In which of the following molecules would you expect the nitrogen-to-nitrogen bond to be the shortest?

Options

A. `N_(2)H_(4)`
B. `N_(2)`
C. `N_(2)O_(4)`
D. `N_(2)O`

Explanation

To determine which molecule has the shortest nitrogen-to-nitrogen bond, we need to analyze the bond order of the nitrogen-nitrogen bonds in the given molecules. The bond order indicates the number of bonds between two atoms; a higher bond order generally corresponds to a shorter bond length.

### Step-by-Step Solution:

1. **Identify the Molecules**: The molecules we need to consider are:
- N₂H₄ (Hydrazine)
- N₂O₄ (Dinitrogen Tetroxide)
- N₂O (Dinitrogen Monoxide)

2. **Determine the Bond Order for Each Molecule**:
- **N₂H₄**:
- In hydrazine, there are two nitrogen atoms bonded to each other and to four hydrogen atoms. The nitrogen-nitrogen bond in N₂H₄ is a single bond (bond order = 1).

- **N₂O₄**:
- In dinitrogen tetroxide, each nitrogen is bonded to two oxygen atoms and there is a nitrogen-nitrogen single bond. The bond order between the two nitrogen atoms is also 1 (bond order = 1).

- **N₂O**:
- In dinitrogen monoxide, there is a nitrogen-nitrogen triple bond. This means the bond order is 3 (bond order = 3).

3. **Compare the Bond Orders**:
- N₂H₄: Bond order = 1
- N₂O₄: Bond order = 1
- N₂O: Bond order = 3

4. **Conclusion**:
- The molecule with the highest bond order is N₂O, which has a bond order of 3. Therefore, the nitrogen-to-nitrogen bond in N₂O is the shortest among the given options.

### Final Answer:
The nitrogen-to-nitrogen bond is expected to be the shortest in **N₂O** (Dinitrogen Monoxide).