The pH of `10^(-8) M` NaOH will be

Options

A. 8
B. 6.96
C. `12.0`
D. `7.02`

Explanation

To find the pH of a `10^(-8) M` NaOH solution, we need to consider both the concentration of hydroxide ions (OH⁻) from NaOH and the contribution of water's autoionization. Here’s a step-by-step solution:

### Step 1: Determine the concentration of OH⁻ from NaOH
Since NaOH is a strong base, it completely dissociates in solution. Therefore, the concentration of OH⁻ from NaOH is:
\[ [OH⁻] = 10^{-8} \, M \]

### Step 2: Consider the contribution of water's autoionization
Water undergoes autoionization, producing a small concentration of hydroxide ions. The concentration of OH⁻ from water at 25°C is:
\[ [OH⁻]_{H_2O} = 10^{-7} \, M \]

### Step 3: Calculate the total concentration of OH⁻
To find the total concentration of OH⁻ in the solution, we add the concentration from NaOH and the concentration from water:
\[ [OH⁻]_{total} = [OH⁻]_{NaOH} + [OH⁻]_{H_2O} = 10^{-8} \, M + 10^{-7} \, M \]
\[ [OH⁻]_{total} = 1 \times 10^{-7} \, M + 1 \times 10^{-8} \, M = 1.1 \times 10^{-7} \, M \]

### Step 4: Calculate pOH
To find the pOH, we use the formula:
\[ pOH = -\log[OH⁻] \]
Substituting the total concentration of OH⁻:
\[ pOH = -\log(1.1 \times 10^{-7}) \]

Using logarithmic properties:
\[ pOH \approx 7 - \log(1.1) \]
Since \(\log(1.1) \approx 0.041\):
\[ pOH \approx 7 - 0.041 \approx 6.96 \]

### Step 5: Calculate pH
Finally, we can find the pH using the relationship:
\[ pH + pOH = 14 \]
Thus,
\[ pH = 14 - pOH \]
Substituting the value of pOH:
\[ pH = 14 - 6.96 \approx 7.04 \]

### Final Answer
The pH of `10^(-8) M` NaOH is approximately **7.04**.

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