Four 1-1 litre flasks are seperately filled with the gases `H_(2)`, He and `O_(2)` and `O_(3)` at the same temperature and pressure. The ratio of total number of atomsof these gases present in different flask would be:

Options

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

Answer

To solve the problem, we need to calculate the total number of atoms present in each of the four flasks filled with different gases: hydrogen (H₂), helium (He), oxygen (O₂), and ozone (O₃).

### Step-by-Step Solution:

1. **Identify the number of moles in each flask**:
Since all flasks are of the same volume (1 litre) and are at the same temperature and pressure, the number of moles of gas in each flask will be the same. Let’s denote the number of moles as \( n \).

2. **Calculate the number of atoms for each gas**:
- **Hydrogen (H₂)**: Each molecule of H₂ contains 2 hydrogen atoms. Therefore, the total number of atoms in the flask containing hydrogen is:
\[ \text{Number of atoms in H₂} = 2n \]
- **Helium (He)**: Helium is a monatomic gas, meaning each helium atom is a single atom. Therefore, the total number of atoms in the flask containing helium is:
\[ \text{Number of atoms in He} = 1n = n \]
- **Oxygen (O₂)**: Each molecule of O₂ contains 2 oxygen atoms. Therefore, the total number of atoms in the flask containing oxygen is:
\[ \text{Number of atoms in O₂} = 2n \]
- **Ozone (O₃)**: Each molecule of O₃ contains 3 oxygen atoms. Therefore, the total number of atoms in the flask containing ozone is:
\[ \text{Number of atoms in O₃} = 3n \]

3. **Write the total number of atoms for each gas**:
- For H₂: \( 2n \)
- For He: \( n \)
- For O₂: \( 2n \)
- For O₃: \( 3n \)

4. **Determine the ratio of total number of atoms**:
To find the ratio of the total number of atoms in the four flasks, we can express it as:
\[ \text{Ratio} = \text{H₂ : He : O₂ : O₃} = 2n : n : 2n : 3n \]
Simplifying this ratio by dividing each term by \( n \):
\[ = 2 : 1 : 2 : 3 \]

5. **Final Ratio**:
The final ratio of the total number of atoms in the flasks containing H₂, He, O₂, and O₃ is:
\[ 2 : 1 : 2 : 3 \]