The ratio of velocity of sound in hydrogen and oxygen at STP is

Options

A. `16:1`
B. `8:0`
C. `4:1`
D. `2:1`

Explanation

To find the ratio of the velocity of sound in hydrogen and oxygen at Standard Temperature and Pressure (STP), we can follow these steps:

### Step-by-Step Solution:

1. **Understand the Formula for Velocity of Sound in Gases**:
The velocity of sound (V) in a gas can be expressed using the formula:
\[ V = \sqrt{\frac{\gamma R T}{M}} \]
where:
- \( \gamma \) = adiabatic constant (ratio of specific heats)
- \( R \) = universal gas constant
- \( T \) = absolute temperature
- \( M \) = molecular mass of the gas

2. **Identify Constants at STP**:
At STP, the temperature (T) and the adiabatic constant (\( \gamma \)) are the same for both hydrogen and oxygen. Therefore, we can simplify our comparison to focus on the molecular masses.

3. **Establish the Ratio of Velocities**:
We can express the ratio of the velocities of sound in hydrogen (VH) and oxygen (VO) as:
\[ \frac{V_H}{V_O} = \sqrt{\frac{M_O}{M_H}} \]
where \( M_O \) is the molecular mass of oxygen and \( M_H \) is the molecular mass of hydrogen.

4. **Determine Molecular Masses**:
- The molecular mass of oxygen (O2) is approximately 32 g/mol (16 g/mol for each oxygen atom).
- The molecular mass of hydrogen (H2) is approximately 2 g/mol (1 g/mol for each hydrogen atom).

5. **Calculate the Ratio**:
Substitute the molecular masses into the equation:
\[ \frac{V_H}{V_O} = \sqrt{\frac{32}{2}} = \sqrt{16} = 4 \]

6. **Final Ratio**:
Therefore, the ratio of the velocity of sound in hydrogen to that in oxygen is:
\[ \frac{V_H}{V_O} = 4:1 \]

### Conclusion:
The ratio of the velocity of sound in hydrogen and oxygen at STP is \( 4:1 \).

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