The van der Waals equation for one mole of a real gas can be written as `(P+(a)/(v^(2))(V-b)=RT`. For the gases `H_(2), NH_(3), and CH_(4)`, the value of 'a' `"bar L"^(-2)"mol"^(-2)` are 0.2453, 4.170 and 2.253` respectively.
Which of the following can be inferred from the 'a' values?

Options

A. `NH_(3)` can be most easily liquified
B. `H_(2)` can be most easily liquified
C. value of 'a' for `CH_(4)` is less than that of `NH_(3)` because it has the lower molar mass
D. intermolecular forces are the strongest in hydrogen

Answer

To solve the problem, we need to analyze the van der Waals equation and the given values of 'a' for the gases H₂, NH₃, and CH₄. The van der Waals equation is given as:

\[ \left(P + \frac{a}{V^2}\right)(V - b) = RT \]

Where:
- \(P\) = pressure
- \(V\) = volume
- \(R\) = universal gas constant
- \(T\) = temperature
- \(a\) = measure of the attraction between particles
- \(b\) = measure of the volume occupied by the gas particles

### Step 1: Understand the significance of 'a'
The value of 'a' in the van der Waals equation represents the strength of the attractive forces between the gas molecules. A higher value of 'a' indicates stronger intermolecular attractions, which can lead to easier liquefaction of the gas.

### Step 2: Compare the values of 'a' for the given gases
The values of 'a' for the gases are:
- For H₂: \(a = 0.2453 \, \text{bar L}^{-2} \text{mol}^{-2}\)
- For NH₃: \(a = 4.170 \, \text{bar L}^{-2} \text{mol}^{-2}\)
- For CH₄: \(a = 2.253 \, \text{bar L}^{-2} \text{mol}^{-2}\)

### Step 3: Analyze the values
- NH₃ has the highest value of 'a' (4.170), indicating it has the strongest intermolecular attractions.
- CH₄ has a moderate value of 'a' (2.253), indicating weaker attractions than NH₃ but stronger than H₂.
- H₂ has the lowest value of 'a' (0.2453), indicating it has the weakest intermolecular attractions.

### Step 4: Make inferences based on 'a'
From the values of 'a', we can infer:
1. NH₃ can be most easily liquefied due to its high value of 'a'.
2. H₂ cannot be easily liquefied as it has the lowest value of 'a'.
3. The strength of intermolecular forces decreases in the order: NH₃ > CH₄ > H₂.

### Conclusion
Based on the analysis, we conclude that the gas which can be most easily liquefied is NH₃, as it has the highest value of 'a'.