The values of van der Waal's constants 'a' for the gases, `O_2, N_2`, `NH_3` and `CH_4` are 1.36, 1.39, 4.17 and 2.253 `L^2` atm mol `e^(-2)` respectively. The gas which can most easily be liquified is

Options

A. `O_2`
B. N_2
C. `NH_3`
D. `CH_4`

Answer

To determine which gas can most easily be liquefied based on the values of van der Waals constants 'a', we can follow these steps:

### Step 1: Understand the van der Waals equation
The van der Waals equation is given by:
\[ P + \frac{a n^2}{V^2} = \frac{nRT}{V - nb} \]
Where:
- \( P \) = pressure
- \( V \) = volume
- \( n \) = number of moles
- \( R \) = universal gas constant
- \( T \) = temperature
- \( a \) = van der Waals constant related to the attraction between particles
- \( b \) = van der Waals constant related to the volume occupied by the gas particles

### Step 2: Analyze the significance of 'a' and 'b'
- The constant 'a' indicates the strength of the attractive forces between the gas molecules. A higher value of 'a' means stronger intermolecular forces, which generally leads to easier liquefaction of the gas.
- The constant 'b' relates to the volume occupied by the gas molecules. A lower value of 'b' means less volume is occupied by the gas particles, which can also favor liquefaction.

### Step 3: Compare the values of 'a' for the given gases
The values of 'a' for the gases are:
- \( O_2 \): 1.36 L² atm mol⁻²
- \( N_2 \): 1.39 L² atm mol⁻²
- \( NH_3 \): 4.17 L² atm mol⁻²
- \( CH_4 \): 2.253 L² atm mol⁻²

### Step 4: Identify the gas with the highest 'a' value
From the values listed:
- The gas with the highest 'a' value is \( NH_3 \) (ammonia) with an 'a' value of 4.17 L² atm mol⁻².

### Step 5: Conclusion
Since \( NH_3 \) has the highest value of 'a', it indicates that it has the strongest intermolecular forces among the gases listed, making it the gas that can most easily be liquefied.

### Final Answer
The gas which can most easily be liquefied is **\( NH_3 \)**.

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