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 is converted into ozone (O3) in an adiabatic rigid container. We will determine which quantities of the gas sample will change as a result of this conversion.

### Step-by-Step Solution:

1. **Understanding the System**:
- We have an adiabatic rigid container, which means no heat is exchanged with the surroundings and the volume of the container remains constant.
- The gas in the container is oxygen (O2), and 50% of it is converted into ozone (O3).

2. **Chemical Reaction**:
- The conversion of oxygen to ozone can be represented by the reaction:
\[ 3 O_2 \rightarrow 2 O_3 \]
- This indicates that three molecules of oxygen yield two molecules of ozone.

3. **Initial and Final Moles**:
- Let’s assume we start with `n` moles of O2. After conversion, 50% of O2 gets converted to O3, so:
- Moles of O2 remaining = \( n - 0.5n = 0.5n \)
- Moles of O3 formed = \( 0.5n \) (since 50% of O2 is converted).

4. **Total Moles Before and After**:
- Initially, we have `n` moles of O2.
- After the reaction, we have \( 0.5n \) moles of O2 and \( 0.5n \) moles of O3.
- Total moles after reaction = \( 0.5n + 0.5n = n \).
- Therefore, the total number of moles remains constant.

5. **Pressure Change**:
- In an adiabatic process, the relationship between pressure (P), volume (V), and temperature (T) is given by the equation \( PV^\gamma = \text{constant} \).
- Since the volume is constant and the conversion of O2 to O3 changes the degrees of freedom of the gas, the value of gamma (γ) increases.
- An increase in γ leads to a decrease in pressure (P) since \( P \propto V^{-\gamma} \) when V is constant.

6. **Average Velocity and Momentum**:
- The average velocity of gas molecules can be affected by the change in the type of gas (from O2 to O3). However, since the average velocity is a vector quantity, the net average velocity remains zero due to random motion.
- The momentum, being a product of mass and velocity, will also remain unchanged in terms of net momentum since the average velocity is zero.

### Conclusion:
From the analysis, the quantities that will change are:
- **Pressure**: It will decrease due to the increase in gamma (γ).
- **Average Velocity**: The type of gas changes, affecting the molecular velocities.
- **Momentum**: Although the net momentum remains zero, the individual momenta of the gas molecules will change due to the change in gas type.

### Final Answer:
- The quantities that will change are **Pressure** and **Average Velocity**.