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We are asked to calculate the pH of a sodium hydroxide (NaOH) solution. Let's break it down:

### Given:
- **Mass of NaOH**: 320 mg = 0.320 g
- **Volume of solution**: 120 mL = 0.120 L
- **Temperature**: 25°C (but this won't affect our calculations for pH)
  
### Step 1: Convert mass to moles.
We need the molar mass of sodium hydroxide (NaOH):
- Sodium (Na): 22.99 g/mol
- Oxygen (O): 16.00 g/mol
- Hydrogen (H): 1.008 g/mol

The molar mass of NaOH is:
\[
M_{\text{NaOH}} = 22.99 + 16.00 + 1.008 = 40.00 \, \text{g/mol}
\]

Now, convert 0.320 g of NaOH to moles:
\[
\text{moles of NaOH} = \frac{0.320 \, \text{g}}{40.00 \, \text{g/mol}} = 0.008 \, \text{mol}
\]

### Step 2: Calculate molarity.
Molarity (\(M\)) is given by:
\[
M = \frac{\text{moles of solute}}{\text{volume of solution in liters}}
\]
\[
M = \frac{0.008 \, \text{mol}}{0.120 \, \text{L}} = 0.067 \, \text{M}
\]

### Step 3: Determine the pOH.
Since NaOH is a strong base, it dissociates completely in water. Therefore, the concentration of hydroxide ions \([OH^-]\) is equal to the molarity of NaOH:
\[
[OH^-] = 0.067 \, \text{M}
\]

The pOH is calculated as:
\[
\text{pOH} = -\log [OH^-] = -\log (0.067) \approx 1.17
\]

### Step 4: Calculate the pH.
The relationship between pH and pOH is:
\[
\text{pH} + \text{pOH} = 14
\]
\[
\text{pH} = 14 - 1.17 = 12.83
\]

### Final Answer:
The pH of the solution is **12.83** (with correct significant figures).

Would you like further details or clarification on any step?

Here are five questions to deepen understanding:
1. What is the significance of molarity in chemical calculations?
2. Why does NaOH dissociate completely in water?
3. How does temperature affect the pH in other scenarios?
4. Can weak bases like ammonia be handled the same way as NaOH in pH calculations?
5. How do you calculate pH if given weak acids instead?

**Tip:** Always ensure correct unit conversions, especially with mass and volume, to avoid errors in molarity calculations.

A chemist dissolves 320 mg of pure sodium hydroxide in enough water to make up 120 mL of solution. Calculate the pH of the solution. (The temperature of the solution is 25°C.)

Learn how to calculate the pH of a sodium hydroxide solution where 320 mg of NaOH is dissolved in 120 mL of water. This solution covers molarity calculations, pOH, and the relationship between pH and pOH.

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