Question

$10^{-6}$ M NaOH is diluted 100 times. The 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

Hint:

For very dilute bases (concentration $\le 10^{-7}$ M), always add $10^{-7}$ M from water to the $[OH^-]$.

Answer 1

The Correct Option is A

Step 1: Find \( \mathrm{OH}^{-} \) Concentration
Initial \( [\mathrm{OH}^{-}] = 10^{-6} \text{ M} \). Diluted 100 times, \( [\mathrm{OH}^{-}]_{\text{base}} = \frac{10^{-6}}{100} = 10^{-8} \text{ M} \).
Step 2: Account for Water dissociation
Total \( [\mathrm{OH}^{-}] = [\mathrm{OH}^{-}]_{\text{base}} + [\mathrm{OH}^{-}]_{\text{water}} = 10^{-8} + 10^{-7} = 1.1 \times 10^{-7} \text{ M} \).
Step 3: Find pOH and pH
\( \mathrm{pOH} = -\log(1.1 \times 10^{-7}) \approx 6.96 \). \( \mathrm{pH} = 14 - 6.96 = 7.04 \). This value is between 7 and 8.
Final Answer: (a)