How many carbon atoms are present in 77.28 g of ethane (C2H6)?

• A. 2.41 × 10^{24}
• B. 3.10 × 10^{24}
• C. 6.02 × 10^{23}
• D. 1.55 × 10^{24}

Answer: (B)

Verified step by step guidance

1. Determine the molar mass of ethane (C2H6) by adding the atomic masses of its constituent atoms: 2 carbon atoms and 6 hydrogen atoms. Use the atomic masses approximately as 12.01 g/mol for carbon and 1.008 g/mol for hydrogen. The molar mass is calculated as \(\text{Molar mass} = 2 \times 12.01 + 6 \times 1.008\) g/mol.
2. Calculate the number of moles of ethane in 77.28 g by dividing the given mass by the molar mass: \(\text{moles of ethane} = \frac{77.28}{\text{molar mass}}\) mol.
3. Use Avogadro's number, \$6.022 \times 10^{23}\( molecules/mol, to find the total number of ethane molecules: \)\text{number of molecules} = \text{moles of ethane} \times 6.022 \times 10^{23}$.
4. Since each ethane molecule contains 2 carbon atoms, multiply the total number of molecules by 2 to find the total number of carbon atoms: \(\text{number of carbon atoms} = \text{number of molecules} \times 2\).
5. Express the final answer in scientific notation to match the format of the options provided.