Find the number of atoms in 48 g of ozone at NTP.

Answer

To find the number of atoms in 48 g of ozone (O₃) at NTP, we can follow these steps:

### Step 1: Determine the molar mass of ozone (O₃)
The molar mass of ozone can be calculated as follows:
- The atomic mass of oxygen (O) = 16 g/mol
- Since ozone has three oxygen atoms, the molar mass of O₃ = 3 × 16 g/mol = 48 g/mol.

### Step 2: Calculate the number of moles of ozone in 48 g
Using the formula:
\[ \text{Number of moles} = \frac{\text{mass (g)}}{\text{molar mass (g/mol)}} \]
Substituting the values:
\[ \text{Number of moles of O₃} = \frac{48 \text{ g}}{48 \text{ g/mol}} = 1 \text{ mol} \]

### Step 3: Calculate the number of molecules of ozone
Using Avogadro's number (Nₐ = \(6.022 \times 10^{23}\) molecules/mol):
\[ \text{Number of molecules of O₃} = \text{Number of moles} \times Nₐ \]
Substituting the values:
\[ \text{Number of molecules of O₃} = 1 \text{ mol} \times 6.022 \times 10^{23} \text{ molecules/mol} = 6.022 \times 10^{23} \text{ molecules} \]

### Step 4: Calculate the number of oxygen atoms
Each molecule of ozone (O₃) contains 3 oxygen atoms. Therefore, the total number of oxygen atoms can be calculated as follows:
\[ \text{Number of oxygen atoms} = \text{Number of molecules of O₃} \times 3 \]
Substituting the values:
\[ \text{Number of oxygen atoms} = 6.022 \times 10^{23} \text{ molecules} \times 3 = 18.066 \times 10^{23} \text{ atoms} \]

### Final Answer
Thus, the total number of oxygen atoms in 48 g of ozone is approximately:
\[ \text{Number of oxygen atoms} \approx 1.8066 \times 10^{24} \text{ atoms} \]