NEET · Chemistry · STD 11 - 6.2. Equilibrium - II (icon Equilibrium)

At 298 K, a certain buffer solution contains equal concentrations of \(X^{-}\)and \(H X, K_b\) for \(X^{-}\)is \(10^{-10}\). What is the pH of this buffer solution ?

A 2
B 4
C 6
D 10

Verified Solution

Answer & Solution

Correct Answer

(B) 4

Step-by-step Solution

Detailed explanation

(B) Given \(K_b\) for \(X^{-}=10^{-10}\).
For a conjugate acid-base pair at \(298 K, K_a \times K_b=K_w=10^{-14}\).
\(K_a=\frac{10^{-14}}{10^{-10}}=10^{-4}\)
The \(p K_a\) of the weak acid \(H X\) is:
\(p K_a=-\log \left(K_a\right)=-\log \left(10^{-4}\right)=4\)
Using the Henderson-Hasselbalch equation for an acidic buffer:
\(pH=p K_a+\log \left(\frac{\left[X^{-}\right]}{[H X]}\right)\)
Since the concentrations of \(X^{-}\)and \(H X\) are equal, \(\left[X^{-}\right]=[H X]\).
\(pH=4+\log (1)=4+0=4\)

Apply the relevant identity from the chapter and substitute the values established in the previous step, keeping the original constraint in view.

Use the simplified expression to isolate the unknown, then plug the result back into the question setup to confirm the working is internally consistent.

Cross-check against a boundary or limiting case. Both the dimensional balance and the qualitative behaviour at the extreme should agree with the candidate answer.

Combine the steps above to identify the correct option. The remaining choices each fail at least one of the consistency, dimensional, or boundary checks.

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