How many grams of SiH_4 contain 8.23 \times 10^{22} atoms of hydrogen?

• A. 2.40 g
• B. 1.20 g
• C. 0.60 g
• D. 0.15 g

Answer: (C)

Verified step by step guidance

1. Identify the given information: the number of hydrogen atoms is \$8.23 \times 10^{22}\( atoms, and the compound is silane, \)\mathrm{SiH_4}$.
2. Determine the number of hydrogen atoms per molecule of \(\mathrm{SiH_4}\). Since the formula is \(\mathrm{SiH_4}\), each molecule contains 4 hydrogen atoms.
3. Calculate the number of \(\mathrm{SiH_4}\) molecules corresponding to the given hydrogen atoms by dividing the total hydrogen atoms by 4: \(\text{molecules of } \mathrm{SiH_4} = \frac{8.23 \times 10^{22}}{4}\).
4. Use Avogadro's number (\$6.022 \times 10^{23}\( molecules/mol) to convert the number of molecules to moles of \)\mathrm{SiH_4}\(: \)\text{moles of } \mathrm{SiH_4} = \frac{\text{number of molecules}}{6.022 \times 10^{23}}$.
5. Calculate the mass of \(\mathrm{SiH_4}\) by multiplying the moles by the molar mass of \(\mathrm{SiH_4}\). The molar mass is calculated as \$28.09 \text{ g/mol (Si)} + 4 \times 1.008 \text{ g/mol (H)}\(. Then, \)\text{mass} = \text{moles} \times \text{molar mass}$.