How would you expect the bond strength to change in the series `C_(2)` to `C_(2)^(-)` to `C_(2)^(2-)`?

Options

A. gets stronger than weaker
B. gets Weaker
C. gets stronger
D. gets weaker than stronger

Explanation

To analyze how bond strength changes in the series \( C_2 \) to \( C_2^{-} \) to \( C_2^{2-} \), we can follow these steps:

### Step 1: Determine the Bond Order for Each Species
1. **For \( C_2 \)**:
- The total number of electrons in \( C_2 \) is \( 6 + 6 = 12 \).
- The bond order can be calculated using the formula:
\[ \text{Bond Order} = \frac{(\text{Number of bonding electrons} - \text{Number of antibonding electrons})}{2} \]
- For \( C_2 \), the bond order is 2.

2. **For \( C_2^{-} \)**:
- The total number of electrons is \( 12 + 1 = 13 \) (due to the extra negative charge).
- The bond order for \( C_2^{-} \) is 2.5.

3. **For \( C_2^{2-} \)**:
- The total number of electrons is \( 12 + 2 = 14 \) (due to two extra negative charges).
- The bond order for \( C_2^{2-} \) is 3.

### Step 2: Analyze the Relationship Between Bond Order and Bond Strength
- Bond strength is directly related to bond order. As bond order increases, bond strength also increases, and bond length decreases.
- Thus, we can summarize:
- \( C_2 \) has a bond order of 2 (lower bond strength).
- \( C_2^{-} \) has a bond order of 2.5 (moderate bond strength).
- \( C_2^{2-} \) has a bond order of 3 (highest bond strength).

### Step 3: Conclusion
- Therefore, the bond strength increases in the order:
\[ C_2 < C_2^{-} < C_2^{2-} \]
- This means that \( C_2^{2-} \) has the strongest bond, followed by \( C_2^{-} \), and then \( C_2 \).

### Final Answer
The bond strength increases from \( C_2 \) to \( C_2^{-} \) to \( C_2^{2-} \).

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