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Let's solve the problem step by step!

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### Problem:
A chemist dissolves **438 mg of KOH (potassium hydroxide)** in **50.0 mL of solution**. The task is to calculate the **pH** of the solution. The temperature of the solution is 25°C.

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### **Steps:**

#### 1. Moles of KOH dissolved
- **Molar mass of KOH**:
  - \( K: 39.1 \, \text{g/mol} \)
  - \( O: 16.0 \, \text{g/mol} \)
  - \( H: 1.0 \, \text{g/mol} \)

\[
\text{Molar mass of KOH} = 39.1 + 16.0 + 1.0 = 56.1 \, \text{g/mol}
\]

- **Mass of KOH used**: 438 mg = 0.438 g

\[
\text{Moles of KOH} = \frac{0.438 \, \text{g}}{56.1 \, \text{g/mol}} = 0.00781 \, \text{mol}
\]

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#### 2. Concentration of OH\(^-\) ions in the solution
- Volume of the solution = 50.0 mL = 0.0500 L

\[
\text{Concentration of OH}^- = \frac{0.00781 \, \text{mol}}{0.0500 \, \text{L}} = 0.156 \, \text{M}
\]

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#### 3. Calculate pOH
\[
\text{pOH} = -\log[OH^-] = -\log(0.156) \approx 0.807
\]

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#### 4. Calculate pH
\[
\text{pH} = 14 - \text{pOH} = 14 - 0.807 = 13.19
\]

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### **Final Answer:**
The **pH of the solution** is approximately:

\[
\boxed{13.2}
\]

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Let me know if you'd like more details or have further questions!

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### 5 Related Questions:
1. How does the temperature affect the pH of a solution?
2. What is the difference between pH and pOH?
3. How would the pH change if the KOH mass was doubled?
4. What happens to the pH when a strong acid is added to this solution?
5. How can we calculate the pH of a weak base solution?

**Tip:** For strong bases like KOH, the concentration of the base equals the concentration of OH\(^-\) ions, simplifying pH calculations!

A chemist dissolves 438. mg of pure potassium hydroxide in enough water to make up 50. 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 by dissolving 438 mg of potassium hydroxide (KOH) in 50.0 mL of water. This problem involves concentration calculations, pOH, and the use of logarithmic functions, suitable for high school or early undergraduate chemistry students.

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