Problem 109 - Chemistry The Molecular Science

Question

Vitamin \(\mathrm{C}\) is ascorbic acid, \(\mathrm{HC}_{6} \mathrm{H}_{7} \mathrm{O}_{6},\) which can be titrated with a strong base. \(\mathrm{HC}_{6} \mathrm{H}_{7} \mathrm{O}_{6}(\mathrm{aq})+\mathrm{NaOH}(\mathrm{aq}) \longrightarrow \mathrm{NaC}_{6} \mathrm{H}_{7} \mathrm{O}_{6}(\mathrm{aq})+\mathrm{H}_{2} \mathrm{O}(\ell)\) A student dissolved a \(500.0-\mathrm{mg}\) vitamin \(\mathrm{C}\) tablet in \(200.0 \mathrm{~mL}\) water and then titrated it with 0.1250 -M \(\mathrm{NaOH}\). It required \(21.30 \mathrm{~mL}\) of the base to reach the equivalence point. Calculate the mass percentage of the tablet that is impurity.

Step-by-Step Solution

Answer

The mass percentage of impurity in the tablet is 6.20%.

Step 1: Calculate moles of NaOH

First, calculate the moles of NaOH used in the titration. You can find this by multiplying the molarity of the NaOH solution (0.1250 M) by the volume of NaOH used (21.30 mL converted into L): \[ \text{Moles of } \text{NaOH} = 0.1250 \, \text{M} \times \frac{21.30 \, \text{mL}}{1000} = 0.0026625 \, \text{mol} \]

Step 2: Determine moles of ascorbic acid

The balanced chemical equation shows that the reaction between ascorbic acid (\( \text{HC}_6\text{H}_7\text{O}_6 \)) and NaOH is a 1:1 molar ratio. Therefore, the moles of ascorbic acid initially present is equal to the moles of NaOH: \[ \text{Moles of } \text{HC}_6\text{H}_7\text{O}_6 = 0.0026625 \, \text{mol} \]

Step 3: Calculate mass of ascorbic acid

Now, convert the moles of ascorbic acid to mass using its molar mass. The molar mass of \( \text{HC}_6\text{H}_7\text{O}_6 \) is approximately 176.12 g/mol: \[ \text{Mass of } \text{HC}_6\text{H}_7\text{O}_6 = 0.0026625 \, \text{mol} \times 176.12 \, \text{g/mol} = 0.469 \text{ g} \]

Step 4: Determine mass of impurity

Subtract the mass of the ascorbic acid from the mass of the tablet to find the mass of the impurity in the tablet: \[ \text{Mass of impurity} = 0.500 \, \text{g} - 0.469 \, \text{g} = 0.031 \, \text{g} \]

Step 5: Calculate mass percentage of impurity

Finally, calculate the mass percentage of impurity by dividing the mass of the impurity by the total mass of the tablet and multiplying by 100 to convert to a percentage: \[ \text{Mass percentage of impurity} = \left( \frac{0.031 \, \text{g}}{0.500 \, \text{g}} \right) \times 100 = 6.20\% \]

Key Concepts

Vitamin C

Vitamin C is an essential nutrient for human health. It's scientifically known as ascorbic acid.

It plays a vital role in the growth and repair of tissues in the body. You'll find Vitamin C primarily in fruits and vegetables.

• It boosts the immune system.
• Acts as a powerful antioxidant.
• Aids in iron absorption.
• Promotes healthy skin.

Despite its importance, the human body cannot produce or store Vitamin C, so it's crucial to include it in our diet daily.

Ascorbic Acid

Ascorbic acid is the chemical name for Vitamin C. In chemical terms, its formula is \( ext{HC}_6 ext{H}_7 ext{O}_6\). This compound is both water-soluble and a weak acidic.

Due to its acidic nature, ascorbic acid can react with certain substances, making it an excellent candidate for titration experiments. Titration helps to determine the concentration of a solute in a solution. Ascorbic acid can undergo a specific reaction with a base, such as sodium hydroxide (\( ext{NaOH}\)), leading to a neutralization reaction. This process is useful in calculating the precise amount of ascorbic acid present in a sample.

Molar Mass Calculation

To understand the molar mass, it's important to remember that it's the mass of one mole of a substance. For ascorbic acid (\( ext{HC}_6 ext{H}_7 ext{O}_6\)), you need to add the atomic masses of its constituent atoms. You have:

• 6 carbons (C), each with an atomic mass of \( ext{12.01 g/mol}\)
• 8 hydrogens (H), each with an atomic mass of \( ext{1.01 g/mol}\)
• 6 oxygens (O), each with an atomic mass of \( ext{16.00 g/mol}\)

Adding these will yield the molar mass:
\( ext{Molar Mass of } ext{HC}_6 ext{H}_7 ext{O}_6 = 6(12.01) + 8(1.01) + 6(16.00) = 176.12 ext{ g/mol}\).This computation is crucial in converting moles to grams during chemical analyses.

Impurity Percentage

The impurity percentage of a tablet tells us how much of the mass is due to substances other than the target compound, in this case, ascorbic acid. To calculate this:

First, determine the exact mass of the pure substance, ascorbic acid, through titration results. In this exercise, the ascorbic acid mass was found to be \( ext{0.469 g}\).
Subtract this from the total mass of the tablet (\( ext{0.500 g}\)), leaving you with \( ext{0.031 g}\) of impurities.

The mass percentage here is determined by the formula:

• \( ext{Mass percentage of impurity} = rac{ ext{mass of impurity}}{ ext{total mass of tablet}} imes 100\)

Using the values gives:
\( ext{6.20}\%\) of the tablet is composed of impurities. This technique is vital for quality control in pharmaceuticals to ensure products meet safety and efficacy standards.