Under similar conditions, in which of the following gases will the speed of sound be the least ?

Options

A. Nitrogen
B. Oxygen
C. Carbon dioxide
D. Sulphur dioxide

Explanation

To determine in which gas the speed of sound is the least under similar conditions, we will follow these steps:

### Step 1: Understand the relationship between speed of sound and density
The speed of sound (V) in a gas is given by the formula:
\[ V = \sqrt{\frac{\gamma \cdot P}{\rho}} \]
Where:
- \( \gamma \) is the adiabatic index (constant for a given gas),
- \( P \) is the pressure,
- \( \rho \) is the density of the gas.

### Step 2: Establish similar conditions
We need to ensure that all gases are under the same conditions:
- Fixed amount: 1 mole of each gas.
- Volume: 22.4 liters (at STP).
- Temperature: 0 degrees Celsius.
- Pressure: 1 atm.

### Step 3: Determine the density of each gas
Density (\( \rho \)) is defined as mass per unit volume. For 1 mole of gas, the mass is equal to the molar mass of the gas. Therefore, we can express density as:
\[ \rho = \frac{\text{Molar Mass}}{\text{Volume}} \]
Since the volume is the same for all gases (22.4 liters), the density will depend solely on the molar mass of each gas.

### Step 4: Identify the molar masses of the gases
- Nitrogen (N₂): ~28 g/mol
- Oxygen (O₂): ~32 g/mol
- Carbon Dioxide (CO₂): ~44 g/mol
- Sulfur Dioxide (SO₂): ~64 g/mol

### Step 5: Compare the molar masses
From the values:
- Nitrogen: 28 g/mol
- Oxygen: 32 g/mol
- Carbon Dioxide: 44 g/mol
- Sulfur Dioxide: 64 g/mol

### Step 6: Determine which gas has the highest molar mass
Sulfur Dioxide (SO₂) has the highest molar mass at 64 g/mol.

### Step 7: Conclude about the speed of sound
Since density is directly proportional to molar mass and inversely proportional to the speed of sound, the gas with the highest molar mass (Sulfur Dioxide) will have the highest density and, therefore, the lowest speed of sound.

### Final Answer
The gas in which the speed of sound will be the least is **Sulfur Dioxide (SO₂)**.

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