Problem 87 - Chemistry The Science in Context

Question

Sour Candy Tartaric acid, \(\mathrm{C}_{4} \mathrm{H}_{6} \mathrm{O}_{6},\) and citric acid, \(\mathrm{C}_{6} \mathrm{H}_{8} \mathrm{O}_{7},\) are both used commercially to give sour candies (Figure \(\mathrm{P} 3.87\) ) their characteristic sour taste. Which compound has the larger percent C by mass? (IMAGE CAN'T COPY)

Step-by-Step Solution

Answer

Answer: Citric Acid has a larger percent of Carbon by mass.

Step 1: Find the molar mass of Tartaric Acid (C4H6O6) and Citric Acid (C6H8O7)

To find the molar mass of each compound, we need to multiply the number of each atom in the compound by its atomic mass, and sum them up. For Tartaric Acid (C4H6O6): Molar mass = (4 * 12.01 [C]) + (6 * 1.01 [H]) + (6 * 16.00 [O]) = 48.04 + 6.06 + 96.00 = 150.10 g/mol For Citric Acid (C6H8O7): Molar mass = (6 * 12.01 [C]) + (8 * 1.01 [H]) + (7 * 16.00 [O]) = 72.06 + 8.08 + 112.00 = 192.14 g/mol

Step 2: Calculate the mass percent of Carbon in Tartaric Acid and Citric Acid

To calculate the mass percent of Carbon, divide the mass of Carbon by the total molar mass of the compound and multiply by 100. For Tartaric Acid: Mass percent of C = (Mass of Carbon / Molar mass of Tartaric Acid) * 100 Mass percent of C = (48.04 / 150.10) * 100 = 32.01% For Citric Acid: Mass percent of C = (Mass of Carbon / Molar mass of Citric Acid) * 100 Mass percent of C = (72.06 / 192.14) * 100 = 37.48%

Step 3: Compare the mass percentages of Carbon in both compounds and determine which compound has the larger value

We compare the mass percent of Carbon in Tartaric Acid (32.01%) and Citric Acid (37.48%). As 37.48% > 32.01%, Citric Acid has the larger percent of Carbon by mass.

Key Concepts

Molar Mass

Understanding molar mass is essential for many chemistry calculations, including determining the percent composition of elements in a compound. Molar mass is the mass of one mole of a substance, typically expressed in grams per mole (g/mol). It is calculated by summing the atomic masses of all atoms present in a chemical formula.
For instance, to find the molar mass of tartaric acid (\( ext{C}_4 ext{H}_6 ext{O}_6 \)), you would multiply the number of each type of atom by its respective atomic mass and then sum these values:

• Carbon: 4 atoms x 12.01 g/mol = 48.04 g/mol
• Hydrogen: 6 atoms x 1.01 g/mol = 6.06 g/mol
• Oxygen: 6 atoms x 16.00 g/mol = 96.00 g/mol
• Total Molar Mass = 150.10 g/mol

Similarly, the molar mass of citric acid (\( ext{C}_6 ext{H}_8 ext{O}_7 \)) is calculated by:

• Carbon: 6 atoms x 12.01 g/mol = 72.06 g/mol
• Hydrogen: 8 atoms x 1.01 g/mol = 8.08 g/mol
• Oxygen: 7 atoms x 16.00 g/mol = 112.00 g/mol
• Total Molar Mass = 192.14 g/mol

Knowing the molar mass of a compound is crucial for calculating other properties like the percent composition of individual elements within the compound.

Tartaric Acid

Tartaric acid is an organic compound that is often found in plants, especially in grapes. It’s well-known for its role in the winemaking process and is also used to give candies a sour taste. Its chemical formula is \( ext{C}_4 ext{H}_6 ext{O}_6 \).
This formula tells us several key things about tartaric acid:

• It contains 4 carbon (C) atoms, 6 hydrogen (H) atoms, and 6 oxygen (O) atoms.
• The molar mass is 150.10 g/mol, calculated from the atomic weights of its elements.

The percent composition of carbon in tartaric acid is determined by comparing the mass of carbon in the compound with its total molar mass. The calculation is as follows:

• Mass of carbon = 48.04 g/mol
• Total molar mass = 150.10 g/mol
• Percent carbon by mass = (48.04 / 150.10) * 100 = 32.01%

Tartaric acid is not just limited to giving a zesty taste in candies. It has applications in baking, where it stabilizes egg whites, and in pharmaceuticals.

Citric Acid

Citric acid, another compound contributing to the sour taste in candies, is a weak organic acid that occurs naturally in citrus fruits. The chemical formula for citric acid is \( ext{C}_6 ext{H}_8 ext{O}_7 \).
This formula presents the structure of citric acid:

• It consists of 6 carbon (C) atoms, 8 hydrogen (H) atoms, and 7 oxygen (O) atoms.
• The molar mass of citric acid is 192.14 g/mol.

To calculate the percent composition of carbon in citric acid, follow this method:

• Mass of carbon = 72.06 g/mol
• Total molar mass = 192.14 g/mol
• Percent carbon by mass = (72.06 / 192.14) * 100 = 37.48%

Citric acid plays a significant role beyond flavoring. It's also commonly used as a natural preservative and helps balance the pH levels in foods. Furthermore, it's a key ingredient in a variety of cleaning products due to its effective, natural cleaning properties.