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

The soft drink contains approximately 0.0218 g of citric acid per 100 mL.

Step 1: Understand the Reaction

Citric acid (\( \mathrm{H}_{3} \mathrm{C}_{6} \mathrm{H}_{5} \mathrm{O}_{7} \)) reacts with sodium hydroxide (\( \mathrm{NaOH} \)) in a 1:3 molar ratio, meaning 1 mole of citric acid reacts with 3 moles of sodium hydroxide.

Step 2: Calculate Moles of NaOH Used

Determine the number of moles of \( \mathrm{NaOH} \) used. You have 33.51 mL of 0.0102 M \( \mathrm{NaOH} \). Moles of \( \mathrm{NaOH} \) = \( 33.51 \text{ mL} \times \frac{0.0102 \text{ mol}}{1000 \text{ mL}} \approx 0.000341802 \text{ mol} \).

Step 3: Calculate Moles of Citric Acid

Since the reaction is 1:3, divide the moles of \( \mathrm{NaOH} \) by 3. \( 0.000341802 \text{ mol} \div 3 \approx 0.000113934 \text{ mol citric acid} \).

Step 4: Calculate Mass of Citric Acid

Use the molar mass of citric acid to find the mass. Molar mass of \( \mathrm{H}_{3} \mathrm{C}_{6} \mathrm{H}_{5} \mathrm{O}_{7} \approx 192.12 \text{ g/mol} \). Mass = \( 0.000113934 \text{ mol} \times 192.12 \text{ g/mol} \approx 0.021884 \text{ g} \).

Step 5: Express Answer Per 100 mL

Since the mass calculated is already for 100 mL of the drink, the drink contains approximately 0.0218 g of citric acid per 100 mL.

Key Concepts

Citric Acid

Citric acid is a natural organic acid found in citrus fruits like lemons, limes, and oranges. It is commonly present in food and beverages to provide a sour taste and to act as a preservative. In the context of acid-base titration, citric acid (\( \mathrm{H}_{3} \mathrm{C}_{6} \mathrm{H}_{5} \mathrm{O}_{7} \)), is often the "acid" component that reacts with a "base" to form water and a salt.
- Chemical formula: \( \mathrm{H}_{3} \mathrm{C}_{6} \mathrm{H}_{5} \mathrm{O}_{7} \)
- Appearance: It is a clear white crystalline powder when isolated
- Function: Citric acid is involved in metabolic pathways in living organisms, such as the citric acid cycle (Krebs cycle) in cellular respiration.
In our exercise, citric acid reacts with sodium hydroxide in a stoichiometric neutralization reaction, where it plays a vital role in determining the concentration of the "base" through titration.

Sodium Hydroxide

Sodium hydroxide (NaOH), also known as lye or caustic soda, is a strong base commonly used in chemical reactions, including the process of titration. It is highly soluble in water and forms a strong alkaline solution.
- Chemical formula: \( \mathrm{NaOH} \)
- Appearance: Often found as a solid white crystal that absorbs moisture from the air
- Uses: Beyond this reaction, sodium hydroxide is used in soap making, cleaning products, and in the preparation of other chemicals.
During titration, NaOH is used as a reactive measuring tool to determine the amount of an acid in a given solution through a neutralization reaction. Its role in the exercise is as a measurable "base" that undergoes a reaction with citric acid to establish the latter’s concentration in the soft drink.

Mole Calculation

Mole calculation is a core concept in chemistry that allows us to understand how substances react in a chemical equation. A "mole" is a unit that measures an amount of substance, where one mole corresponds to \(6.022 \times 10^{23}\) particles, such as atoms or molecules.

• Mole Concept: Enables the conversion between the amount of substance (in moles), its mass, and the number of molecules or atoms.
• Conversion Between Volume and Moles: In our example, we use the volume of a sodium hydroxide solution in liters and its concentration (in molarity, \(M = \text{mol/L}\)) to calculate the number of moles:
• Formula Used: Moles of NaOH = Volume (L) \(\times\) Molarity (mol/L)

In the exercise, the moles of NaOH are calculated using a known concentration and volume, and then adjusted for the 1:3 molar ratio of citric acid to sodium hydroxide to find the moles of citric acid. This step is crucial to determine the mass of citric acid in the solution.

Neutralization Reaction

Neutralization reactions are essential chemical processes where an acid and a base react to form water and a salt. These reactions are fundamental in titration experiments because they allow us to determine the concentration of an unknown solution.

• Definition: A neutralization reaction involves the reaction of hydronium (\( \mathrm{H}^{+} \)) ions from the acid with hydroxide (\( \mathrm{OH}^{-} \)) ions from the base to form water (\( \mathrm{H}_{2} \mathrm{O} \)).
• Example Reaction: In the given exercise, citric acid and sodium hydroxide react to create sodium citrate and water as follows:
• \( \mathrm{H}_{3} \mathrm{C}_{6} \mathrm{H}_{5} \mathrm{O}_{7} \) + 3 \( \mathrm{NaOH} \) → \( \mathrm{Na}_{3} \mathrm{C}_{6} \mathrm{H}_{5} \mathrm{O}_{7} \) + 3 \( \mathrm{H}_{2} \mathrm{O} \)

Understanding the stoichiometry, or the relative quantities of reactants and products in the reaction, is crucial for calculating the amount of product formed or reactant needed. The balanced chemical equation provided gives the exact mole ratio needed to complete the reaction smoothly.