Question

The amount of ascorbic acid (vitamin \(\left.\mathrm{C}, \mathrm{C}_{6} \mathrm{H}_{8} \mathrm{O}_{6}\right)\) in tablets is determined by reaction with bromine and then titration of the hydrobromic acid with standard base: $$ \begin{array}{l} \mathrm{C}_{6} \mathrm{H}_{8} \mathrm{O}_{6}(a q)+\mathrm{Br}_{2}(a q) \longrightarrow \mathrm{C}_{6} \mathrm{H}_{6} \mathrm{O}_{6}(a q)+2 \mathrm{HBr}(a q) \\ \mathrm{HBr}(a q)+\mathrm{NaOH}(a q) \longrightarrow \mathrm{NaBr}(a q)+\mathrm{H}_{2} \mathrm{O}(l) \end{array} $$ A certain tablet is advertised as containing \(500 \mathrm{mg}\) of vitamin \(\mathrm{C}\). One tablet was dissolved in water and reacted with \(\mathrm{Br}_{2}\). The solution was then titrated with \(43.20 \mathrm{~mL}\) of \(0.1350 \mathrm{M} \mathrm{NaOH}\). Did the tablet contain the advertised quantity of vitamin C?

Short answer

The tablet contained 513.6 mg of vitamin C, which is more than the advertised 500 mg.

Step-by-step solution

Write down the balanced chemical equations

First, write the balanced equations for the reactions involved: 1. \[ \mathrm{C_{6}H_{8}O_{6}}(aq) + \mathrm{Br_{2}}(aq) \longrightarrow \mathrm{C_{6}H_{6}O_{6}}(aq) + 2\mathrm{HBr}(aq) \] 2. \[ \mathrm{HBr}(aq) + \mathrm{NaOH}(aq) \longrightarrow \mathrm{NaBr}(aq) + \mathrm{H_{2}O}(l) \]

Calculate the moles of NaOH used

Use the volume and molarity of NaOH to calculate the moles of NaOH used in the titration. Given: \( \text{Volume of } \mathrm{NaOH} = 43.20\, \mathrm{mL} = 0.04320\, \mathrm{L} \) \( \text{Molarity of } \mathrm{NaOH} = 0.1350\, \mathrm{M} \) Use the formula: \( \text{Moles of } \mathrm{NaOH} = \text{Molarity} \times \text{Volume} \) \[ \text{Moles of } \mathrm{NaOH} = 0.1350 \, \mathrm{M} \times 0.04320 \, \mathrm{L} = 0.005832 \, \mathrm{mol} \]

Determine the moles of HBr reacted

According to the second balanced equation, 1 mole of NaOH reacts with 1 mole of HBr. Therefore, moles of HBr = moles of NaOH. \( \text{Moles of HBr} = 0.005832 \, \mathrm{mol} \)

Calculate the moles of vitamin C reacted

According to the first balanced equation, 2 moles of HBr are produced for each mole of vitamin C. Using the moles of HBr, calculate the moles of vitamin C: \( \text{Moles of vitamin C} = \frac{\text{Moles of HBr}}{2} \) \[ \text{Moles of Vitamin C} = \frac{0.005832 \, \mathrm{mol}}{2} = 0.002916 \, \mathrm{mol} \]

Calculate the mass of vitamin C reacted

Convert the moles of vitamin C into grams using its molar mass. Molar mass of vitamin C, \( \mathrm{C_{6}H_{8}O_{6}} \): \[ 6 \times 12.01 \; (C) + 8 \times 1.01 \; (H) + 6 \times 16.00 \; (O) = 176.12 \; \mathrm{g/mol} \] Now, calculate the mass: \( \text{Mass of vitamin C} = \text{Moles} \times \text{Molar Mass} \) \[ \text{Mass of Vitamin C} = 0.002916 \, \mathrm{mol} \times 176.12 \, \mathrm{g/mol} = 0.5136 \, \mathrm{g} = 513.6 \, \mathrm{mg} \]

Compare with the advertised quantity

Compare the calculated mass of vitamin C with the advertised quantity of 500 mg. The tablet contained \(513.6\, \mathrm{mg}\) of Vitamin C, which is more than the advertised \(500\, \mathrm{mg}\).

Key concepts

Balanced Chemical Equations

Chemical reactions are represented by balanced chemical equations. Balancing equations means making sure there are equal numbers of each type of atom on both sides of the equation. In the exercise, there are two key reactions: the conversion of vitamin C to hydrobromic acid (HBr) and the neutralization of HBr with sodium hydroxide (NaOH). The balanced equations show the exact number of molecules involved in these reactions:

1. Vitamin C reacts with bromine: \[ \text{C}_{6}\text{H}_{8}\text{O}_{6} (aq) + \text{Br}_{2} (aq) \rightarrow \text{C}_{6}\text{H}_{6}\text{O}_{6} (aq) + 2\text{HBr} (aq) \]2. The acid-base titration: \[ \text{HBr} (aq) + \text{NaOH} (aq) \rightarrow \text{NaBr} (aq) + \text{H}_{2}\text{O} (l) \]In these equations, each side has the same number of each atom, showing the conservation of mass.

Molarity and Volume Calculations

The molarity of a solution tells us the concentration of solute in terms of moles per liter (M). To find the number of moles of a substance in a given volume of solution, we use the formula: \[ \text{Moles} = \text{Molarity} \times \text{Volume} \] In the exercise, the solution used in titration is NaOH with a molarity of 0.1350 M and a volume of 43.20 mL. We need to convert the volume from milliliters to liters (43.20 mL = 0.04320 L). Then, we can find the moles of NaOH: \[ \text{Moles of NaOH} = 0.1350 \text{ M} \times 0.04320 \text{ L} = 0.005832 \text{ mol} \]This step converts volume and concentration into moles, which are needed for further calculations.

Mole-to-Mole Relationships

Mole-to-mole relationships are crucial for understanding how different substances interact in a chemical reaction. Based on the balanced equations, we can determine how many moles of one reactant correspond to moles of another. In the exercise:

1. For the equation involving HBr and NaOH, a 1:1 ratio means 1 mole of NaOH reacts with 1 mole of HBr.
2. For the equation involving vitamin C and HBr, 1 mole of vitamin C produces 2 moles of HBr.

Using these relationships, we determine the moles of substances as follows:

- Moles of HBr = Moles of NaOH = 0.005832 mol
- Moles of Vitamin C = \[ \frac{\text{Moles of HBr}}{2} = \frac{0.005832}{2} = 0.002916 \text{ mol} \]Understanding these stoichiometric ratios allows us to interconvert between moles of different reactants and products accurately.

Mass Calculation from Moles

After determining the moles of a substance, we can find its mass using the molar mass. The molar mass of a compound is the sum of the atomic masses of all atoms in the molecular formula. For vitamin C (C\text{_6}H\text{_8}O\text{_6}), the molar mass is:

6(C) + 8(H) + 6(O) = 6 × 12.01 + 8 × 1.01 + 6 × 16.00 = 176.12 g/mol

Next, convert moles of vitamin C into grams using the molar mass:

\text{Mass of Vitamin C} = \[ \text{Moles} \times \text{Molar Mass} \] \( = 0.002916 \text{ mol} \times 176.12 \text{ g/mol} = 0.5136 \text{ g} \)

Converting grams to milligrams: 0.5136 g = 513.6 mg

Finally, comparing this mass to the advertised 500 mg shows the tablet contains 513.6 mg of vitamin C, confirming a higher content than claimed.