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 sulfur trioxide (SO₃), we can follow these steps:

### Step 1: Calculate the molar mass of SO₃
The molar mass of sulfur trioxide (SO₃) can be calculated using the atomic masses of sulfur and oxygen:
- Atomic mass of sulfur (S) = 32 g/mol
- Atomic mass of oxygen (O) = 16 g/mol

Since there are one sulfur atom and three oxygen atoms in SO₃, the molar mass is calculated as:
\[ \text{Molar mass of SO}_3 = 32 + (3 \times 16) = 32 + 48 = 80 \text{ g/mol} \]

### Step 2: Calculate the number of moles of SO₃ in 20 g
Using the formula for moles:
\[ \text{Moles} = \frac{\text{Given mass}}{\text{Molar mass}} \]
Substituting the values:
\[ \text{Moles of SO}_3 = \frac{20 \text{ g}}{80 \text{ g/mol}} = 0.25 \text{ moles} \]

### Step 3: Calculate the number of molecules in 0.25 moles of SO₃
Using Avogadro's number, which is \( 6.022 \times 10^{23} \) molecules/mol, we can find the number of molecules in 0.25 moles:
\[ \text{Number of molecules} = 0.25 \text{ moles} \times 6.022 \times 10^{23} \text{ molecules/mole} \]
Calculating this gives:
\[ \text{Number of molecules} = 0.25 \times 6.022 \times 10^{23} \approx 1.5055 \times 10^{23} \text{ molecules} \]

### Step 4: Calculate the number of atoms in SO₃
Each molecule of SO₃ contains 4 atoms (1 sulfur atom and 3 oxygen atoms). Therefore, the total number of atoms is:
\[ \text{Number of atoms} = \text{Number of molecules} \times 4 \]
Substituting the value from the previous step:
\[ \text{Number of atoms} = 1.5055 \times 10^{23} \text{ molecules} \times 4 \approx 6.022 \times 10^{23} \text{ atoms} \]

### Conclusion
The number of atoms in 20 g of SO₃ is approximately \( 6.022 \times 10^{23} \) atoms.

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