Problem 74 - Chemistry and Chemical Reactivity

Question

Vitamin C has the formula \(\mathrm{C}_{6} \mathrm{H}_{8} \mathrm{O}_{6} .\) Besides being an acid, it is a reducing agent. One method for determining the amount of vitamin \(\mathrm{C}\) in a sample is to titrate it with a solution of bromine, \(\mathrm{Br}_{2},\) an oxidizing agent. $$ \mathrm{C}_{6} \mathrm{H}_{8} \mathrm{O}_{6}(\mathrm{aq})+\mathrm{Br}_{2}(\mathrm{aq}) \rightarrow 2 \mathrm{HBr}(\mathrm{aq})+\mathrm{C}_{6} \mathrm{H}_{6} \mathrm{O}_{6}(\mathrm{aq}) $$ A \(1.00-\mathrm{g}\) "chewable" vitamin C tablet requires \(27.85 \mathrm{mL}\) of \(0.102 \mathrm{M} \mathrm{Br}_{2}\) for titration to the equivalence point. What is the mass of vitamin \(\mathrm{C}\) in the tablet?

Step-by-Step Solution

Answer

The mass of vitamin C in the tablet is 0.500 g.

Step 1: Write the balanced chemical equation

The balanced chemical equation for the reaction of vitamin C (ascorbic acid) with bromine is: \[ \mathrm{C}_{6} \mathrm{H}_{8} \mathrm{O}_{6} + \mathrm{Br}_{2} \rightarrow 2 \mathrm{HBr} + \mathrm{C}_{6} \mathrm{H}_{6} \mathrm{O}_{6} \] This equation shows that one mole of vitamin C reacts with one mole of bromine.

Step 2: Calculate moles of bromine

Use the molarity formula \( M = \frac{n}{V} \) to find the moles of bromine. Given \( M = 0.102\, \text{mol/L} \) and \( V = 27.85\, \text{mL} = 0.02785\, \text{L} \), the moles of \( \mathrm{Br}_2 \) are: \[ n = MV = 0.102 \times 0.02785 = 0.00284\, \text{mol} \]

Step 3: Use stoichiometry to find moles of vitamin C

From the balanced equation, the stoichiometry is 1:1 for vitamin C to bromine. Therefore, moles of vitamin C are equal to moles of bromine: \[ n_{\text{vitamin C}} = 0.00284\, \text{mol} \]

Step 4: Calculate the mass of vitamin C

Use the molar mass of vitamin C, \( \mathrm{C}_{6} \mathrm{H}_{8} \mathrm{O}_{6} \), which is approximately 176.12 g/mol, to find the mass. The mass of vitamin C is: \[ m = n \times \text{molar mass} = 0.00284 \times 176.12 = 0.5001\, \text{g} \]

Key Concepts

Chemical Stoichiometry

Stoichiometry allows us to determine the quantities of substances consumed or produced in a chemical reaction. It is based on the balanced chemical equation.
The balanced equation gives us the mole ratio of reactants and products. For example, in our vitamin C titration, the equation \( \text{C}_6\text{H}_8\text{O}_6 + \text{Br}_2 \to 2 \text{HBr} + \text{C}_6\text{H}_6\text{O}_6 \) tells us that 1 mole of vitamin C (\( \text{C}_6\text{H}_8\text{O}_6 \)) reacts with 1 mole of bromine (\( \text{Br}_2 \)).
This 1:1 mole ratio informs us that if we know the moles of bromine used, we also know the moles of vitamin C that reacted.
By converting moles into grams using the molar mass, stoichiometry directly leads to the answer about how much vitamin C is there in the sample.

Molarity Calculations

Molarity is a concept in chemistry that expresses the concentration of a solution.
It is calculated as moles of solute divided by liters of solution: \( M = \frac{n}{V} \), where \( M \) is the molarity, \( n \) is the number of moles, and \( V \) is the volume in liters.
In the vitamin C titration problem, the molarity of the bromine solution was given as 0.102 M, and the volume used was 27.85 mL, which converts to 0.02785 L when divided by 1000.
Multiplying the molarity by the volume gives the moles of bromine (\(0.00284\) mol). This calculation is crucial for finding how much bromine reacted with vitamin C.

Balanced Chemical Equation

A balanced chemical equation accurately represents the chemical reaction.
It shows the identities and the exact amounts of reactants and products. Each side of the equation must have the same number of each type of atom.
In our example, vitamin C reacts with bromine to form hydrobromic acid and dehydroascorbic acid. Notice the equation: \( \text{C}_6\text{H}_8\text{O}_6 + \text{Br}_2 \to 2 \text{HBr} + \text{C}_6\text{H}_6\text{O}_6 \).
Every atom is balanced, with one \( \text{Br}_2 \) yielding two hydrogen bromides and not altering the overall carbon, hydrogen, and oxygen atom counts. This balance is essential so stoichiometry calculations give accurate results.

Chemical Reactions and Equations

Chemical reactions represent processes where substances transform into different substances.
Reactions are depicted by chemical equations, which provide a concise description of the change.
In a vitamin C titration, the equation \( \text{C}_6\text{H}_8\text{O}_6 + \text{Br}_2 \to 2 \text{HBr} + \text{C}_6\text{H}_6\text{O}_6 \) shows a redox process where vitamin C, a reducing agent, loses electrons to bromine, an oxidizing agent.
Chemical equations must be balanced to accurately follow the conservation of mass and charge principles. This ensures that the stoichiometry and the moles of the reactants and products remain reliable for quantitative analysis.