The doctor wants you to dispense 500 mL of drug X such that when the patient dilutes it 1 in 40 with water just prior to use as a disinfectant, a 0.1% w/v solution is produced. You have 2 litres of a 10% w/v stock bottle solution of drug X in your pharmacy.

What volume (mL) of the stock solution is required to dispense the prescription. Give your answer to the nearest whole number.

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!

The doctor wants you to dispense 500 mL of drug X such that when the patient dilutes it 1 in 40 with water just prior to use as a disinfectant, a 0.1% w/v solution is produced. You have 2 litres of a 10% w/v stock bottle solution of drug X in your pharmacy. What volume (mL) of the stock solution is required to dispense the prescription? Give your answer to the nearest whole number.

Learn how to calculate the volume of a 10% w/v stock solution required to dispense a 500 mL prescription that, when diluted 1 in 40 with water, produces a 0.1% w/v disinfectant solution. This problem covers key concepts in dilution and concentration calculations. Suitable for high school students in Grades 10-12.

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