KCET · Chemistry · Ionic Equilibrium

\(10^{-6} \mathrm{M} \mathrm{NaOH}\) is diluted 100 times. The \(\mathrm{pH}\) of the diluted base is

A between 7 and 8
B between 5 and 6
C between 6 and 7
D between 10 and 11

Verified Solution

Answer & Solution

Correct Answer

(A) between 7 and 8

Step-by-step Solution

Detailed explanation

\(\left[\mathrm{OH}^{-}\right]\)in the diluted base \(=\frac{10^{-6}}{10^{2}}=10^{-8}\)
Total \(\left[\mathrm{OH}^{-}\right]=10^{-8}+\left[\mathrm{OH}^{-}\right]\)of water
\[
\begin{aligned}
&=\left(10^{-8}+10^{-7}\right) \mathrm{M} \\
&=10^{-8}[1+10] \mathrm{M}
\end{aligned}
\]
\(\begin{aligned} &=11 \times 10^{-8} \mathrm{M} \\ \mathrm{pOH} &=-\log 11 \times 10^{-8} \\ &=-\log 11+8 \log 10 \\ &=6.9586 \\ \mathrm{pH} &=14-6.9586 \\ &=7.0414 \end{aligned}\)

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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