Question

A typical vitamin C tablet (containing pure ascorbic acid, \(\mathrm{H}_{2} \mathrm{C}_{6} \mathrm{H}_{6} \mathrm{O}_{6}\) ) weighs \(500 . \mathrm{mg}\). One vitamin C tablet is dissolved in enough water to make \(200.0 \mathrm{~mL}\) of solution. Calculate the pH of this solution. Ascorbic acid is a diprotic acid.

Short answer

The mass of ascorbic acid in the tablet is 500 mg. The molar mass of ascorbic acid is approximately 176.13 g/mol. To find the moles of ascorbic acid, we use the equation: \(\text{moles of ascorbic acid} = \frac{500\ \text{mg} \times \frac{1}{1000}\ \text{g/mg}}{176.13\ \text{g/mol}}\) Then, we find the concentration of ascorbic acid by dividing the moles of ascorbic acid by the volume of the solution (0.200 L): \(\text{concentration of ascorbic acid} = \frac{\text{moles of ascorbic acid}}{0.200\ \text{L}}\) Since ascorbic acid is diprotic, the concentration of H+ ions is twice the concentration of ascorbic acid. Finally, we can calculate the pH of the solution using the following formula: \(\text{pH} = -\log_{10}([\text{H}^{+}])\) Substitute the concentration of H+ into the pH formula to find the pH of the vitamin C solution.

Step-by-step solution

Calculate the mass of ascorbic acid in the vitamin C tablet

The mass of one vitamin C tablet is given as 500 mg. Since it contains pure ascorbic acid, the mass of ascorbic acid in the tablet is the same as the mass of the tablet: 500 mg.

Convert mass to moles

To convert the mass of ascorbic acid into moles, we need to use the molar mass of ascorbic acid, which is \(\mathrm{H}_{2}\mathrm{C}_{6}\mathrm{H}_{6}\mathrm{O}_{6}\). Therefore the molar mass of ascorbic acid is: 2(1.01) + 6(12.01) + 6(1.01) + 6(16.00) g/mol, which is approximately 176.13 g/mol. Now, we can convert the mass of ascorbic acid (500 mg) into moles using the molar mass: \(\text{moles of ascorbic acid} = \frac{500\ \text{mg} \times \frac{1}{1000}\ \text{g/mg}}{176.13\ \text{g/mol}}\)

Calculate the concentration of ascorbic acid

To find the concentration of ascorbic acid in the solution, we will divide the moles of ascorbic acid by the volume of the solution: \(\text{concentration of ascorbic acid} = \frac{\text{moles of ascorbic acid}}{\text{volume of solution}}\) The volume of the solution is given as 200.0 mL, which we should convert to liters: \(\text{volume of solution} = 200.0\ \text{mL} \times \frac{1}{1000}\ \text{L/mL}= 0.200\ \text{L}\) \(\text{concentration of ascorbic acid} = \frac{\text{moles of ascorbic acid}}{0.200\ \text{L}}\)

Calculate the concentration of hydrogen ions (H+)

Since ascorbic acid is diprotic, it can donate two H+ ions per molecule: \(\text{concentration of H}^{+} = 2 \times \text{concentration of ascorbic acid}\)

Calculate the pH of the solution

Using the concentration of hydrogen ions (H+), we can calculate the pH of the solution using the following formula: \(\text{pH} = -\log_{10}([\text{H}^{+}])\) Now, substitute the concentration of H+ obtained in step 4 into the pH formula to calculate the pH of the vitamin C solution.

Key concepts

Ascorbic Acid

Ascorbic acid, commonly known as vitamin C, is a vital nutrient for many animals. It serves various roles, including being an antioxidant and acting as a coenzyme in some metabolic pathways. Chemically, ascorbic acid is represented by the formula \(\mathrm{H}_{2}\mathrm{C}_{6}\mathrm{H}_{6}\mathrm{O}_{6}\).
This compound is a white crystalline powder that is highly soluble in water.
It is often used in dietary supplements to prevent deficiency diseases like scurvy.

• Plays a role in collagen synthesis.
• Boosts the immune system.
• Promotes iron absorption from plant-based foods.

Understanding the chemical nature of ascorbic acid is essential when doing calculations involving its concentration and its role in solution chemistry.

Diprotic Acid

Ascorbic acid is classified as a diprotic acid.
This means it can donate two protons (H\(^{+}\) ions) to a solution.
Being diprotic makes it more reactive than monoprotic acids like hydrochloric acid, which only releases one proton.

When dissolved in water, ascorbic acid undergoes ionization in two steps:

• The first ionization releases one H\(^{+}\) ion.
• The second ionization releases another H\(^{+}\) ion.

This multi-step ionization impacts how we calculate the concentration of hydrogen ions and, subsequently, the pH of solutions containing diprotic acids.
For complete ionization, each molecule of ascorbic acid contributes two protons to the solution, thus impacting the acidity and lowering the pH value.

Concentration Calculation

Calculating the concentration of a solution is a common process in chemistry.
In the case of the vitamin C tablet, we need to find how many moles of ascorbic acid are present and then determine their concentration in the solution.
This involves converting mass to moles, using the molar mass, and dividing by the volume of the solution in liters. The formula for concentration is:\[\text{Concentration} = \frac{\text{Moles of solute}}{\text{Volume of solution (L)}}\]

• Convert mass to moles using molar mass.
• Convert volume from mL to L (1 mL = 0.001 L).
• Apply the concentration formula.

For instance, a 500 mg tablet with a molar mass of 176.13 g/mol and dissolved in 200 mL of water needs these conversions to find the concentration before proceeding with further calculations.

Molar Mass

Molar mass is a critical factor in transforming mass measurements into moles, which are necessary for concentration calculations.
For ascorbic acid, its molar mass is calculated based on its chemical composition: \(\mathrm{H}_{2}\mathrm{C}_{6}\mathrm{H}_{6}\mathrm{O}_{6}\).
The calculation is achieved by summing up the atomic weights of all atoms in the molecule:

• Hydrogen (H): 1.01 g/mol, multiplied by 2.
• Carbon (C): 12.01 g/mol, multiplied by 6.
• Oxygen (O): 16.00 g/mol, multiplied by 6.

Summing these yields a molar mass of approximately 176.13 g/mol.
This value is vital as it allows chemists to convert mass to moles using the relationship: \[\text{Moles} = \frac{\text{Mass (g)}}{\text{Molar Mass (g/mol)}}\]Such conversions are necessary when you want to calculate concentrations and understand the compound's role in a chemical reaction.

Solution Chemistry

Solution chemistry focuses on the properties and behavior of solutes and solvents.
When dissolving substances like ascorbic acid, understanding ionic interactions, solubility, and pH changes are essential.
The process includes:

• Dissolving: Distributing the solute particles uniformly in the solvent.
• Ionization: Conversion of molecules into ions within the solvent, significant for acids like ascorbic acid.
• pH Calculation: Based on the concentration of hydrogen ions (H\(^{+}\)) in the solution.

The pH is a measure of how acidic or basic a solution is, calculated via the formula:\[\text{pH} = -\log_{10}[\text{H}^{+}]\]Considering ascorbic acid is a diprotic acid that donates two H\(^{+}\) ions, the pH is affected such that calculating the exact concentration of H\(^{+}\) is crucial for determining the solution's acetic strength.