Two containers are of equal volume.One contains `O_(2)` while the other has `H_(2)` Both are kept at same temperature. The ratio of their pressure will be (rms velocity of these gases have ratio as 1:4) for 1 mole of each gas-

Options

A. `1:1`
B. `1:4`
C. `1:8`
D. `1:2`

Explanation

To solve the problem, we will use the ideal gas law and the relationship between the root mean square (rms) velocity of the gases and their respective pressures.

### Step-by-Step Solution:

1. **Understand the Given Information**:
- We have two containers of equal volume.
- One container has oxygen gas (O₂) and the other has hydrogen gas (H₂).
- Both containers are kept at the same temperature (T).
- The ratio of the rms velocities of H₂ to O₂ is given as 1:4.

2. **Use the Ideal Gas Law**:
The ideal gas law is given by:
\[ PV = nRT \]
Where:
- \( P \) = pressure
- \( V \) = volume
- \( n \) = number of moles
- \( R \) = ideal gas constant
- \( T \) = temperature

3. **Find the Pressure for Each Gas**:
For 1 mole of each gas, the pressures can be expressed as:
\[ P_1 = \frac{nRT}{V} \quad \text{(for O₂)} \]
\[ P_2 = \frac{nRT}{V} \quad \text{(for H₂)} \]
Since both gases have the same volume (V), number of moles (n = 1), and temperature (T), we can simplify:
\[ P_1 = \frac{RT}{V} \quad \text{and} \quad P_2 = \frac{RT}{V} \]

4. **Calculate the Ratio of Pressures**:
Since both pressures are equal:
\[ P_1 = P_2 \]
Therefore, the ratio of the pressures is:
\[ \frac{P_1}{P_2} = 1 \]

5. **Conclusion**:
The ratio of the pressures of the two gases (O₂ and H₂) is:
\[ \frac{P_1}{P_2} = 1:1 \]

### Final Answer:
The ratio of their pressures is \( 1:1 \).

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