The correct order of normal boiling of `O_(2), N_(2), NH_(3)` and `CH_(4)` for whom the values of van der Waals constant `'a'` are `1.360, 1.390, 4.170` and `2.253 L^(2) atm mol^(-2)` respectively, is:

Options

A. `O_(2) lt N_(2) lt NH_(3) lt CH_(4)`
B. `O_(2) lt N_(2) lt CH_(4) lt NH_(3)`
C. `NH_(3) lt CH_(4) lt N_(2) lt O_(2)`
D. `NH_(3) lt CH_(4) lt O_(2) lt N_(2)`

Answer

To determine the correct order of normal boiling points for the gases \( O_2 \), \( N_2 \), \( NH_3 \), and \( CH_4 \) based on their van der Waals constant \( a \), we can follow these steps:

### Step 1: Understand the van der Waals equation
The van der Waals equation is given by:
\[ \left(P + \frac{a n^2}{V^2}\right)(V - nb) = nRT \]
Where:
- \( P \) is the pressure,
- \( V \) is the volume,
- \( n \) is the number of moles,
- \( R \) is the gas constant,
- \( T \) is the temperature,
- \( a \) and \( b \) are the van der Waals constants.

### Step 2: Analyze the given values of the van der Waals constant \( a \)
The values of the van der Waals constant \( a \) for the gases are:
- \( O_2 \): \( 1.360 \, L^2 \, atm \, mol^{-2} \)
- \( N_2 \): \( 1.390 \, L^2 \, atm \, mol^{-2} \)
- \( NH_3 \): \( 4.170 \, L^2 \, atm \, mol^{-2} \)
- \( CH_4 \): \( 2.253 \, L^2 \, atm \, mol^{-2} \)

### Step 3: Determine the relationship between \( a \) and boiling point
The van der Waals constant \( a \) is a measure of the attractive forces between particles. A higher value of \( a \) indicates stronger intermolecular forces, which typically results in a higher boiling point.

### Step 4: Compare the values of \( a \)
Now, we will compare the values of \( a \):
- \( NH_3 \) has the highest \( a \) value: \( 4.170 \)
- \( CH_4 \) is next: \( 2.253 \)
- \( N_2 \): \( 1.390 \)
- \( O_2 \): \( 1.360 \)

### Step 5: Order the boiling points based on \( a \)
Based on the values of \( a \):
1. \( NH_3 \) (highest boiling point)
2. \( CH_4 \)
3. \( N_2 \)
4. \( O_2 \) (lowest boiling point)

### Conclusion
The correct order of normal boiling points from highest to lowest is:
\[ NH_3 > CH_4 > N_2 > O_2 \]

### Final Answer
The correct order of normal boiling points is \( NH_3 > CH_4 > N_2 > O_2 \).

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