Problem 106 - Chemistry and Chemical Reactivity

Question

A noncarbonated soft drink contains an unknown amount of citric acid, \(\mathrm{H}_{3} \mathrm{C}_{6} \mathrm{H}_{5} \mathrm{O}_{7}\). If \(100 .\) mL of the soft drink requires \(33.51 \mathrm{mL}\) of \(0.0102 \mathrm{M} \mathrm{NaOH}\) to neutralize the citric acid completely, what mass of citric acid does the soft drink contain per 100. mL? The reaction of citric acid and NaOH is $$\mathrm{H}_{3} \mathrm{C}_{6} \mathrm{H}_{5} \mathrm{O}_{7}(\mathrm{aq})+3 \mathrm{NaOH}(\mathrm{aq}) \rightarrow \mathrm{Na}_{3} \mathrm{C}_{6} \mathrm{H}_{5} \mathrm{O}_{7}(\mathrm{aq})+3 \mathrm{H}_{2} \mathrm{O}(\ell)$$

Step-by-Step Solution

Answer

0.02188 g of citric acid per 100 mL of the drink.

Step 1: Write the Balanced Chemical Equation

The balanced equation for the neutralization of citric acid by sodium hydroxide is already provided:\[\mathrm{H}_{3} \mathrm{C}_{6} \mathrm{H}_{5} \mathrm{O}_{7}(\mathrm{aq}) + 3 \mathrm{NaOH}(\mathrm{aq}) \rightarrow \mathrm{Na}_{3} \mathrm{C}_{6} \mathrm{H}_{5} \mathrm{O}_{7}(\mathrm{aq}) + 3 \mathrm{H}_{2} \mathrm{O}(\ell)\]

Step 2: Calculate Moles of NaOH Used

The concentration of NaOH is given as \(0.0102\,\text{M}\) and the volume used is \(33.51 \text{ mL}\). We first convert the volume to liters:\[33.51 \text{ mL} = 0.03351\,\text{L}\] Then, calculate the moles of NaOH:\[\text{moles of NaOH} = 0.0102\,\text{M} \times 0.03351\,\text{L} = 3.41802 \times 10^{-4} \text{ moles}\]

Step 3: Determine Moles of Citric Acid

According to the reaction, one mole of citric acid reacts with three moles of NaOH. Thus, we calculate the moles of citric acid using:\[\text{moles of citric acid} = \frac{3.41802 \times 10^{-4}}{3} = 1.13934 \times 10^{-4} \text{ moles}\]

Step 4: Calculate Mass of Citric Acid

The molar mass of citric acid \((\mathrm{H}_{3} \mathrm{C}_{6} \mathrm{H}_{5} \mathrm{O}_{7})\) is approximately \(192.13\,\text{g/mol}\). Use this to find the mass of citric acid:\[\text{mass of citric acid} = 1.13934 \times 10^{-4} \text{ moles} \times 192.13\,\text{g/mol} = 0.02188\,\text{g}\]

Step 5: Express Mass per 100 mL of Drink

Since the volume of the drink considered in the calculation was \(100\,\text{mL}\), the mass of citric acid per 100 mL of the drink is \(0.02188\,\text{g}\). Therefore, the drink contains roughly \(0.02188\,\text{g}\) of citric acid per 100 mL.

Key Concepts

Citric Acid

Citric acid is a weak organic acid found naturally in citrus fruits. It's commonly used in food and beverages to provide a tart flavor and as a preservative. In chemistry, citric acid is known for being a triprotic acid, which means it can donate three protons (hydrogen ions) in a reaction. Its chemical formula is \(\mathrm{H}_{3} \mathrm{C}_{6} \mathrm{H}_{5} \mathrm{O}_{7}\).
This triprotic nature is significant in titration reactions. During neutralization with a base like sodium hydroxide \((\mathrm{NaOH})\), all three acidic hydrogens of citric acid react with \(\mathrm{NaOH}\). In the given exercise, this reaction is used to determine how much citric acid is present in a soft drink by observing how much \(\mathrm{NaOH}\) is required for neutralization. This process illustrates the practical application of stoichiometry and impact of weak acids.
In practice, titration can help measure substances like citric acid in various products, ensuring flavor consistency, safety, and quality in food and beverages.

Molarity

Molarity is a measure of the concentration of a solution. It's defined as the number of moles of solute per liter of solution, typically represented by \(\mathrm{M}\). Molarity is crucial in stoichiometric calculations and chemical reactions because it provides a way to quantify reactants and products.
In the original exercise, the molarity of \(\mathrm{NaOH}\) used is \(0.0102\,\mathrm{M}\). This molarity value helps determine the exact amount of \(\mathrm{NaOH}\) used to neutralize the citric acid in the soft drink. By knowing the volume of \(\mathrm{NaOH}\) used, one can calculate the moles of \(\mathrm{NaOH}\) present, which is the essential step in finding out the moles of citric acid assuming full neutralization.
Understanding molarity allows chemists to use solutions of known concentrations in laboratory settings, facilitating precise experimental outcomes and consistent measurements.

Neutralization

Neutralization is a chemical reaction between an acid and a base that results in the formation of water and a salt. This process is crucial in many analytical and environmental applications. For a complete neutralization reaction, the moles of acid must equal the moles of base reacting.
In our exercise with citric acid and \(\mathrm{NaOH}\), the balanced chemical equation shows one mole of citric acid reacting with three moles of \(\mathrm{NaOH}\). This stoichiometric relationship is essential for calculating the amount of citric acid in the drink. By titrating with a base like \(\mathrm{NaOH}\), the endpoint is reached when all acidic protons are neutralized. This allows us to determine the precise concentration of the acid.
This method is widely used in industries for quality control to verify the acid content in consumable products like soft drinks, ensuring they meet safety standards and desired taste profiles.