The pH of `10^(-7)M` NaOH is

Options

A. 7.01
B. Between 7 and 8
C. Between 9 and 10
D. Greater than 10

Explanation

To find the pH of a `10^(-7) M` NaOH solution, follow these steps:

### Step 1: Understand the dissociation of NaOH
NaOH is a strong base and dissociates completely in water:
\[ \text{NaOH} \rightarrow \text{Na}^+ + \text{OH}^- \]

From a `10^(-7) M` NaOH solution, we get:
\[ [\text{OH}^-] = 10^{-7} \, M \]

### Step 2: Consider the contribution of water
Pure water also contributes to the concentration of hydroxide ions. At 25°C, the concentration of hydroxide ions in pure water is:
\[ [\text{OH}^-] = 10^{-7} \, M \]

### Step 3: Calculate the total concentration of hydroxide ions
Since both the NaOH and the water contribute to the hydroxide ion concentration, we add them together:
\[ [\text{OH}^-]_{\text{total}} = 10^{-7} \, M + 10^{-7} \, M = 2 \times 10^{-7} \, M \]

### Step 4: Calculate pOH
Now we can calculate the pOH using the formula:
\[ \text{pOH} = -\log[\text{OH}^-] \]
Substituting the total concentration:
\[ \text{pOH} = -\log(2 \times 10^{-7}) \]

Using the logarithmic properties:
\[ \text{pOH} = -\log(2) - \log(10^{-7}) \]
\[ \text{pOH} = -0.301 - (-7) \]
\[ \text{pOH} = 7 - 0.301 = 6.699 \approx 6.7 \]

### Step 5: Calculate pH
Using the relationship between pH and pOH:
\[ \text{pH} + \text{pOH} = 14 \]
We can find pH:
\[ \text{pH} = 14 - \text{pOH} \]
\[ \text{pH} = 14 - 6.7 = 7.3 \]

### Final Answer
The pH of `10^(-7) M` NaOH is approximately **7.3**.

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