For the reaction `N_2O_4 hArr 2NO_2(g)`, if percentage dissociation of `N_2O_4` are 20%, 45%, 65%, 80% then the sequence of observed vapour densities wil be :

Options

A. `d_(20) gt d_45 gtd_65 gt d_80`
B. `d_(80) gt d_65 gtd_45 gt d_20`
C. `d_(20) =d_45 =d_65 = d_80`
D. `(d_20 =d_45) gt (d_65 = d_80)`

Answer

To solve the problem regarding the sequence of observed vapor densities for the dissociation of \( N_2O_4 \) into \( 2NO_2 \), we will follow these steps:

### Step 1: Understand the Reaction and Dissociation
The reaction is given as:
\[ N_2O_4 \rightleftharpoons 2NO_2 \]
Let’s denote the initial amount of \( N_2O_4 \) as \( n_0 \).

### Step 2: Define Percentage Dissociation
Percentage dissociation (\( \alpha \)) is given for different cases:
- 20%
- 45%
- 65%
- 80%

This means:
- For 20% dissociation, \( \alpha = 0.20 \)
- For 45% dissociation, \( \alpha = 0.45 \)
- For 65% dissociation, \( \alpha = 0.65 \)
- For 80% dissociation, \( \alpha = 0.80 \)

### Step 3: Calculate the Vapor Density
The vapor density (\( d \)) can be related to the degree of dissociation using the formula:
\[ d = \frac{d_0}{1 + \alpha} \]
where \( d_0 \) is the vapor density of the undissociated \( N_2O_4 \).

### Step 4: Calculate for Each Percentage Dissociation
Now we will calculate the vapor density for each percentage dissociation:

1. **For 20% Dissociation** (\( \alpha = 0.20 \)):
\[ d_{20} = \frac{d_0}{1 + 0.20} = \frac{d_0}{1.20} \]

2. **For 45% Dissociation** (\( \alpha = 0.45 \)):
\[ d_{45} = \frac{d_0}{1 + 0.45} = \frac{d_0}{1.45} \]

3. **For 65% Dissociation** (\( \alpha = 0.65 \)):
\[ d_{65} = \frac{d_0}{1 + 0.65} = \frac{d_0}{1.65} \]

4. **For 80% Dissociation** (\( \alpha = 0.80 \)):
\[ d_{80} = \frac{d_0}{1 + 0.80} = \frac{d_0}{1.80} \]

### Step 5: Compare the Vapor Densities
Since \( d_0 \) is constant, we can compare the denominators:
- \( 1.20 \) for 20% dissociation
- \( 1.45 \) for 45% dissociation
- \( 1.65 \) for 65% dissociation
- \( 1.80 \) for 80% dissociation

The smaller the denominator, the larger the vapor density. Therefore, the order of vapor densities from highest to lowest is:
\[ d_{20} > d_{45} > d_{65} > d_{80} \]

### Final Answer
The sequence of observed vapor densities will be:
\[ d_{20}, d_{45}, d_{65}, d_{80} \]