To solve this, we will calculate how much of the 10% w/v stock solution is needed to produce 500 mL of a solution that will dilute to a 0.1% w/v solution when mixed with water at a 1:40 ratio.

Step 1: Calculate the concentration of the 500 mL solution before dilution.

The problem states that when the solution is diluted 1 in 40 with water, the final concentration will be 0.1% w/v.

So, let’s first calculate the concentration of the solution before it’s diluted. Since the solution is diluted 40 times, we multiply the final concentration by 40:

$\text{Concentration before dilution} = 0.1\% \times 40 = 4\% \text{ w/v}$

Therefore, the 500 mL solution must be a 4% w/v solution before dilution.

Step 2: Use dilution formula to find the volume of stock solution needed.

Now we have to calculate how much of the 10% w/v stock solution is required to make 500 mL of a 4% w/v solution. We use the dilution formula:

$C_1 V_1 = C_2 V_2$

Where:

• $C_1 = 10\%$ (concentration of stock solution)
• $V_1 = ?$ (volume of stock solution to use)
• $C_2 = 4\%$ (desired concentration of the final solution)
• $V_2 = 500 \, \text{mL}$ (final volume of the solution)

Rearranging to solve for $V_1$:

$V_1 = \frac{C_2 \times V_2}{C_1} = \frac{4\% \times 500 \, \text{mL}}{10\%} = \frac{2000}{10} = 200 \, \text{mL}$

Final Answer:

You will need 200 mL of the 10% w/v stock solution to prepare the 500 mL solution.

Would you like more details or have any further questions?

---

Here are 5 related questions you might find interesting:

1. How do you prepare dilutions for solutions with different concentrations?
2. What is the difference between w/v and v/v percentage concentrations?
3. How do you convert between moles and weight/volume percentages in solutions?
4. How does the dilution factor affect the concentration of a solution?
5. How would the calculation change if the stock solution were 20% w/v instead?

Tip: When preparing dilutions, always check that your units for volume and concentration are consistent throughout the calculation!