Which of the following carboxylic acid has the least pKa value among all?
Step 1: Understanding pKa and Acidity
- The pKa value is the negative logarithm of the acid dissociation constant (\( K_a \)), which measures the strength of an acid.
- A lower pKa value indicates a stronger acid, meaning the acid ionizes more easily in solution.
Step 2: Comparing Carboxylic Acids
- Carboxylic acids (\( R-COOH \)) have different pKa values depending on the electron-withdrawing or electron-donating nature of the substituent group (\( R \)).
- Formic acid (HCOOH) has the lowest pKa value among carboxylic acids because:
- It lacks an alkyl group, so there is no electron-donating effect to stabilize the carboxylate ion.
- It is the simplest carboxylic acid, making it the strongest among its homologs.
Step 3: Conclusion
- Since HCOOH (Formic Acid) has the least pKa value, it is the strongest carboxylic acid among common carboxylic acids.
If the value of \( \cos \alpha \) is \( \frac{\sqrt{3}}{2} \), then \( A + A = I \), where \[ A = \begin{bmatrix} \sin\alpha & -\cos\alpha \\ \cos\alpha & \sin\alpha \end{bmatrix}. \]