What is the percent by mass of carbon in C_{10}H_{14}N_{2}?

• A. 81.2%
• B. 52.3%
• C. 60.5%
• D. 74.1%

Answer: (D)

Verified step by step guidance

1. Identify the molecular formula given: \(C_{10}H_{14}N_{2}\), which means the compound contains 10 carbon atoms, 14 hydrogen atoms, and 2 nitrogen atoms.
2. Find the atomic masses of each element from the periodic table: Carbon (C) is approximately 12.01 g/mol, Hydrogen (H) is about 1.008 g/mol, and Nitrogen (N) is about 14.01 g/mol.
3. Calculate the molar mass of the compound by multiplying the number of atoms of each element by their atomic masses and then summing all contributions: \(\text{Molar mass} = (10 \times 12.01) + (14 \times 1.008) + (2 \times 14.01)\).
4. Calculate the total mass of carbon in the compound by multiplying the number of carbon atoms by the atomic mass of carbon: \(\text{Mass of C} = 10 \times 12.01\).
5. Determine the percent by mass of carbon using the formula: \(\% \text{C} = \left( \frac{\text{Mass of C}}{\text{Molar mass of compound}} \right) \times 100\%\).