Problem 76 - Chemistry and Chemical Reactivity

Question

Vitamin C has the formula \(\mathrm{C}_{6} \mathrm{H}_{8} \mathrm{O}_{6}\). Besides being an acid, it is a reducing agent. One method for determining the amount of vitamin \(\mathrm{C}\) in a sample is to titrate it with a solution of bromine, \(\mathrm{Br}_{2}\), an oxidizing agent. $$\mathrm{C}_{6} \mathrm{H}_{8} \mathrm{O}_{6}(\mathrm{aq})+\mathrm{Br}_{2}(\mathrm{aq}) \rightarrow 2 \mathrm{HBr}(\mathrm{aq})+\mathrm{C}_{6} \mathrm{H}_{6} \mathrm{O}_{6}(\mathrm{aq})$$ A 1.00 -g "chewable" vitamin C tablet requires \(27.85 \mathrm{mL}\) of \(0.102 \mathrm{M} \mathrm{Br}_{2}\) for titration to the equivalence point. What is the mass of vitamin \(\mathrm{C}\) in the tablet?

Step-by-Step Solution

Answer

The mass of vitamin C in the tablet is 0.500 g.

Step 1: Determine Moles of Bromine

First, calculate the moles of \( \mathrm{Br}_{2} \) required for the titration: \[ \text{moles of } \mathrm{Br}_{2} = \text{volume in L} \times \text{molarity} = 0.02785 \text{ L} \times 0.102 \frac{\text{mol}}{\text{L}} = 0.0028417 \text{ mol} \]

Step 2: Establish Stoichiometry of Reaction

Use the stoichiometry of the balanced equation to relate moles of \( \mathrm{Br}_{2} \) to moles of vitamin C. The balanced equation gives a 1:1 mole ratio between \( \mathrm{Br}_{2} \) and \( \mathrm{C}_{6} \mathrm{H}_{8} \mathrm{O}_{6} \). Therefore, the moles of vitamin C are also \( 0.0028417 \text{ mol} \).

Step 3: Calculate the Mass of Vitamin C

Calculate the mass of vitamin C using its molar mass (\( \mathrm{C}_{6} \mathrm{H}_{8} \mathrm{O}_{6} \)) which is approximately \( 176.12 \text{ g/mol} \).\[\text{mass} = \text{moles} \times \text{molar mass} = 0.0028417 \text{ mol} \times 176.12 \frac{\text{g}}{\text{mol}} = 0.5003 \text{ g}\]

Key Concepts

Titration

Titration is a common laboratory technique used to determine the concentration of an unknown substance. In simple terms, it involves adding a titrant with a known concentration to a solution containing the unknown concentration until a reaction is complete. This point is called the equivalence point.
The titration process is crucial for accurately finding the amount of a particular substance in a sample, such as vitamin C in a chewable tablet. By using a solution of bromine, a known oxidizing agent, we can titrate vitamin C to find its precise quantity.

• The known concentration of bromine for this exercise was 0.102 M.
• The endpoint of the titration is pronounced by the complete reaction, where no more bromine reacts with the vitamin C.

Calculating the amount of bromine used allows us to then compute the amount of vitamin C in the sample.

Reducing Agent

In chemical reactions, a reducing agent is a substance that donates electrons to another substance, effectively reducing the latter. In the context of vitamin C analysis, vitamin C acts as the reducing agent.
It reacts with bromine, an oxidizing agent, and in this process, bromine gets reduced, while vitamin C gets oxidized.

• Vitamin C (ascorbic acid) loses electrons in the reaction with bromine.
• The loss results in the transformation of vitamin C to dehydroascorbic acid.
• This redox reaction is fundamental for assessing the potency and effectiveness of vitamin C in samples.

Understanding this electron exchange is vital for accurately carrying out the titration and related calculations.

Stoichiometry

Stoichiometry is a branch of chemistry that studies the quantitative relationships between reactants and products in a chemical reaction. It offers a mathematical means to calculate just how much of each substance is involved in a reaction.
In the balanced chemical equation for the reaction between vitamin C and bromine, the stoichiometry tells us there is a 1:1 mole ratio.

• This means one mole of vitamin C reacts with one mole of bromine.
• Thus, by knowing the moles of bromine used, we directly equate that value to the moles of vitamin C.

This simple relationship is key in titration calculations since it allows the concentration of the unknown to be determined swiftly from the known reactant.

Molar Mass Calculation

Molar mass calculation is essential when trying to convert moles of a substance into grams, which is a more practical unit for measurement in laboratory settings.
Vitamin C, with the chemical formula \( \mathrm{C}_6 \mathrm{H}_8 \mathrm{O}_6 \), has a molar mass of about 176.12 g/mol.

• To find the mass of vitamin C from its moles, multiply the moles by the molar mass.
• In this scenario, we had 0.0028417 moles of vitamin C.
• By multiplying by 176.12 g/mol, we found the mass to be about 0.5003 grams.

This conversion crucially enables us to relate laboratory data (like titration volumes) back to real-life quantities such as grams for practical applications.