At the room temperature the velocity of sound in `O_(2)` gas is v. Then in mixture of `H_(2)` and `O_(2)` gas the speed of sound at same temperature :-

Options

A. will be less than v
B. wil be more than v
C. will be equal to v
D. nothing can be said

Explanation

To find the speed of sound in a mixture of hydrogen (H₂) and oxygen (O₂) gases at room temperature, we can follow these steps:

### Step-by-Step Solution:

1. **Understand the Formula for Speed of Sound**:
The speed of sound \( v \) in a gas can be expressed using the formula:
\[ v = \sqrt{\frac{\gamma RT}{M}} \]
where:
- \( \gamma \) is the adiabatic index (ratio of specific heats),
- \( R \) is the universal gas constant,
- \( T \) is the absolute temperature,
- \( M \) is the molar mass of the gas.

2. **Identify the Molar Mass of the Gases**:
- The molar mass of oxygen (O₂) is approximately 32 g/mol.
- The molar mass of hydrogen (H₂) is approximately 2 g/mol.

3. **Determine the Molar Mass of the Mixture**:
When mixing gases, the average molar mass \( M_{mix} \) can be calculated based on the proportions of each gas in the mixture. However, since we are only comparing the speed of sound in the mixture to that in O₂, we can note that:
- The molar mass of the mixture (H₂ and O₂) will be less than that of O₂ alone because H₂ has a much lower molar mass.

4. **Analyze the Effect on Speed of Sound**:
Since the speed of sound is inversely proportional to the square root of the molar mass, if the molar mass of the mixture is less than that of O₂, the speed of sound in the mixture will be greater than the speed of sound in O₂.

5. **Conclusion**:
Therefore, the speed of sound in the mixture of H₂ and O₂ at the same temperature will be more than \( v \), the speed of sound in O₂.

### Final Answer:
The speed of sound in the mixture of H₂ and O₂ will be **more than \( v \)**.

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