The speed of sound in hydrogen at N.T.P. is 1270 metres per second. Thenthe speed in a mixture of hydrogen and oxygen containing hydrogen and oxygen in the ration ` 4 : 1` by volume, will be

Options

A. 317 metre/sec
B. 635 metre/sec
C. 830 metre/sec
D. 950 metre/sec

Explanation

To solve the problem of finding the speed of sound in a mixture of hydrogen and oxygen with a volume ratio of 4:1, we can follow these steps:

### Step-by-Step Solution:

1. **Understand the Given Data**:
- Speed of sound in hydrogen (v_H2) = 1270 m/s.
- Volume ratio of hydrogen to oxygen = 4:1.

2. **Determine the Total Volume**:
- Let the volume of oxygen (V_O2) = V.
- Then, the volume of hydrogen (V_H2) = 4V.
- Total volume (V_total) = V_H2 + V_O2 = 4V + V = 5V.

3. **Calculate the Mass of Each Gas**:
- The molar mass of hydrogen (H2) = 2 g/mol.
- The molar mass of oxygen (O2) = 32 g/mol.
- Mass of hydrogen (m_H2) = volume × density = 4V × (2 g/mol) = 8V g.
- Mass of oxygen (m_O2) = volume × density = V × (32 g/mol) = 32V g.

4. **Calculate the Total Mass of the Mixture**:
- Total mass (m_total) = m_H2 + m_O2 = 8V + 32V = 40V g.

5. **Calculate the Density of the Mixture**:
- Density of the mixture (ρ_mixture) = total mass / total volume = (40V g) / (5V) = 8 g/V.

6. **Calculate the Density of Hydrogen**:
- Density of hydrogen (ρ_H2) = mass of hydrogen / volume of hydrogen = (8V g) / (4V) = 2 g/V.

7. **Find the Ratio of Densities**:
- Ratio of density of mixture to density of hydrogen = ρ_mixture / ρ_H2 = 8 g/V / 2 g/V = 4.

8. **Use the Speed of Sound Formula**:
- The speed of sound in a gas is inversely proportional to the square root of its density.
- Therefore, we can write:
\[ \frac{v_H2}{v_mixture} = \sqrt{\frac{\rho_{mixture}}{\rho_{H2}}} \]
- Substituting the values:
\[ \frac{1270}{v_mixture} = \sqrt{4} \]

9. **Solve for the Speed of Sound in the Mixture**:
- Since \(\sqrt{4} = 2\):
\[ \frac{1270}{v_mixture} = 2 \implies v_mixture = \frac{1270}{2} = 635 \text{ m/s}. \]

### Final Answer:
The speed of sound in the mixture of hydrogen and oxygen is **635 m/s**.

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