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 nitrogen-to-nitrogen bond is the shortest among the given molecules, we need to analyze the bond types present in each molecule. The bond length is inversely related to bond strength, meaning that as bond strength increases (due to higher bond order), the bond length decreases.

### Step-by-Step Solution:

1. **Identify the Molecules**: We need to consider the nitrogen-containing molecules provided in the question. Common examples include N2 (dinitrogen), N2H4 (hydrazine), and N2O4 (dinitrogen tetroxide).

2. **Determine the Bond Types**:
- **N2 (Dinitrogen)**: This molecule has a triple bond between the two nitrogen atoms. The bond order here is 3.
- **N2H4 (Hydrazine)**: In hydrazine, there is a single bond between the two nitrogen atoms. The bond order is 1.
- **N2O4 (Dinitrogen Tetroxide)**: In this molecule, the nitrogen atoms are connected by a single bond, and there are also double bonds with oxygen. The bond order between the nitrogen atoms is also 1.

3. **Compare Bond Orders**:
- N2 has a bond order of 3 (triple bond).
- N2H4 has a bond order of 1 (single bond).
- N2O4 has a bond order of 1 (single bond).

4. **Conclusion**: The bond length is shortest for the bond with the highest bond order. Therefore, the nitrogen-to-nitrogen bond in N2 (triple bond) is the shortest among the given options.

### Final Answer:
The nitrogen-to-nitrogen bond in **N2 (dinitrogen)** is the shortest.