The number of atoms in 20 g of `SO_(3)` is approximately

Options

A. `1 xx 10^(23)`
B. `1.5 xx 10^(23)`
C. `2 xx 10^(23)`
D. `6 xx 10^(23)`

Answer

To find the number of atoms in 20 g of \( SO_3 \), we can follow these steps:

### Step 1: Calculate the molar mass of \( SO_3 \)
The molar mass of \( SO_3 \) can be calculated by adding the atomic masses of sulfur (S) and oxygen (O):
- Atomic mass of Sulfur (S) = 32 g/mol
- Atomic mass of Oxygen (O) = 16 g/mol

Since there are three oxygen atoms in \( SO_3 \):
\[ \text{Molar mass of } SO_3 = 32 \, \text{g/mol} + (3 \times 16 \, \text{g/mol}) = 32 \, \text{g/mol} + 48 \, \text{g/mol} = 80 \, \text{g/mol} \]

### Step 2: Calculate the number of moles of \( SO_3 \) in 20 g
Using the formula for moles:
\[ \text{Number of moles} = \frac{\text{mass (g)}}{\text{molar mass (g/mol)}} \]
Substituting the values:
\[ \text{Number of moles of } SO_3 = \frac{20 \, \text{g}}{80 \, \text{g/mol}} = 0.25 \, \text{moles} \]

### Step 3: Calculate the number of molecules in 0.25 moles of \( SO_3 \)
Using Avogadro's number, which is \( 6.022 \times 10^{23} \) molecules/mol:
\[ \text{Number of molecules} = \text{Number of moles} \times \text{Avogadro's number} \]
Substituting the values:
\[ \text{Number of molecules of } SO_3 = 0.25 \, \text{moles} \times 6.022 \times 10^{23} \, \text{molecules/mol} \approx 1.5055 \times 10^{23} \, \text{molecules} \]

### Step 4: Calculate the number of atoms in \( SO_3 \)
Each molecule of \( SO_3 \) contains 4 atoms (1 sulfur atom and 3 oxygen atoms). Therefore, the total number of atoms can be calculated as:
\[ \text{Number of atoms} = \text{Number of molecules} \times 4 \]
Substituting the values:
\[ \text{Number of atoms} = 1.5055 \times 10^{23} \, \text{molecules} \times 4 \approx 6.022 \times 10^{23} \, \text{atoms} \]

### Conclusion
The number of atoms in 20 g of \( SO_3 \) is approximately \( 6.022 \times 10^{23} \) atoms.