Problem 127 - Chemistry Matter and Change

Question

Which of these contains the most moles of carbon atoms per mole of the compound ascorbic acid \(\left(\mathrm{C}_{6} \mathrm{H}_{8} \mathrm{O}_{6}\right)\) glycerin \(\left(\mathrm{C}_{3} \mathrm{H}_{8} \mathrm{O}_{3}\right),\) or vanillin \(\left(\mathrm{C}_{8} \mathrm{H}_{8} \mathrm{O}_{3}\right) ?\) Explain.

Step-by-Step Solution

Answer

Vanillin \(\left(\mathrm{C}_{8} \mathrm{H}_{8} \mathrm{O}_{3}\right)\) contains the most moles of carbon atoms per mole of the compound, with a ratio of 0.632 moles of carbon atoms per mole of vanillin. This is because its ratio of carbon atoms to the entire molar mass (0.632) is greater than the ratios for ascorbic acid (0.409) and glycerin (0.391).

Step 1: Recall relevant information of carbon atoms

Carbon has a molecular mass of 12 g/mol according to the periodic table.

Step 2: Calculate molar mass of compounds

For each compound, we calculate the molar mass as follows: 1. Ascorbic acid (C6H8O6): \(M_{ascorbic} = 6 \times 12 + 8 \times 1 + 6 \times 16 = 72 + 8 + 96 = 176 \: g/mol\) 2. Glycerin (C3H8O3): \(M_{glycerin} = 3 \times 12 + 8 \times 1 + 3 \times 16 = 36 + 8 + 48 = 92 \: g/mol\) 3. Vanillin (C8H8O3): \(M_{vanillin} = 8 \times 12 + 8 \times 1 + 3 \times 16 = 96 + 8 + 48 = 152 \: g/mol\)

Step 3: Calculate the ratio of carbon atoms in each compound to the molar mass of the entire compound

We then calculate the ratio as follows: 1. Ascorbic acid: \(Ratio_{ascorbic} = \frac{6 \times 12}{176} = \frac{72}{176} = 0.409\) 2. Glycerin: \(Ratio_{glycerin} = \frac{3 \times 12}{92} = \frac{36}{92} = 0.391\) 3. Vanillin: \(Ratio_{vanillin} = \frac{8 \times 12}{152} = \frac{96}{152} = 0.632\)

Step 4: Determine the compound with the highest ratio

Comparing the calculated ratios for each compound, we can see that vanillin has the highest ratio of carbon atoms to the entire molar mass, with a ratio of 0.632. Therefore, vanillin contains the most moles of carbon atoms per mole of the compound.

Key Concepts

Ascorbic Acid

Ascorbic acid, commonly known as Vitamin C, is a vital nutrient that supports various functions in the human body. Structurally, it is known by its chemical formula \( \text{C}_6\text{H}_8\text{O}_6 \). This means each molecule contains 6 carbon atoms, 8 hydrogen atoms, and 6 oxygen atoms.

The role of ascorbic acid in our body cannot be overstated. It is crucial for collagen synthesis, which helps maintain the integrity of skin, blood vessels, bones, and cartilage.

When examining its molecular composition in terms of carbon atoms, we calculate the molar mass of ascorbic acid as follows:

• Carbon: 6 atoms with atomic mass of 12, totaling \( 6 \times 12 = 72 \) g/mol
• Hydrogen: 8 atoms with atomic mass of 1, totaling \( 8 \times 1 = 8 \) g/mol
• Oxygen: 6 atoms with atomic mass of 16, totaling \( 6 \times 16 = 96 \) g/mol

The total molar mass is \( 176 \) g/mol. Although it includes 6 carbon atoms, when calculating the ratio of these carbon atoms over its entire molecular weight, the proportion comes to approximately \(0.409\), making it less compared to some other compounds.

This indicates that, per mole, ascorbic acid holds a moderate amount of carbon atoms compared to others discussed here.

Glycerin

Glycerin, also spelled glycerine, is a simple polyol compound, denoted by its chemical formula \( \text{C}_3\text{H}_8\text{O}_3 \). In everyday life, you can find glycerin in products like soaps, moisturizers, and medicine.

Let's break down glycerin's chemical composition:

• Carbon: 3 atoms, giving us \( 3 \times 12 = 36 \) g/mol
• Hydrogen: 8 atoms, equivalent to \( 8 \times 1 = 8 \) g/mol
• Oxygen: 3 atoms at \( 3 \times 16 = 48 \) g/mol

The molar mass of the entire glycerin molecule equates to \( 92 \) g/mol.

In terms of carbon content, we calculate the carbon atom ratio as \( \frac{36}{92} \), resulting in a ratio of approximately \(0.391\).

Though glycerin has important uses, particularly in softening and moisturizing applications, it does not contain as many moles of carbon as vanillin in relation to its total molar mass. Thus, within this context, glycerin presents a relatively lower carbon content.

Vanillin

Vanillin is an aromatic compound most famously responsible for the characteristic flavor and smell of vanilla. Chemically, it is represented by \( \text{C}_8\text{H}_8\text{O}_3 \), incorporating 8 carbon atoms, 8 hydrogen atoms, and 3 oxygen atoms.

When evaluated for its molecular makeup, the calculation of vanillin's molar mass is as follows:

• Carbon: 8 atoms, total \( 8 \times 12 = 96 \) g/mol
• Hydrogen: 8 atoms, total \( 8 \times 1 = 8 \) g/mol
• Oxygen: 3 atoms, total \( 3 \times 16 = 48 \) g/mol

The molar mass for a vanillin molecule is \( 152 \) g/mol.

In comparing the ratio of carbon atoms to its molar mass, we find \( \frac{96}{152} \) which equates to about \(0.632\) - the highest among the compounds compared.

This demonstrates vanillin’s unique property of having the highest moles of carbon atoms per mole of the compound among the three presented, making it rich in carbon content. So, when looking purely at carbon presence, vanillin stands out significantly.