The pH of 0.016 M NaOH solution is

Options

A. 1.796
B. 12.204
C. 11
D. None of these

Answer

To find the pH of a 0.016 M NaOH solution, we can follow these steps:

### Step 1: Determine the concentration of hydroxide ions (OH⁻)
Since NaOH is a strong base, it completely dissociates in water:
\[ \text{NaOH} \rightarrow \text{Na}^+ + \text{OH}^- \]
Thus, the concentration of OH⁻ ions is equal to the concentration of NaOH, which is:
\[ [\text{OH}^-] = 0.016 \, \text{M} \]

**Hint:** Remember that strong bases dissociate completely in solution.

### Step 2: Calculate the pOH
The pOH can be calculated using the formula:
\[ \text{pOH} = -\log[\text{OH}^-] \]
Substituting the concentration of OH⁻:
\[ \text{pOH} = -\log(0.016) \]

**Hint:** Use the logarithmic properties to simplify calculations.

### Step 3: Simplify the logarithm
To calculate \(-\log(0.016)\), we can express 0.016 in scientific notation:
\[ 0.016 = 1.6 \times 10^{-2} \]
Thus,
\[ \text{pOH} = -\log(1.6 \times 10^{-2}) \]
Using the property of logarithms:
\[ \text{pOH} = -\log(1.6) - \log(10^{-2}) \]
\[ \text{pOH} = -\log(1.6) + 2 \]

**Hint:** Recall that \(-\log(10^{-n}) = n\).

### Step 4: Calculate \(-\log(1.6)\)
Using a calculator or logarithm table, we find:
\[ \log(1.6) \approx 0.204 \]
Thus,
\[ \text{pOH} = -0.204 + 2 = 1.796 \]

**Hint:** You can use approximations for common logarithms if needed.

### Step 5: Calculate the pH
Now, we can find the pH using the relationship:
\[ \text{pH} + \text{pOH} = 14 \]
So,
\[ \text{pH} = 14 - \text{pOH} \]
Substituting the value of pOH:
\[ \text{pH} = 14 - 1.796 = 12.204 \]

**Hint:** Always remember the relationship between pH and pOH.

### Step 6: Round the pH
Rounding to two decimal places, we get:
\[ \text{pH} \approx 12.20 \]

**Final Answer:** The pH of the 0.016 M NaOH solution is approximately **12.20**.