pH of 0.1 N NaOH(aq) solution

Options

A. 2.7
B. 4.7
C. 7
D. 13

Answer

To find the pH of a 0.1 N NaOH(aq) solution, we can follow these steps:

### Step 1: Understand the dissociation of NaOH
Sodium hydroxide (NaOH) is a strong base that completely dissociates in water:
\[ \text{NaOH} \rightarrow \text{Na}^+ + \text{OH}^- \]
Since NaOH is a strong base, the concentration of hydroxide ions \([OH^-]\) will be equal to the concentration of NaOH.

### Step 2: Determine the concentration of OH⁻ ions
Given that the solution is 0.1 N NaOH, we can conclude that:
\[ [OH^-] = 0.1 \, \text{N} = 0.1 \, \text{M} \]

### Step 3: Calculate pOH
The pOH is calculated using the formula:
\[ \text{pOH} = -\log[OH^-] \]
Substituting the concentration of hydroxide ions:
\[ \text{pOH} = -\log(0.1) \]

### Step 4: Simplify the logarithm
We can express 0.1 as:
\[ 0.1 = \frac{1}{10} \]
Thus:
\[ \text{pOH} = -\log\left(\frac{1}{10}\right) = -(\log(1) - \log(10)) \]
Since \(\log(1) = 0\) and \(\log(10) = 1\):
\[ \text{pOH} = - (0 - 1) = 1 \]

### Step 5: Calculate pH
Using the relationship between pH and pOH:
\[ \text{pH} + \text{pOH} = 14 \]
Substituting the value of pOH:
\[ \text{pH} + 1 = 14 \]
Thus:
\[ \text{pH} = 14 - 1 = 13 \]

### Conclusion
The pH of a 0.1 N NaOH solution is 13.

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