How many molecules of CH_4 are present in 48.2 g of this compound?

• A. 1.81 × 10^{24} molecules
• B. 2.90 × 10^{24} molecules
• C. 9.02 × 10^{23} molecules
• D. 3.01 × 10^{23} molecules

Answer: (A)

Verified step by step guidance

1. Determine the molar mass of methane (CH_4) by adding the atomic masses of carbon and hydrogen: \(Molar\ mass = (1 \times 12.01\ g/mol) + (4 \times 1.008\ g/mol)\).
2. Calculate the number of moles of CH_4 in 48.2 g using the formula: \(n = \frac{mass}{molar\ mass} = \frac{48.2\ g}{Molar\ mass}\).
3. Recall that one mole of any substance contains Avogadro's number of molecules, which is \$6.022 \times 10^{23}$ molecules/mol.
4. Calculate the number of molecules by multiplying the number of moles by Avogadro's number: \(Number\ of\ molecules = n \times 6.022 \times 10^{23}\).
5. Express the final answer in scientific notation to match the format of the given options.