The correct order of `pK_(a)` values for the following compounds is :

Options

A. `agtbgtcgtd`
B. `bgtagtdgtc`
C. `bgtdgtagtc`
D. `cgtagtdgtb`

Answer

To determine the correct order of \( pK_a \) values for the given compounds A, B, C, and D, we need to analyze the acidity of each compound based on the substituents present and their effects on the acidity.

### Step-by-Step Solution:

1. **Understanding \( pK_a \)**:
- The \( pK_a \) value is the negative logarithm of the acid dissociation constant (\( K_a \)). A lower \( pK_a \) value indicates a stronger acid, while a higher \( pK_a \) value indicates a weaker acid.
- Therefore, to find the order of \( pK_a \) values, we need to assess the relative acidity of the compounds.

2. **Analyzing Compound C**:
- Compound C has a nitro group (\(-NO_2\)), which is a strong electron-withdrawing group through the -M (mesomeric) effect. This increases the acidity of the compound significantly.
- As a result, compound C will have the lowest \( pK_a \) value among the four compounds.

3. **Analyzing Compound D**:
- Compound D has a substituent that is an electron-donating group (possibly an alkyl group, such as \(-N(CH_3)_2\)). Electron-donating groups decrease acidity because they increase electron density on the acidic hydrogen, making it less likely to dissociate.
- Therefore, D will have a higher \( pK_a \) value than C.

4. **Analyzing Compound A**:
- Compound A has no substituents. In the absence of any electron-withdrawing or electron-donating groups, its acidity will be moderate, placing its \( pK_a \) value between that of C and D.

5. **Comparing B**:
- Without specific information about compound B, we can assume that it might have a substituent that is less impactful than the nitro group in C but more impactful than the electron-donating group in D.
- Thus, we can tentatively place B's \( pK_a \) value between A and D.

6. **Final Order of \( pK_a \)**:
- Based on the analysis:
- C (lowest \( pK_a \))
- B (next)
- A (next)
- D (highest \( pK_a \))
- Therefore, the correct order of \( pK_a \) values is: **C < B < A < D**.

### Conclusion:
The correct order of \( pK_a \) values for the compounds is **C < B < A < D**.