Problem 46 - Chemistry: Principles and Reactions

Question

A capsule of vitamin \(\mathrm{C}\), a weak acid, is analyzed by titrating it with \(0.425 M\) sodium hydroxide. It is found that \(6.20 \mathrm{~mL}\) of base is required to react with a capsule weighing \(0.628 \mathrm{~g}\). What is the percentage of vitamin \(\mathrm{C}\) \(\left(\mathrm{C}_{6} \mathrm{H}_{8} \mathrm{O}_{6}\right)\) in the capsule? (One mole of vitamin \(\mathrm{C}\) reacts with one mole of hydroxide ion.)

Step-by-Step Solution

Answer

Answer: To find the percentage of vitamin C in the capsule, follow the steps below: Step 1: Calculate the moles of sodium hydroxide used in the titration. moles of NaOH = molarity × volume = (0.425 M) × (6.20 mL × 0.001 L/mL) = 2.65 × 10^-3 moles Step 2: Calculate the moles of vitamin C. moles of vitamin C = moles of NaOH = 2.65 × 10^-3 moles Step 3: Calculate the mass of vitamin C. molar mass of vitamin C = (6 × 12.01 g/mol) + (8 × 1.01 g/mol) + (6 × 16.00 g/mol) = 176.13 g/mol mass of vitamin C = moles of vitamin C × molar mass of vitamin C = (2.65 × 10^-3 moles) × 176.13 g/mol = 0.466 g Step 4: Calculate the percentage of vitamin C in the capsule. percentage of vitamin C = (mass of vitamin C / mass of capsule) × 100 = (0.466 g / 0.628 g) × 100 = 74.2% The percentage of vitamin C in the capsule is 74.2%.

Step 1: Calculate the moles of sodium hydroxide used in the titration

Firstly, we need to convert the volume of sodium hydroxide used in the titration from milliliters to liters in order to use the molarity value. Then, we can find the moles of sodium hydroxide as follows: $$ \text{moles of NaOH} = \text{molarity} \times \text{volume} $$

Step 2: Calculate the moles of vitamin C

Since one mole of vitamin C reacts with one mole of hydroxide ion, the moles of vitamin C will be equal to the moles of sodium hydroxide: $$ \text{moles of vitamin C} = \text{moles of NaOH} $$

Step 3: Calculate the mass of vitamin C

To find the mass of vitamin C present in the capsule, we will use the molar mass of vitamin C (C6H8O6) and the moles of vitamin C calculated in the previous step: $$ \text{mass of vitamin C} = \text{moles of vitamin C} \times \text{molar mass of vitamin C} $$ The molar mass of vitamin C (C6H8O6) can be calculated by adding the molar masses of its constituent elements: 6C + 8H + 6O.

Step 4: Calculate the percentage of vitamin C in the capsule

Finally, we will calculate the percentage of vitamin C in the capsule using the mass of vitamin C and the given mass of the capsule: $$ \text{percentage of vitamin C} = \frac{\text{mass of vitamin C}}{\text{mass of capsule}} \times 100 $$

Key Concepts

Vitamin C

Vitamin C, also known as ascorbic acid, is an essential nutrient for maintaining optimal health. It's a water-soluble vitamin, meaning our bodies do not store it and we must consume it regularly. When present in capsules, Vitamin C can be quantitatively analyzed using various chemical methods, one of which is titration analysis. Vitamin C acts as a weak acid in these reactions. This property allows it to react with a strong base, such as sodium hydroxide, in a controlled environment to determine its concentration within a sample. This kind of analysis is crucial not only for understanding the quantity of a nutrient in dietary supplements but also for ensuring product quality and consumer safety.

Molarity Calculation

Molarity is a measure of the concentration of a solution, expressed as moles of solute per liter of solution. It's an essential concept in chemistry, particularly in titration analysis, where the precise measurement of reactants is fundamental. To calculate molarity, we use the formula:\[\text{Molarity (M)} = \frac{\text{moles of solute}}{\text{liters of solution}}\]In the context of this exercise, sodium hydroxide (NaOH) is used to titrate the vitamin C solution. By knowing the volume of NaOH used and its molarity, we can calculate the moles of NaOH involved in the reaction. In this exercise, converting milliliters to liters is crucial for accurate calculations because molarity is defined per liter. This conversion ensures that our calculations are consistent and reliable.

Acid-Base Reaction

An acid-base reaction is a chemical process that involves the transfer of protons between a proton donor (acid) and a proton acceptor (base). In this exercise, vitamin C acts as the weak acid, while sodium hydroxide is the strong base. The reaction can be represented as follows:\[\text{C}_6\text{H}_8\text{O}_6 + \text{NaOH} \rightarrow \text{C}_6\text{H}_7\text{O}_6\text{Na} + \text{H}_2\text{O}\]This chemical equation shows the interaction between vitamin C and sodium hydroxide, resulting in the formation of water and a sodium ascorbate salt. Acid-base titration is a vital method for analytical purposes, as it allows for the precise determination of concentration in a sample through the careful measurement of the base needed to neutralize the acid.

Percentage Composition

Percentage composition refers to the proportion of a specific component within a compound relative to the entire sample, expressed as a percentage. In this analysis, our goal is to determine the percentage of vitamin C in a capsule. Once the mass of vitamin C is calculated from its moles, we can use the percentage composition formula:\[\text{Percentage of Vitamin C} = \left(\frac{\text{mass of vitamin C}}{\text{mass of capsule}}\right) \times 100\]This calculation gives us a clear picture of how much vitamin C is present compared to the total capsule mass. Understanding percentage composition ensures accuracy in labeling and informs consumers accurately about the contents of their supplements.

Mole-to-Mole Ratio

Understanding the mole-to-mole ratio is essential for any chemical reaction analysis. It indicates the proportion of moles of reactants that react to form products based on the balanced chemical equation. For this exercise, one mole of vitamin C reacts with one mole of sodium hydroxide. This relationship is integral for accurately calculating the moles of vitamin C based on the moles of NaOH used during titration. Being familiar with mole-to-mole ratios allows chemists to predict the quantity of products formed in a reaction and to determine the amounts of reactants needed. In our example, since they react in a one-to-one ratio, the moles of vitamin C directly equal the moles of sodium hydroxide, which simplifies the calculation significantly.