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The problem asks for the volume of a 0.180 mol/L potassium permanganate (\( KMnO_4 \)) solution that contains 125 g of potassium permanganate. Here’s how to solve it:

### Step 1: Calculate the molar mass of \( KMnO_4 \)
To find the molar mass of potassium permanganate (\( KMnO_4 \)), sum the atomic masses of the individual atoms:

- Potassium (K): 39.10 g/mol
- Manganese (Mn): 54.94 g/mol
- Oxygen (O): 16.00 g/mol (since there are 4 oxygen atoms, multiply this by 4)

\[
\text{Molar mass of } KMnO_4 = 39.10 + 54.94 + (4 \times 16.00) = 158.04 \, \text{g/mol}
\]

### Step 2: Calculate the number of moles of \( KMnO_4 \)
Use the formula:

\[
\text{moles} = \frac{\text{mass}}{\text{molar mass}}
\]

Given that the mass is 125 g:

\[
\text{moles of } KMnO_4 = \frac{125 \, \text{g}}{158.04 \, \text{g/mol}} \approx 0.791 \, \text{mol}
\]

### Step 3: Use molarity to calculate the volume
Molarity is given by:

\[
M = \frac{\text{moles}}{\text{volume in liters}}
\]

Rearranging to solve for volume:

\[
\text{volume (L)} = \frac{\text{moles}}{M}
\]

Given that the molarity is 0.180 mol/L:

\[
\text{volume (L)} = \frac{0.791 \, \text{mol}}{0.180 \, \text{mol/L}} \approx 4.395 \, \text{L}
\]

### Final Answer:
The volume of the solution is approximately **4.40 L** (rounded to three significant figures, as given in the problem).

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Would you like further details on any part of the solution or additional explanations?

### Related Questions:
1. What is molarity and how is it calculated in different types of solutions?
2. How can you determine the molar mass of any compound?
3. Why is it important to use significant figures in calculations?
4. How does temperature affect the molarity of a solution?
5. How can molarity be used to calculate the mass of a solute in a solution?

### Tip:
Always keep track of significant figures throughout your calculations to ensure the final answer is as accurate as required.

Calculate the volume in liters of a 0.180 mol/L potassium permanganate solution that contains 125 g of potassium permanganate (KMnO4). Be sure your answer has the correct number of significant digits.

Find the volume of a potassium permanganate solution with a molarity of 0.180 mol/L that contains 125 g of KMnO4. Learn how to apply molarity and stoichiometry concepts to calculate the solution volume, including detailed steps for working with significant figures.

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