How many molecules of N_2O_4 are present in 76.3 g of N_2O_4? (Molar mass of N_2O_4 = 92.02 g/mol)

• A. 1.00 × 10^{23} molecules
• B. 5.00 × 10^{23} molecules
• C. 8.00 × 10^{22} molecules
• D. 2.50 × 10^{24} molecules

Answer: (B)

Verified step by step guidance

1. Identify the given information: mass of N_2O_4 is 76.3 g and the molar mass of N_2O_4 is 92.02 g/mol.
2. Calculate the number of moles of N_2O_4 using the formula: \(\text{moles} = \frac{\text{mass}}{\text{molar mass}} = \frac{76.3\ \text{g}}{92.02\ \text{g/mol}}\).
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 moles of N_2O_4 by Avogadro's number: \(\text{molecules} = \text{moles} \times 6.022 \times 10^{23}\).
5. Express the final answer in scientific notation to match the options provided.