The correct stability order of the following resonance structures is
`(I)H_(2)C = overset(+)N = overset(-)N" "(II)H_(2)overset(+)C - N = overset(-)N`
`(III)H_(2)overset(-)C - overset(+)N = N" "(IV)H_(2)overset(-)C - N = overset(+)N`

Options

A. `I gt II gt IV gt III`
B. `I gt III gt II gt IV`
C. `II gt I gt III gt IV`
D. `III gt I gt IV gt II`

Answer

To determine the correct stability order of the given resonance structures, we need to analyze each structure based on several criteria, including the completeness of the octet, the location of charges, and the overall electron distribution. Here are the steps to solve the problem:

### Step 1: Analyze the Resonance Structures
We have four resonance structures to analyze:
1. (I) \( H_2C = \overset{+}{N} = \overset{-}{N} \)
2. (II) \( H_2\overset{+}{C} - N = \overset{-}{N} \)
3. (III) \( H_2\overset{-}{C} - \overset{+}{N} = N \)
4. (IV) \( H_2\overset{-}{C} - N = \overset{+}{N} \)

### Step 2: Check the Octet Rule
- **Structure I**: Carbon has 8 electrons (2 from H and 6 from the double bond with nitrogen). The nitrogen atoms also have 8 electrons (5 from the double bond and 3 from the lone pairs). This structure satisfies the octet rule.

- **Structure II**: The carbon has 8 electrons (2 from H and 6 from the bond with nitrogen). The negatively charged nitrogen has 8 electrons (5 from the bond and 3 from the lone pairs), while the positively charged nitrogen has 7 electrons (5 from the bond and 2 from the lone pairs). This structure is stable but one nitrogen does not complete the octet.

- **Structure III**: The carbon has 6 electrons (4 from bonds with H and 2 from the bond with nitrogen). The positively charged nitrogen has 8 electrons (5 from the bond and 3 from the lone pairs), while the other nitrogen has 7 electrons. This structure does not satisfy the octet rule for carbon.

- **Structure IV**: The carbon has 6 electrons (4 from bonds with H and 2 from the bond with nitrogen). The negatively charged nitrogen has 8 electrons, while the positively charged nitrogen has 7 electrons. This structure does not satisfy the octet rule for carbon.

### Step 3: Evaluate Charge Proximity
- Structures with charges that are closer together tend to be more stable due to the attraction between opposite charges.
- **Structure I**: Charges are separated by a double bond, which is relatively stable.
- **Structure II**: The positive charge on carbon is separated from the negative charge on nitrogen, which is stable.
- **Structure III**: The positive and negative charges are on different atoms, but the carbon does not satisfy the octet rule, making it less stable.
- **Structure IV**: Similar to III, but with charges on different atoms and carbon not satisfying the octet rule.

### Step 4: Stability Order
Based on the octet rule and the proximity of charges, we can rank the stability:
1. Structure I: Most stable (both nitrogens complete octet).
2. Structure II: Stable (carbon completes octet, but one nitrogen does not).
3. Structure IV: Less stable (carbon does not complete octet).
4. Structure III: Least stable (carbon does not complete octet).

### Final Stability Order
The correct stability order is:
**I > II > IV > III**