The atomic weight of silicon is 28.086 and that of oxygen is 15.9994 on the C¹² scale. Calculate the mass in grams of a single molecule of SiO₂.

• A. 9.977 × 10^-23 gm
• B. 9.8 × 10^-22 gm
• C. 1 × 10^-22 gm
• D. 6.6 × 10^-23 gm

To find the mass of a single molecule of silicon dioxide (SiO₂), we first need to calculate the molar mass of SiO₂.

Step 1: Calculate Molar Mass

The molar mass of SiO₂ is determined by adding the atomic weights of silicon and oxygen:

• Silicon (Si): 28.086 g/mol
• Oxygen (O): 15.9994 g/mol

Since there are two oxygen atoms in SiO₂, the calculation is as follows:

Molar Mass of SiO₂ = 28.086 g/mol + (2 × 15.9994 g/mol)

Molar Mass of SiO₂ = 28.086 g/mol + 31.9988 g/mol = 60.0848 g/mol

Step 2: Convert Molar Mass to Mass of a Single Molecule

Next, we need to find the mass of one molecule. To do this, we divide the molar mass by Avogadro's number (approximately 6.022 × 10²³ molecules/mol):

Mass of one molecule = Molar Mass / Avogadro's Number

Mass of one molecule = 60.0848 g/mol / (6.022 × 10²³ molecules/mol)

Mass of one molecule ≈ 9.977 × 10^-23 g

Final Answer

The mass of a single molecule of SiO₂ is approximately 9.977 × 10^-23 grams. Therefore, the correct option is A. 9.977 × 10^-23 gm.