`10^(-6)` M NaOH solution is diluted 100 times. Calculate the pH of the diluted base.

Explanation

To solve the problem of calculating the pH of a diluted NaOH solution, we will follow these steps:

### Step 1: Determine the concentration of the diluted NaOH solution
The initial concentration of NaOH is \(10^{-6} \, \text{M}\). When this solution is diluted 100 times, the concentration of NaOH after dilution can be calculated as follows:

\[ \text{Concentration after dilution} = \frac{10^{-6} \, \text{M}}{100} = 10^{-8} \, \text{M} \]

### Step 2: Calculate the concentration of hydroxide ions \([OH^-]\)
In a \(10^{-8} \, \text{M}\) NaOH solution, the concentration of hydroxide ions \([OH^-]\) is equal to the concentration of NaOH, which is \(10^{-8} \, \text{M}\). However, we also need to consider the contribution of hydroxide ions from the water itself. The concentration of hydroxide ions from pure water at 25°C is \(10^{-7} \, \text{M}\).

Thus, the total concentration of hydroxide ions in the solution is:

\[ [OH^-]_{\text{total}} = [OH^-]_{\text{NaOH}} + [OH^-]_{\text{water}} = 10^{-8} \, \text{M} + 10^{-7} \, \text{M} = 1.1 \times 10^{-7} \, \text{M} \]

### Step 3: Calculate the pOH of the solution
To find the pOH of the solution, we use the formula:

\[ \text{pOH} = -\log[OH^-] \]

Substituting the total concentration of hydroxide ions:

\[ \text{pOH} = -\log(1.1 \times 10^{-7}) \]

Calculating this gives:

\[ \text{pOH} \approx 6.958 \]

### Step 4: Calculate the pH of the solution
The relationship between pH and pOH is given by:

\[ \text{pH} + \text{pOH} = 14 \]

Thus, we can calculate the pH:

\[ \text{pH} = 14 - \text{pOH} = 14 - 6.958 \approx 7.042 \]

### Final Answer
The pH of the diluted NaOH solution is approximately **7.04**.

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