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 analyze the van der Waals constants 'a' for the gases H₂, NH₃, and CH₄, we can follow these steps:

### Step 1: Understand the van der Waals equation
The van der Waals equation is given by:
\[ P + \frac{a}{V^2}(V - b) = RT \]
Where:
- \( P \) = pressure
- \( V \) = volume
- \( T \) = temperature
- \( R \) = universal gas constant
- \( a \) = van der Waals constant related to the attractive forces between molecules
- \( b \) = volume occupied by one mole of gas molecules

### Step 2: Analyze the values of 'a'
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: Compare the values of 'a'
- The highest value of 'a' is for NH₃ (4.170), indicating it has the strongest intermolecular forces among the three gases.
- The second highest is for CH₄ (2.253), which indicates it has moderate intermolecular forces.
- The lowest value is for H₂ (0.2453), indicating it has the weakest intermolecular forces.

### Step 4: Draw conclusions based on 'a' values
1. **Liquefaction tendency**: A higher 'a' value means stronger intermolecular forces, which leads to easier liquefaction of the gas. Therefore, NH₃ will be the most easily liquefied gas, followed by CH₄, and H₂ will be the least easily liquefied.
2. **Intermolecular forces**: The order of strength of intermolecular forces is NH₃ > CH₄ > H₂. NH₃ has hydrogen bonding, which is stronger than the van der Waals forces present in CH₄ and H₂.

### Conclusion
From the analysis, we can infer:
- Ammonia (NH₃) is the most easily liquefied due to its high 'a' value.
- Hydrogen (H₂) will be liquefied the least easily due to its low 'a' value.
- The intermolecular forces in NH₃ are stronger than those in CH₄ and H₂ due to the presence of hydrogen bonding.