Question

A capsule of vitamin \(\mathrm{C}\), a weak acid, is analyzed by titration with \(0.450 \mathrm{M}\) potassium hydroxide. It is found that 5.94 \(\mathrm{mL}\) of the base are required to react with the contents of a capsule. If the contents have a mass of \(0.634 \mathrm{~g}\), what is the mass percent of vitamin \(\mathrm{C}\left(\mathrm{C}_{6} \mathrm{H}_{8} \mathrm{O}_{6}\right)\) in the capsule? \((\) One \(\mathrm{mol}\) of vi\(\operatorname{tamin} \mathrm{C}\) reacts with one \(\mathrm{mol}\) of \(\mathrm{OH}^{-} .\).)

Short answer

Answer: The mass percent of Vitamin C in the capsule is approximately 74.29%.

Step-by-step solution

Calculate moles of potassium hydroxide

First, we'll find the moles of potassium hydroxide (KOH) used in the titration. To do this, we can use the formula: moles = concentration x volume, where concentration is given as 0.450 M and volume is given as 5.94 mL. We need to convert the volume from mL to Liters to make the units consistent: 5.94 mL = 0.00594 L. Now we can calculate the moles of KOH: moles_KOH = (0.450 M)(0.00594 L) = 0.002673 mol

Determine moles of Vitamin C

We're given that Vitamin C reacts with OH- ions in a 1:1 ratio. Therefore, moles of Vitamin C = moles of OH- which is equal to the moles of KOH we found in Step 1: moles_Vitamin_C = 0.002673 mol

Calculate the mass of Vitamin C

Now, we'll find the mass of Vitamin C present in the capsule. We'll use the molar mass of Vitamin C which is C6H8O6: (6(12.01) + 8(1.01) + 6(16.00)) g/mol = 176.14 g/mol. Using the moles of Vitamin C found in Step 2, we can calculate the mass of Vitamin C in the capsule: mass_Vitamin_C = (0.002673 mol)(176.14 g/mol) = 0.471 g

Find the mass percent of Vitamin C in the capsule

Lastly, we'll find the mass percent of Vitamin C in the capsule. The formula for mass percent is: (mass of solute / mass of solution) x 100 According to the problem, the mass of the contents of the capsule is 0.634 g. Mass percent of Vitamin C = (0.471 g / 0.634 g) x 100 = 74.29 % So, the mass percent of Vitamin C in the capsule is approximately 74.29%.