Which of the following has longest mean free path under identical conditions of temperature and pressure ?

Options

A. `H_(2)`
B. `N_(2)`
C. `O_(2)`
D. `CO_(2)`

Explanation

To determine which gas has the longest mean free path under identical conditions of temperature and pressure, we can follow these steps:

### Step 1: Understand Mean Free Path
The mean free path (λ) is defined as the average distance a particle travels between successive collisions. It is influenced by the size of the particles (molecular diameter) and the number density of the particles in the gas.

### Step 2: Identify the Factors Affecting Mean Free Path
The mean free path is inversely proportional to the molecular weight of the gas and directly related to the molecular diameter. The formula for mean free path can be expressed as:
\[ λ = \frac{1}{\sqrt{2} \pi \sigma^2 n} \]
where:
- \( λ \) = mean free path
- \( σ \) = molecular diameter
- \( n \) = number density of the gas (number of moles per unit volume)

### Step 3: Compare Gases
To find out which gas has the longest mean free path, we need to consider the molecular weights and diameters of the gases in question. Generally, lighter gases with smaller molecular diameters will have longer mean free paths.

### Step 4: Analyze Given Gases
If we are given a list of gases (for example: H₂, O₂, N₂, CO₂), we can analyze their molecular weights:
- H₂ (Hydrogen) has a low molecular weight (2 g/mol).
- O₂ (Oxygen) has a higher molecular weight (32 g/mol).
- N₂ (Nitrogen) has a molecular weight of 28 g/mol.
- CO₂ (Carbon Dioxide) has a molecular weight of 44 g/mol.

### Step 5: Conclusion
Among these gases, H₂ has the lowest molecular weight, which means it will have the longest mean free path under identical conditions of temperature and pressure.

### Final Answer
The gas with the longest mean free path under identical conditions of temperature and pressure is **Hydrogen (H₂)**.

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