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The problem involves calculating the pH of a solution made by dissolving sodium hydroxide (NaOH) in water. Let's break it down step-by-step:

### Given Data:
- Mass of sodium hydroxide (NaOH): 274 mg = 0.274 g
- Volume of solution: 110 mL = 0.110 L
- Temperature: 25°C (for reference, but it's not necessary to solve this since pH at 25°C follows typical water ionization constants)

### Steps to solve:

1. **Moles of NaOH**:
   - Molar mass of NaOH = 23 (Na) + 16 (O) + 1 (H) = 40 g/mol
   - Moles of NaOH \( n = \frac{\text{mass}}{\text{molar mass}} \):
     \[
     n = \frac{0.274 \, \text{g}}{40 \, \text{g/mol}} = 0.00685 \, \text{mol}
     \]

2. **Concentration of NaOH**:
   The concentration of NaOH in moles per liter is given by:
   \[
   \text{Concentration} = \frac{\text{moles of NaOH}}{\text{volume of solution in liters}} = \frac{0.00685 \, \text{mol}}{0.110 \, \text{L}} = 0.0623 \, \text{mol/L}
   \]

3. **pOH Calculation**:
   Sodium hydroxide is a strong base, meaning it fully dissociates in water. The concentration of hydroxide ions [OH⁻] is the same as the concentration of NaOH:
   \[
   [\text{OH}^-] = 0.0623 \, \text{mol/L}
   \]
   The pOH is calculated using:
   \[
   \text{pOH} = -\log[\text{OH}^-] = -\log(0.0623) = 1.205
   \]

4. **pH Calculation**:
   Since pH + pOH = 14 (at 25°C):
   \[
   \text{pH} = 14 - \text{pOH} = 14 - 1.205 = 12.795
   \]

### Final Answer:
The pH of the solution is **12.8** (rounded to 3 significant digits, as required by the problem).

Would you like further clarification on any steps, or do you have any questions?

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### Related Questions:
1. What is the difference between pH and pOH in a solution?
2. How does temperature affect the pH of a solution?
3. What are the properties of a strong base like sodium hydroxide in water?
4. How do significant digits affect the accuracy of chemical calculations?
5. What is the role of molarity in determining the pH of a solution?

### Tip:
Always ensure that when you're converting units in chemistry problems, you handle significant digits carefully to maintain precision throughout the calculations.

A chemist dissolves 274 mg of pure sodium hydroxide in enough water to make up 110 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 solution containing 274 mg of sodium hydroxide dissolved in 110 mL of water. This problem involves key concepts like concentration, pOH calculation, and the pH-pOH relationship. Suitable for students in Grades 11-12.

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