Question

\(10^{-6}\,\text{M}\) 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 acids or bases (\(\leq 10^{-6}\,\text{M}\)), always include the contribution of water (\(10^{-7}\,\text{M}\)) while calculating pH or pOH.

Answer 1

The Correct Option is A

Step 1: Given concentration of NaOH \[ [\text{NaOH}] = 10^{-6}\,\text{M} \] After dilution by 100 times: \[ [\text{NaOH}]_{\text{new}} = \frac{10^{-6}}{100} = 10^{-8}\,\text{M} \] Step 2: Consider contribution of water. Pure water contributes: \[ [\text{OH}^-] = 10^{-7}\,\text{M} \] Total hydroxide ion concentration: \[ [\text{OH}^-]_{\text{total}} = 10^{-8} + 10^{-7} = 1.1 \times 10^{-7}\,\text{M} \] Step 3: Calculate pOH: \[ \text{pOH} = -\log(1.1 \times 10^{-7}) \approx 6.96 \] Step 4: Calculate pH: \[ \text{pH} = 14 - \text{pOH} = 14 - 6.96 = 7.04 \] Since the pH is slightly greater than 7, it lies between 7 and 8.