Question

\- Vomitoxin is produced by some fungi that grow on wheat and barley. It derives its name from the fact that it causes pigs that eat contaminated wheat to vomit. The chemical formula for vomitoxin is \(\mathrm{C}_{15} \mathrm{H}_{20} \mathrm{O}_{6}\). What is the percent composition of this compound?

Short answer

The percent composition of vomitoxin is 60.77\% C, 6.82\% H, and 32.37\% O.

Step-by-step solution

- Calculate Molar Mass

First, calculate the molar mass of vomitoxin by summing up the atomic masses of all the atoms in its formula \( \mathrm{C}_{15} \mathrm{H}_{20} \mathrm{O}_{6} \). The atomic masses are: C = 12.01 g/mol, H = 1.01 g/mol, O = 16.00 g/mol. Therefore, the molar mass is: \[ M = (15 \times 12.01) + (20 \times 1.01) + (6 \times 16.00) \ = 180.15 + 20.20 + 96.00 \ = 296.35 \text{ g/mol} \].

- Calculate Percent Composition of Carbon

Next, find the percent composition of carbon (C) using the formula: \[ \text{Percent Composition of C} = \left( \frac{\text{Mass of C in 1 mol of compound}}{\text{Molar mass of compound}} \right) \times 100 \].The mass of C is: \( 15 \times 12.01 = 180.15 \text{ g} \). Therefore, the percent composition of C is: \[ \left( \frac{180.15}{296.35} \right) \times 100 = 60.77\% \].

- Calculate Percent Composition of Hydrogen

Now, find the percent composition of hydrogen (H): The mass of H is: \( 20 \times 1.01 = 20.20 \text{ g} \). Therefore, the percent composition of H is: \[ \left( \frac{20.20}{296.35} \right) \times 100 = 6.82\% \].

- Calculate Percent Composition of Oxygen

Finally, find the percent composition of oxygen (O): The mass of O is: \( 6 \times 16.00 = 96.00 \text{ g} \). Therefore, the percent composition of O is: \[ \left( \frac{96.00}{296.35} \right) \times 100 = 32.37\% \].

Key concepts

molar mass calculation

To determine the percent composition of a compound, the first step is calculating its molar mass. Molar mass is the mass of one mole of a substance (usually in grams per mole). It is calculated by summing up the atomic masses of all the atoms in the compound's chemical formula.
In our example, we have vomitoxin with the chemical formula \(\text{C}_{15}\text{H}_{20}\text{O}_{6} \). Here's how you calculate it:

• Look up the atomic masses of Carbon (C), Hydrogen (H), and Oxygen (O):
  - C = 12.01 g/mol
  - H = 1.01 g/mol
  - O = 16.00 g/mol
• Multiply the atomic mass of each element by the number of atoms of that element in the formula, and then sum these values:
  \[\text{M} = (15 \times 12.01) + (20 \times 1.01) + (6 \times 16.00) = 180.15 + 20.20 + 96.00 = 296.35 \text{ g/mol} \]

This gives us the molar mass of vomitoxin, 296.35 g/mol. This value is essential for calculating the percent composition of each element in the compound.

percent composition calculation

The percent composition reflects the percentage by mass of each element in a compound. To find it, you use the molar mass calculated previously. The formula to determine the percent composition for an element is:
\[ \text{Percent Composition} = \frac{\text{Mass of element in 1 mole of compound}}{\text{Molar mass of compound}} \times 100 \]

• For Carbon (C):
  \[\text{Mass of C in 1 mole} = 15 \times 12.01 = 180.15 \text{ g} \]
  \[\text{Percent Composition of C} = \frac{180.15}{296.35} \times 100 = 60.77\text{\textpercent} \]
• For Hydrogen (H):
  \[\text{Mass of H in 1 mole} = 20 \times 1.01 = 20.20 \text{ g} \]
  \[\text{Percent Composition of H} = \frac{20.20}{296.35} \times 100 = 6.82\text{\textpercent} \]
• For Oxygen (O):
  \[\text{Mass of O in 1 mole} = 6 \times 16.00 = 96.00 \text{ g} \]
  \[\text{Percent Composition of O} = \frac{96.00}{296.35} \times 100 = 32.37\text{\textpercent} \]

These calculations show us the percent of each element in vomitoxin, important in fields like chemistry, nutrition, and environmental science.

chemical formula

The chemical formula of a compound tells us the types and numbers of atoms in one molecule of the compound. This information is crucial for understanding the compound's composition.

• For example, vomitoxin has a chemical formula of \(\text{C}_{15}\text{H}_{20}\text{O}_{6} \). This means it contains 15 carbon atoms, 20 hydrogen atoms, and 6 oxygen atoms in each molecule.
• Knowing the chemical formula helps chemists and scientists predict how the compound will react with other substances, its properties, and its overall structure.
• Without knowing the chemical formula, accurate calculations of molar mass and percent composition would be impossible.

This step lays the foundation for a deeper understanding of the compound's behavior and characteristics. It's like having a detailed recipe, telling you exactly what ingredients are included.