Out of the following gases under similar condition of temperature and pressure, the velocity of sound will be maximum in a) hydrogen b) nitrogen c) oxygen d) chlorine

Options

A. hydrogen
B. nitrogen
C. oxygen
D. chlorine

Explanation

To determine which gas has the maximum velocity of sound under similar conditions of temperature and pressure, we can use the formula for the velocity of sound in a gas:

### Step 1: Write the formula for the velocity of sound
The velocity of sound \( V \) in a gas is given by the formula:
\[ V = \sqrt{\frac{\gamma R T}{M}} \]
Where:
- \( \gamma \) = adiabatic index (constant for a given gas)
- \( R \) = universal gas constant (constant)
- \( T \) = absolute temperature (constant)
- \( M \) = molecular mass of the gas

### Step 2: Analyze the relationship
From the formula, we can see that the velocity of sound is inversely proportional to the square root of the molecular mass \( M \):
\[ V \propto \frac{1}{\sqrt{M}} \]
This means that as the molecular mass decreases, the velocity of sound increases.

### Step 3: Determine the molecular masses of the given gases
Now, let's find the molecular masses of the gases provided:
- Hydrogen (H₂): Molecular mass = 2 g/mol
- Nitrogen (N₂): Molecular mass = 28 g/mol (14 g/mol per nitrogen atom)
- Oxygen (O₂): Molecular mass = 32 g/mol (16 g/mol per oxygen atom)
- Chlorine (Cl₂): Molecular mass = 71 g/mol (35.45 g/mol per chlorine atom)

### Step 4: Compare the molecular masses
Now we can compare the molecular masses:
- Hydrogen: 2 g/mol
- Nitrogen: 28 g/mol
- Oxygen: 32 g/mol
- Chlorine: 71 g/mol

### Step 5: Identify the gas with the smallest molecular mass
Among these gases, hydrogen has the smallest molecular mass (2 g/mol).

### Step 6: Conclusion
Since the velocity of sound is inversely proportional to the square root of the molecular mass, the gas with the smallest molecular mass will have the maximum velocity of sound. Therefore, the velocity of sound will be maximum in hydrogen.

### Final Answer:
The velocity of sound will be maximum in **a) hydrogen**.

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