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 solve the problem of finding 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 in 16 g
The molar mass of O₂ (oxygen) is 32 g/mol.

\[ \text{Number of moles of O}_2 = \frac{\text{mass}}{\text{molar mass}} = \frac{16 \text{ g}}{32 \text{ g/mol}} = 0.5 \text{ moles} \]

### Step 2: Calculate the number of atoms in O₂
Each molecule of O₂ contains 2 atoms of oxygen. Therefore, the total number of atoms in 16 g of O₂ can be calculated as follows:

\[ \text{Number of atoms in O}_2 = \text{Number of moles} \times \text{Avogadro's number} \times \text{Number of atoms per molecule} \]

Using Avogadro's number (approximately \(6.022 \times 10^{23}\) mol⁻¹):

\[ \text{Number of atoms in O}_2 = 0.5 \text{ moles} \times 6.022 \times 10^{23} \text{ mol}^{-1} \times 2 = 6.022 \times 10^{23} \text{ atoms} \]

### Step 3: Calculate the number of moles of O₃ in 32 g
The molar mass of O₃ (ozone) is 48 g/mol.

\[ \text{Number of moles of O}_3 = \frac{32 \text{ g}}{48 \text{ g/mol}} = \frac{2}{3} \text{ moles} \]

### Step 4: Calculate the number of atoms in O₃
Each molecule of O₃ contains 3 atoms of oxygen. Therefore, the total number of atoms in 32 g of O₃ can be calculated as follows:

\[ \text{Number of atoms in O}_3 = \text{Number of moles} \times \text{Avogadro's number} \times \text{Number of atoms per molecule} \]

\[ \text{Number of atoms in O}_3 = \frac{2}{3} \text{ moles} \times 6.022 \times 10^{23} \text{ mol}^{-1} \times 3 = 4.014 \times 10^{23} \text{ atoms} \]

### Step 5: Find the ratio of the number of atoms in O₂ to the number of atoms in O₃
Now, we can find the ratio of the number of atoms in O₂ to the number of atoms in O₃:

\[ \text{Ratio} = \frac{\text{Number of atoms in O}_2}{\text{Number of atoms in O}_3} = \frac{6.022 \times 10^{23}}{4.014 \times 10^{23}} = \frac{6.022}{4.014} \approx 1.5 \]

### Step 6: Simplify the ratio
To express the ratio in simplest form, we can convert it to a fraction:

\[ \text{Ratio} = \frac{3}{2} \]

### Final Answer
The ratio of the number of atoms present in 16 g of O₂ to the number of atoms present in 32 g of O₃ is \(3:2\).

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