Certainly! To solve this problem, we follow these steps:
1. Determine the Molar Mass of C₇H₁₂N₂O₃:
- Carbon (C): There are 7 carbon atoms, and the atomic mass of carbon is approximately [tex]\( 12.01 \)[/tex] grams/mol.
[tex]\[
\text{Mass of Carbon} = 7 \times 12.01 = 84.07 \text{ grams/mol}
\][/tex]
- Hydrogen (H): There are 12 hydrogen atoms, and the atomic mass of hydrogen is approximately [tex]\( 1.008 \)[/tex] grams/mol.
[tex]\[
\text{Mass of Hydrogen} = 12 \times 1.008 = 12.096 \text{ grams/mol}
\][/tex]
- Nitrogen (N): There are 2 nitrogen atoms, and the atomic mass of nitrogen is approximately [tex]\( 14.01 \)[/tex] grams/mol.
[tex]\[
\text{Mass of Nitrogen} = 2 \times 14.01 = 28.02 \text{ grams/mol}
\][/tex]
- Oxygen (O): There are 3 oxygen atoms, and the atomic mass of oxygen is approximately [tex]\( 16.00 \)[/tex] grams/mol.
[tex]\[
\text{Mass of Oxygen} = 3 \times 16.00 = 48.00 \text{ grams/mol}
\][/tex]
- Now, sum up all the atomic masses to get the molar mass of C₇H₁₂N₂O₃:
[tex]\[
\text{Molar Mass of C}_{7}\text{H}_{12}\text{N}_{2}\text{O}_{3} = 84.07 + 12.096 + 28.02 + 48.00 = 172.186 \text{ grams/mol}
\][/tex]
2. Calculate the Number of Moles in the 10.0g Sample:
- The formula to calculate the number of moles is given by:
[tex]\[
\text{Number of moles} = \frac{\text{Mass of the sample}}{\text{Molar Mass}}
\][/tex]
- Plugging in the given values:
[tex]\[
\text{Number of moles} = \frac{10.0 \text{ grams}}{172.186 \text{ grams/mol}}
\][/tex]
- Performing the division gives:
[tex]\[
\text{Number of moles} = 0.0581 \text{ (rounded to 4 decimal places)}
\][/tex]
Therefore, in a 10.0g sample of C₇H₁₂N₂O₃, there are approximately [tex]\( 0.0581 \)[/tex] moles.
