Question

One cup of fresh orange juice contains \(124 \mathrm{mg}\) of ascorbic acid (vitamin \(\mathrm{C}, \mathrm{C}_{6} \mathrm{H}_{8} \mathrm{O}_{6}\) ). Given that one cup \(=236.6 \mathrm{~mL}\), calculate the molarity of vitamin \(\mathrm{C}\) in organic juice.

Short answer

The molarity of vitamin C in fresh orange juice is \(2.98 \times 10^{-3}\ \mathrm{M}\).

Step-by-step solution

Find the molar mass of vitamin C

The molecular formula for vitamin C is C6H8O6. To find the molar mass of vitamin C, we need to add the atomic masses of all the atoms present in the vitamin C molecule. Molar mass of Carbon (C): \(6 \times 12.01 \mathrm{g/mol}\) Molar mass of Hydrogen (H): \(8 \times 1.01 \mathrm{g/mol}\) Molar mass of Oxygen (O): \(6 \times 16.00 \mathrm{g/mol}\) Now, add all these molar masses to find the total molar mass of Vitamin C: Molar mass of Vitamin C: \( (6 \times 12.01) + (8 \times 1.01) + (6 \times 16.00) \mathrm{g/mol}\) = 176.14 g/mol

Convert mass of vitamin C to moles

Now that we have the molar mass of Vitamin C, we can convert the mass of vitamin C present in one cup of orange juice to moles using the following formula: Number of moles = (mass of the substance) / (molar mass of the substance) Given, one cup of orange juice contains 124 mg of ascorbic acid (vitamin C). First, convert mg to g: 124 mg = 0.124 g Now, use the formula to calculate the number of moles of vitamin C: Number of moles = \( \frac{0.124 \mathrm{g}}{176.14 \mathrm{g/mol}} \) = \(7.04 \times 10^{-4} \mathrm{mol}\)

Calculate the volume of the solution in liters

Given that one cup of orange juice is equal to 236.6 mL. To calculate the molarity, we need to convert this volume to liters. Since 1 L = 1000 mL, we can make the conversion using the following formula: Volume in liters = Volume in mL / 1000 Volume in liters = \( \frac{236.6 \mathrm{mL}}{1000} \) = 0.2366 L

Calculate the molarity of the solution

Now that we have the number of moles of vitamin C and the volume of the solution in liters, we can calculate the molarity of vitamin C in orange juice using the following formula: Molarity = \( \frac{Number\ of\ moles}{Volume\ in\ liters} \) Molarity = \( \frac{7.04 \times 10^{-4} \mathrm{mol}}{0.2366 \mathrm{L}} \) = \(2.98 \times 10^{-3}\ \mathrm{M}\) Therefore, the molarity of vitamin C in fresh orange juice is \(2.98 \times 10^{-3}\ \mathrm{M}\).

Key concepts

Ascorbic Acid

Ascorbic acid, commonly known as vitamin C, is an essential nutrient found in various fruits and vegetables. It plays a key role in collagen synthesis, antioxidant protection, and immune defense. The biologically active form of ascorbic acid acts as a reducing agent, donates electrons, and supports numerous enzymatic reactions.
In the context of chemistry, ascorbic acid is an organic compound with the molecular formula \( C_{6}H_{8}O_{6} \). It is often emphasized in nutritional discussions because human organisms cannot synthesize it, necessitating its acquisition through diet.

• Key Roles: Supports the immune system, aids in collagen synthesis, and acts as an antioxidant.
• Sources: Citrus fruits like oranges, as well as strawberries, kiwis, and bell peppers.

Despite its common use, many might not realize the importance of ascorbic acid in maintaining overall health and its various applications in scientific studies.

Molecular Formula

The molecular formula provides a description of the types and numbers of atoms in a molecule. For vitamin C, this is \( C_{6}H_{8}O_{6} \).
Each element in the formula is represented by its chemical symbol, followed by a subscript indicating the number of atoms of that element present in one molecule.

• Carbon (C): In vitamin C, there are 6 atoms of carbon.
• Hydrogen (H): There are 8 atoms of hydrogen present.
• Oxygen (O): Vitamin C contains 6 atoms of oxygen.

The molecular formula is crucial for determining the molar mass, which is required for various chemical calculations, such as finding molarity. A simple molecular formula provides insights into the actual composition of the compound and assists in predicting its behavior in chemical reactions.

Molar Mass

Molar mass is a property that represents the mass of one mole of a substance, measured in grams per mole (g/mol). It serves as a bridge between the mass of the substance and the amount of substance in terms of moles.
For vitamin C, the process of determining its molar mass involves summing the atomic masses of all atoms present as per its molecular formula \( C_{6}H_{8}O_{6} \):
- **Carbon:** 6 atoms at \(12.01 \ ext{g/mol}\) each, totaling \(72.06 \ ext{g/mol}\)
- **Hydrogen:** 8 atoms at \(1.01 \ ext{g/mol}\) each, totaling \(8.08 \ ext{g/mol}\)
- **Oxygen:** 6 atoms at \(16.00 \ ext{g/mol}\) each, totaling \(96.00 \ ext{g/mol}\)
By adding these together, the molar mass of vitamin C is calculated to be \(176.14 \ ext{g/mol}\). Understanding the molar mass is vital when converting between mass and moles, a common necessity in chemical calculations like molarity.

Unit Conversion

Unit conversion is essential in chemistry to ensure that measurements are in compatible units for calculations. It allows for the easy transformation of values into units best suited for specific calculations.
In the exercise involving vitamin C in orange juice, several conversions were required:

• **Mass Conversion:** Converting 124 mg of vitamin C to grams since molar mass is typically expressed in grams per mole. This is done by dividing by 1000, resulting in 0.124 g.
• **Volume Conversion:** Since the molarity calculation requires volume in liters, converting 236.6 mL of juice to liters by dividing by 1000, results in a volume of 0.2366 L.

Overall, these conversions are crucial in effectively applying formulas, such as calculating molarity. They help bridge different units and measurement systems, making it easier to precisely handle and interpret data within scientific problems.