Problem 16 - Chemical Principles: The Quest for Insight

Question

A vitamin C tablet was analyzed to detcrmine whether it did in fact contain, as the manufacturer claimed, \(1.0 \mathrm{~g}\) of the vitamin. A tablet was dissolved in water to form a \(100.00-\mathrm{mL}\). solution, and a \(10.0-\mathrm{mL}\). sample was titrated with iodine (as potassium triiodide). It required \(10.1 \mathrm{~mL}\) of \(0.0521 \mathrm{MI}_{3}\) (aq) to reach the stoichiometric point in the titration, Given that \(1 \mathrm{~mol} \mathrm{I}_{3}^{-}-1 \mathrm{~mol}\) vitamin \(\mathrm{C}\) in the reaction, is the manufacturer's claim correct? The molar mass of vitamin \(\mathrm{C}\) is \(176 \mathrm{~g} \cdot \mathrm{mol}^{-1}\).

Step-by-Step Solution

Answer

After calculating the moles of vitamin C based on the titration and converting this to grams, the total mass of vitamin C in the tablet should be compared to the manufacturer's claim of 1.0 g.

Step 1: Determine the moles of I3- used in the titration

Calculate the moles of I3- by using the volume of I3- solution and its concentration. Use the formula: moles = concentration (M) x volume (L). In this case, moles of I3- = 0.0521 M x 10.1 mL = 0.0521 moles/L x 0.0101 L.

Step 2: Determine the moles of vitamin C

Using the stoichiometry of the reaction, which is 1 mol I3- to 1 mol vitamin C, we can determine the moles of vitamin C. Since the ratio is 1:1, the moles of vitamin C will be the same as the I3-, which is the moles calculated in Step 1.

Step 3: Calculate the mass of vitamin C in the titrated sample

To find the mass of vitamin C, multiply the moles of vitamin C by its molar mass. Mass = moles of vitamin C x molar mass of vitamin C = moles from step 2 x 176 g/mol.

Step 4: Calculate the total mass of vitamin C in the full solution

Since the 10.0 mL of the solution that was titrated is only a portion of the total 100.00 mL solution, multiply the mass of vitamin C found in the 10.0 mL sample by 10 to find the total mass in the full solution.

Step 5: Compare the calculated mass of vitamin C to the manufacturer's claim

After calculating the total mass of vitamin C present in the dissolved tablet, compare this mass to the manufacturer's claim of 1.0 g. If the calculated mass is close to 1.0 g, within experimental error, then the claim may be considered correct.

Key Concepts

Stoichiometry

Stoichiometry is the section of chemistry that involves using balanced chemical equations to calculate the quantities of reactants and products. It is based on the conservation of mass and the concept of moles, which allows chemists to count entities in chemical reactions by weighing them. Understanding stoichiometry is essential for vitamin C titration analysis since it helps to establish a clear relationship between the amount of iodine used in the titration (the titrant) and the amount of vitamin C present in the solution (the analyte). Essentially, the stoichiometry in our exercise is given as a 1:1 molar ratio, meaning that 1 mole of iodine reacts with 1 mole of vitamin C. This ratio allows us to directly translate the moles of iodine used in the titration to the moles of vitamin C in the sample.

Molar Mass Calculation

The molar mass of a substance is the mass of one mole of that substance, typically expressed in grams per mole (g/mol). Calculating molar mass is a fundamental step in chemical analyses as it bridges the gap between the mole concept and measurable quantities. For a complex molecule like vitamin C, molar mass can be found by summing the atomic masses of all the atoms in a single molecule of that substance. The molar mass of vitamin C is given as 176 g/mol. When analyzing vitamin C content, as detailed in our exercise, knowing the molar mass lets us convert moles of vitamin C to grams, providing a direct way to check whether the tablet meets the manufacturer's claimed amount.

Solution Concentration

Solution concentration is a measure of the quantity of solute present in a given quantity of solvent or solution. It's commonly expressed in molarity (M), which is the number of moles of solute per liter of solution. Understanding solution concentration is vital in titration analysis because it allows us to determine the amount of solute present in a certain volume of solution. By knowing the concentration of iodine in the titrant solution, we can calculate the number of moles of iodine that reacted with the vitamin C. In our example, the concentration of the iodine solution is 0.0521 M. This information, combined with the volume of iodine solution used in the titration, is crucial for determining the moles of iodine that reacted, and thus the moles of vitamin C in the sample.

Titration

Titration is an analytical technique used to determine the concentration of a solute in a solution. It involves the precise addition of a solution of known concentration (the titrant) to a solution of the solute whose concentration is unknown (the analyte), until the reaction reaches the stoichiometric point or endpoint. The volume of titrant required to reach this point allows for the calculation of the analyte's concentration. In the context of our exercise, a vitamin C solution was titrated using iodine. By reaching the stoichiometric point and measuring the volume of iodine solution used, we can calculate the concentration and therefore the mass of vitamin C in the tablet, verifying the manufacturer's claims. The key in titration is the use of a balanced chemical reaction and understanding the stoichiometry involved to ascertain the exact concentration of the analyte.