Question

The flavor of the first batch of Gatorade was improved by adding lemon juice, which contains citric acid \(\left(\mathrm{H}_{3} \mathrm{C}_{6} \mathrm{H}_{5} \mathrm{O}_{7}\right) .\) Citric acid is still added as flavoring to sports drinks today. The concentration of citric acid in a beverage was determined by titration with sodium hydroxide according to the reaction: $$ \mathrm{H}_{3} \mathrm{C}_{6} \mathrm{H}_{3} \mathrm{O}_{7}(a q)+3 \mathrm{NaOH}(a q) \longrightarrow \mathrm{Na}_{3} \mathrm{C}_{6} \mathrm{H}_{5} \mathrm{O}_{7}(a q)+3 \mathrm{H}_{2} \mathrm{O}(l) $$ If \(25.0 \mathrm{~mL}\) of the beverage required \(35.6 \mathrm{~mL}\) of \(0.0400 \mathrm{M} \mathrm{NaOH}\) for a complete reaction, calculate the molarity of citric acid.

Short answer

The molarity of citric acid is 0.0190 M.

Step-by-step solution

Write down the balanced chemical equation

The titration involves citric acid and sodium hydroxide. The balanced chemical equation for the reaction is: \[ \mathrm{H}_{3} \mathrm{C}_{6} \mathrm{H}_{5} \mathrm{O}_{7}(aq) + 3 \mathrm{NaOH}(aq) \longrightarrow \mathrm{Na}_{3} \mathrm{C}_{6} \mathrm{H}_{5} \mathrm{O}_{7}(aq) + 3 \mathrm{H}_{2} \mathrm{O}(l) \] This indicates that 1 mole of citric acid reacts with 3 moles of sodium hydroxide.

Calculate moles of NaOH used

Determine the moles of sodium hydroxide used in the titration:\[ \text{Moles of NaOH} = \text{Volume (L)} \times \text{Molarity (M)} \]Convert 35.6 mL of NaOH to liters (\(35.6 \times 10^{-3} \) L) and multiply by the molarity (0.0400 M):\[ \text{Moles of NaOH} = 35.6 \times 10^{-3} \times 0.0400 = 0.001424 \]

Use stoichiometry to find moles of citric acid

From the balanced equation, 3 moles of NaOH react with 1 mole of citric acid. Therefore, the moles of citric acid is:\[ \text{Moles of Citric Acid} = \frac{0.001424}{3} \approx 0.0004747 \]

Calculate molarity of the citric acid

The molarity of citric acid is calculated using:\[ \text{Molarity} = \frac{\text{Moles}}{\text{Volume (L)}} \]Convert 25.0 mL of the beverage to liters (\(25.0 \times 10^{-3} \text{ L} \)):\[ \text{Molarity} = \frac{0.0004747}{25.0 \times 10^{-3}} = 0.0190 \text{ M} \]

Key concepts

Citric Acid

Citric acid, a weak organic acid, is naturally found in citrus fruits like lemons and oranges. In the context of the exercise, it plays a crucial role as a flavoring agent in beverages like sports drinks. Its chemical formula is \( \mathrm{H}_{3} \mathrm{C}_{6} \mathrm{H}_{5} \mathrm{O}_{7} \), indicating that it has three acidic hydrogen atoms. This makes it triprotic, meaning it can donate three protons in reactions with bases such as sodium hydroxide (NaOH).

• Citric acid contributes a sour taste to foods and drinks.
• It acts as a natural preservative by lowering the pH to prevent microbial growth.
• In chemistry, citric acid is used in titration to standardize solutions and determine concentrations.

Molarity Calculation

Molarity is a measure of concentration that expresses the number of moles of a solute in one liter of solution. In titration exercises like the one described, calculating molarity involves several steps.Firstly, identify the volume of the titrant (sodium hydroxide, in this case) used and its known molarity. Convert the volume from milliliters to liters before proceeding with further calculations. The moles of titrant can be calculated using the equation:\[\text{Moles of \( \mathrm{NaOH} \)} = \text{Volume (L)} \times \text{Molarity (M)}\]In our example, 0.0400 M NaOH titrated 35.6 mL of solution. Converting 35.6 mL to liters gives 0.0356 L, leading to 0.001424 moles of NaOH.Lastly, use the moles of NaOH and the volume of the beverage sample to calculate the molarity of citric acid, again converting milliliters to liters:\[\text{Molarity of \( \mathrm{H}_{3} \mathrm{C}_{6} \mathrm{H}_{5} \mathrm{O}_{7} \)} = \frac{\text{Moles of citric acid}}{\text{Volume of solution (L)}}\]This results in a molarity of 0.0190 M for the citric acid in the beverage.

Chemical Stoichiometry

Chemical stoichiometry is vital for understanding reactions and determining the quantities of reactants and products. It involves using balanced chemical equations to relate the amounts of substances involved in a reaction.In the given titration exercise, the key stoichiometric relationship comes from the balanced chemical equation:\[\mathrm{H}_{3} \mathrm{C}_{6} \mathrm{H}_{5} \mathrm{O}_{7}(aq) + 3 \mathrm{NaOH}(aq) \rightarrow \mathrm{Na}_{3} \mathrm{C}_{6} \mathrm{H}_{5} \mathrm{O}_{7}(aq) + 3 \mathrm{H}_{2} \mathrm{O}(l)\]This equation indicates that three moles of NaOH are needed to fully react with one mole of citric acid. By using the moles of NaOH, which is 0.001424, you can find the moles of citric acid by dividing by the coefficient from the balanced equation:\[\text{Moles of citric acid} = \frac{0.001424}{3} \approx 0.0004747\]This stoichiometric approach is essential to determine the mole relationship and ensure precise molarity calculations in the broader context of chemical analysis.