Find the ratio of the number of atoms present in 16 g of O_2 and 32 g of O_3.

Options

A. 1 : 1
B. 2 : 1
C. 1 : 3
D. 1 : 2

Answer

To find the ratio of the number of atoms present in 16 g of O₂ (oxygen) and 32 g of O₃ (ozone), we can follow these steps:

### Step 1: Calculate the number of moles of O₂
The molar mass of O₂ (oxygen) is calculated as follows:
- Each oxygen atom has a mass of approximately 16 g/mol.
- Therefore, the molar mass of O₂ = 2 × 16 g/mol = 32 g/mol.

Now, we can calculate the number of moles of O₂ in 16 g:
\[ \text{Number of moles of O₂} = \frac{\text{Given mass}}{\text{Molar mass}} = \frac{16 \, \text{g}}{32 \, \text{g/mol}} = 0.5 \, \text{moles} \]

### Step 2: Calculate the number of atoms in O₂
Each molecule of O₂ contains 2 oxygen atoms. Therefore, the number of atoms in O₂ can be calculated as:
\[ \text{Number of atoms in O₂} = \text{Number of moles} \times \text{Avogadro's number} \times \text{Atomicity} \]
\[ = 0.5 \, \text{moles} \times 6.022 \times 10^{23} \, \text{molecules/mole} \times 2 \, \text{atoms/molecule} \]
\[ = 0.5 \times 6.022 \times 10^{23} \times 2 = 6.022 \times 10^{23} \, \text{atoms} \]

### Step 3: Calculate the number of moles of O₃
The molar mass of O₃ (ozone) is calculated as follows:
- Each oxygen atom has a mass of approximately 16 g/mol.
- Therefore, the molar mass of O₃ = 3 × 16 g/mol = 48 g/mol.

Now, we can calculate the number of moles of O₃ in 32 g:
\[ \text{Number of moles of O₃} = \frac{\text{Given mass}}{\text{Molar mass}} = \frac{32 \, \text{g}}{48 \, \text{g/mol}} = \frac{2}{3} \, \text{moles} \]

### Step 4: Calculate the number of atoms in O₃
Each molecule of O₃ contains 3 oxygen atoms. Therefore, the number of atoms in O₃ can be calculated as:
\[ \text{Number of atoms in O₃} = \text{Number of moles} \times \text{Avogadro's number} \times \text{Atomicity} \]
\[ = \frac{2}{3} \, \text{moles} \times 6.022 \times 10^{23} \, \text{molecules/mole} \times 3 \, \text{atoms/molecule} \]
\[ = \frac{2}{3} \times 6.022 \times 10^{23} \times 3 = 4.014 \times 10^{23} \, \text{atoms} \]

### Step 5: Calculate the ratio of the number of atoms in O₂ to O₃
Now we can find the ratio of the number of atoms in O₂ to the number of atoms in O₃:
\[ \text{Ratio} = \frac{\text{Number of atoms in O₂}}{\text{Number of atoms in O₃}} = \frac{6.022 \times 10^{23}}{4.014 \times 10^{23}} = \frac{6.022}{4.014} \approx 1.5 \]

To express this ratio in simplest form:
\[ \text{Ratio} = \frac{3}{2} \quad \text{or} \quad 1:2 \]

### Final Answer
The ratio of the number of atoms present in 16 g of O₂ to 32 g of O₃ is **1:2**.