Assertion (A): `pK_(a)` of a weak acid become equal of the `pH` of the solution at the mid-point of titration.
Reason (R) : The molar concentration of the proton donor an proton acceptor beomes equal at the mid-point.

Options

A. If both (A) and (R) are correc, and (R) is the correct explanation of (A).
B. If both (A) and (R) are correct but (R) is not the correct explanation of (A).
C. If (A) is correct, but (R) is incorrect.
D. If (A) is incorrect, but (R) is correct.

Explanation

To solve the question, we need to analyze both the assertion (A) and the reason (R) provided.

### Step 1: Understand the Assertion
The assertion states that the \( pK_a \) of a weak acid becomes equal to the \( pH \) of the solution at the midpoint of titration.

- In a titration of a weak acid with a strong base, the midpoint is defined as the point where half of the weak acid has been neutralized. At this point, the concentration of the weak acid (\( HA \)) is equal to the concentration of its conjugate base (\( A^- \)).
- According to the Henderson-Hasselbalch equation:
\[ pH = pK_a + \log\left(\frac{[A^-]}{[HA]}\right) \]
- At the midpoint, since \([A^-] = [HA]\), the ratio \(\frac{[A^-]}{[HA]} = 1\), and thus \(\log(1) = 0\). Therefore, we have:
\[ pH = pK_a + 0 \implies pH = pK_a \]
- Thus, the assertion is **true**.

### Step 2: Understand the Reason
The reason states that the molar concentrations of the proton donor (weak acid) and proton acceptor (conjugate base) become equal at the midpoint.

- At the midpoint of the titration, indeed, the amount of weak acid that remains is equal to the amount of its conjugate base that has formed. This means that the concentrations of the proton donor (weak acid) and proton acceptor (conjugate base) are equal.
- Therefore, the reason is also **true**.

### Step 3: Evaluate the Relationship Between Assertion and Reason
While both the assertion and reason are true, the reason does not directly explain why the \( pK_a \) equals the \( pH \). The equality of concentrations leads to the conclusion, but it does not provide the underlying rationale for the relationship between \( pK_a \) and \( pH \).

### Conclusion
Both the assertion and the reason are correct, but the reason is not the correct explanation of the assertion.

### Final Answer
The correct option is: Both assertion and reason are correct, but R is not the correct explanation of A.

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