If `eta=50%` of oxygen gas kept in an adiabatic rigid container gets converted into ozone `(O_(3))`. Then which of the following quantities of this gas sample will change.

Options

A. Volume
B. Pressure
C. Average velocity
D. Average momentum

Explanation

To solve the problem, we need to analyze the situation where 50% of oxygen gas (O2) in an adiabatic rigid container is converted into ozone (O3). We will look at the quantities that may change as a result of this conversion.

### Step-by-Step Solution:

1. **Understanding the System**:
- The container is adiabatic, meaning there is no heat exchange with the surroundings (ΔQ = 0).
- The container is rigid, indicating that the volume of the gas does not change.

2. **Adiabatic Process**:
- For an adiabatic process, the relationship between pressure (P), volume (V), and temperature (T) can be described by the equation \(PV^\gamma = \text{constant}\), where γ (gamma) is the adiabatic index.

3. **Conversion of O2 to O3**:
- When 50% of O2 is converted into O3, the number of moles of gas changes. O3 is more stable than O2, which implies that it has a lower degree of freedom.

4. **Effect on Degrees of Freedom**:
- The degree of freedom (F) for O2 is higher than that for O3. Since γ is related to the degree of freedom (γ = 1 + 2/F), a decrease in degrees of freedom leads to an increase in γ.

5. **Pressure Change**:
- Since the volume is constant and γ has increased due to the conversion, we can infer from the equation \(P \propto V^{-\gamma}\) that the pressure (P) must decrease as γ increases.

6. **Average Velocity**:
- The average velocity of gas molecules is determined by their random motion. Since the conversion does not affect the random motion of the remaining gas molecules, the average velocity remains zero.

7. **Average Momentum**:
- Average momentum is calculated as the product of mass and velocity. Since the average velocity is zero, the average momentum will also remain zero.

8. **Conclusion**:
- The only quantity that changes in this process is the pressure of the gas sample. The volume remains constant, and both the average velocity and average momentum remain unchanged.

### Final Answer:
The quantity that will change is **pressure**.

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