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The problem involves a dilution calculation where the chemist is preparing a less concentrated solution from a more concentrated stock solution. The relevant formula for dilutions is:

\[
C_1 V_1 = C_2 V_2
\]

Where:
- \(C_1\) is the concentration of the stock solution,
- \(V_1\) is the volume of the stock solution,
- \(C_2\) is the concentration of the working (diluted) solution (which we are solving for),
- \(V_2\) is the total volume of the working solution.

### Given:
- \(C_1 = 0.468 \, \text{M}\) (the concentration of the stock solution),
- \(V_1 = 50.0 \, \text{mL} = 0.0500 \, \text{L}\),
- \(V_2 = 540 \, \text{mL} = 0.540 \, \text{L}\) (the total volume of the diluted solution).

### Solution:
We want to calculate \(C_2\), the concentration of the diluted solution.

\[
C_2 = \frac{C_1 V_1}{V_2}
\]

Substituting the given values:

\[
C_2 = \frac{(0.468 \, \text{M}) \times (0.0500 \, \text{L})}{0.540 \, \text{L}}
\]

Let's calculate \(C_2\):

\[
C_2 = \frac{0.0234}{0.540} = 0.0433 \, \text{M}
\]

### Final Answer:
The concentration of the chemist's working solution is **0.0433 M**.

Would you like more details or have any questions about this calculation? Here are some follow-up questions:

1. What would happen if a smaller volume of stock solution was used for the same final volume?
2. How would the concentration change if the final volume were doubled?
3. How can you use this method to prepare a solution of a different concentration?
4. What role does the total volume play in determining the final concentration?
5. How would errors in measuring the stock solution volume affect the final concentration?

**Tip:** Always remember to convert all units to the same system (e.g., mL to L) when using the dilution formula!

A chemist makes 540. mL of potassium permanganate (KMnO4) working solution by adding distilled water to 50.0 mL of a 0.468 M stock solution of potassium permanganate in water. Calculate the concentration of the chemist's working solution.

Learn how to calculate the concentration of a potassium permanganate (KMnO4) working solution using a stock solution and the dilution formula. In this problem, a 0.468 M stock solution is diluted to 540 mL. Perfect for high school chemistry students.

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