per liter of solution. It's a crucial concept in chemistry, especially in titration experiments, where we want to know how concentrated a substance is in a mixture.
The formula for molarity

• \( M = \frac{n}{V} \)
• \( M \) is the molarity,
• \( n \) is the number of moles of solute,
• \( V \) is the volume of the solution in liters.

In our exercise, the molarity of the \( \text{NaOH} \) solution was given as \( 0.513 \text{ M} \), and this information was used to calculate the moles of \( \text{NaOH} \) needed to completely react with the unknown solid acid.

Moles

The concept of moles is foundational in chemistry. A mole is a unit that measures the amount of a substance. It is equivalent to Avogadro's number, which is approximately \( 6.022 \times 10^{23} \) entities (atoms, molecules, etc.). This makes it easier to calculate and communicate results when handling large quantities of molecules.
In the context of this titration exercise, moles are used to understand how much \( \text{NaOH} \) reacts with each potential acid candidate. Calculating moles involved using the molarity formula, as the number of moles of \( \text{NaOH} \) was determined by multiplying the molarity by the volume used in liters. Subsequently, this information helped to ascertain the moles of the unknown acid that reacted, taking into account the specific reaction ratio for both citric acid and tartaric acid.

Molar Mass

Molar mass is the mass of one mole of a given substance and is usually expressed in grams per mole (g/mol). It provides a bridge between the macroscopic and atomic worlds, allowing chemists to weigh substances and relate those weights to numbers of molecules.
Calculating molar mass is pivotal in our titration problem to identify the unknown acid. By knowing the mass of the sample and the determined moles of the acid, the molar mass was calculated for each potential acid (citric and tartaric).

• For citric acid: \( \text{Molar mass} = \frac{\text{mass}}{\text{moles of citric acid}} \)
• For tartaric acid: \( \text{Molar mass} = \frac{\text{mass}}{\text{moles of tartaric acid}} \)

The calculated molar mass that matched closest to the known molar mass values for these acids indicates the identity of the unknown acid sample.

Acid-Base Reaction

An acid-base reaction involves an acid and a base reacting to form a salt and typically water. In the context of titration, these reactions allow us to determine certain properties of the reactants, such as concentration or molar mass.
This exercise dealt specifically with identifying an unknown acid through titration with \( \text{NaOH} \), a base. Whether citric or tartaric acid is present, both undergo a neutralization reaction with \( \text{NaOH} \). This reaction consumes the \( \text{NaOH} \) added, leading us to understand how many moles of acid are present depending on the reaction stoichiometry.

• Citric acid and \( \text{NaOH} \) react in a 1:3 ratio.
• Tartaric acid and \( \text{NaOH} \) react in a 1:2 ratio.

Knowing these ratios allowed us to calculate how much of each acid would react with the amount of \( \text{NaOH} \) given, enabling us to determine the unknown acid by molar mass comparison.