Problem 74 - Chemistry and Chemical Reactivity

Question

A 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 NaOH. The appropriate reactions are as follows: Citric acid: \(\mathrm{H}_{3} \mathrm{C}_{6} \mathrm{H}_{5} \mathrm{O}_{7}(\mathrm{aq})+3 \mathrm{NaOH}(\mathrm{aq}) \longrightarrow\) $$ 3 \mathrm{H}_{2} \mathrm{O}(\ell)+\mathrm{Na}_{3} \mathrm{C}_{6} \mathrm{H}_{5} \mathrm{O}_{7}(\mathrm{aq}) $$ Tartaric acid: \(\mathrm{H}_{2} \mathrm{C}_{4} \mathrm{H}_{4} \mathrm{O}_{6}(\mathrm{aq})+2 \mathrm{NaOH}(\mathrm{aq}) \longrightarrow\) $$2 \mathrm{H}_{2} \mathrm{O}(\ell)+\mathrm{Na}_{2} \mathrm{C}_{4} \mathrm{H}_{4} \mathrm{O}_{6}(\mathrm{aq})$$ A \(0.956-\mathrm{g}\) sample requires \(29.1 \mathrm{mL}\) of \(0.513 \mathrm{M} \mathrm{NaOH}\) for titration to the equivalence point. What is the unknown acid?

Step-by-Step Solution

Answer

The unknown acid is citric acid.

Step 1: Calculate Moles of NaOH Used

Given the concentration of NaOH solution is 0.513 M and the volume used is 29.1 mL, convert the volume to liters by dividing by 1000: \( 29.1 \text{ mL} = 0.0291 \text{ L} \). Then, calculate the moles of NaOH using the formula: \[ \text{moles of NaOH} = M \times V = 0.513 \times 0.0291 = 0.0149283 \text{ moles}\].

Step 2: Determine Moles of Acid

The reaction between the unknown acid and NaOH indicates a certain stoichiometric ratio. For citric acid, every 1 mole of acid reacts with 3 moles of NaOH while for tartaric acid, every 1 mole of acid reacts with 2 moles of NaOH. Assume the moles of acid are \( x \) and solve based on these ratios: \(\begin{aligned}\text{Citric acid: } & x : 3x = 0.0149283 \\text{Tartaric acid: } & x : 2x = 0.0149283 \\end{aligned}\)

Step 3: Calculate Molar Mass of Each Acid

For citric acid (\( \mathrm{H}_3 \mathrm{C}_6 \mathrm{H}_5 \mathrm{O}_7 \)), determine molar mass by adding the atomic masses: \[ 3 \times 1.01 + 6 \times 12.01 + 5 \times 1.01 + 7 \times 16.00 \approx 192.1 \text{ g/mol} \]For tartaric acid (\( \mathrm{H}_2 \mathrm{C}_4 \mathrm{H}_4 \mathrm{O}_6 \)), determine molar mass by adding the atomic masses: \[ 2 \times 1.01 + 4 \times 12.01 + 4 \times 1.01 + 6 \times 16.00 \approx 150.1 \text{ g/mol} \]

Step 4: Calculate the Molar Mass of the Unknown Acid

For citric acid, the number of moles is \( \frac{0.0149283}{3} \approx 0.0049761 \) moles. For tartaric acid, the moles would be \( \frac{0.0149283}{2} \approx 0.00746415 \) moles. Using the given sample mass, calculate the molar mass:\(\begin{aligned}\text{Molar mass (citric):} & \frac{0.956}{0.0049761} \approx 192.1 \, \text{g/mol}, \\text{Molar mass (tartaric):} & \frac{0.956}{0.00746415} \approx 128.1 \, \text{g/mol}.\end{aligned} \)

Step 5: Identify the Unknown Acid

Compare the calculated molar mass of the unknown acid with the expected molar masses of citric and tartaric acids. Since the calculated molar mass (192.1 g/mol) closely matches the molar mass of citric acid, the unknown acid is citric acid.

Key Concepts

Citric Acid

Citric acid is a natural weak acid commonly found in citrus fruits such as lemons and limes. It is a tricarboxylic acid, meaning it has three carboxyl functional groups, which makes it capable of donating three hydrogen ions (protons) in reactions. This property is crucial when it comes to titration where citric acid reacts with a base, such as sodium hydroxide (NaOH).

• Chemical formula: \( \mathrm{H}_3 \mathrm{C}_6 \mathrm{H}_5 \mathrm{O}_7 \)
• Molar mass: approximately 192.1 g/mol

When citric acid is used in titration, every mole of citric acid requires three moles of NaOH to reach the equivalence point. This is due to the triprotic nature of citric acid, demonstrating its ability to neutralize three hydroxide ions. Citric acid is essential in food and beverage industries, not only for its sour flavor but also as a preservative due to its antioxidant properties.

Tartaric Acid

Tartaric acid is another type of weak acid, often found in grapes and bananas. It is known for its role in winemaking where it is used to control acidity levels, enhancing the wine's taste and stability. Tartaric acid, however, is a diprotic acid, which means it has two hydrogen ions available to react with a base.

• Chemical formula: \( \mathrm{H}_2 \mathrm{C}_4 \mathrm{H}_4 \mathrm{O}_6 \)
• Molar mass: approximately 150.1 g/mol

In a titration process with NaOH, tartaric acid reacts in a 1:2 ratio, meaning each mole of tartaric acid reacts with two moles of NaOH. This stoichiometry is due to its two available acidic hydrogens. It's valued in the baking industry as a component of baking powder and as an acid to create cream of tartar which helps to stabilize whipped egg whites and adds volume to baked goods.

Molar Mass Determination

Determining the molar mass of an unknown acid is a crucial step in identifying the substance present in a given sample. This is done through a titration process, where a known concentration of a solution is used to determine the concentration of an unknown solute. In our exercise involving citric and tartaric acids, we used titration with NaOH to deduce which acid was present based on its molar mass.The titration process involves recording the volume of titrant used to reach the equivalence point, where all acidic ions have been reacted. By knowing the moles of NaOH used, the stoichiometric relation allows us to calculate the moles of acid. The molar mass can then be determined by dividing the mass of the sample by the moles of acid calculated.Steps:

• Convert volume of titrant to liters
• Calculate moles of titrant using molarity
• Determine moles of acid using the stoichiometric ratio
• Find molar mass using the formula: \( \text{Molar mass} = \frac{\text{mass of sample}}{\text{moles of acid}} \)

Given results helped us conclude that the molar mass calculated was closest to citric acid, allowing us to identify it confidently.