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The problem asks for the minimum mass of acetaminophen that the new system must be able to detect, with dissolved acetaminophen concentrations ranging from 10 to 30 µg/mL, and a blood sample volume of 130 µL.

### Step-by-step solution:

1. **Convert blood sample volume:**
   - The blood sample volume is given as 130 µL. Since 1 µL = \(10^{-3}\) mL, we convert it to mL:
   \[
   130 \, \mu L = 130 \times 10^{-3} \, mL = 0.130 \, mL
   \]

2. **Determine the minimum concentration:**
   - The minimum concentration of acetaminophen is given as 10 µg/mL.

3. **Calculate the mass of acetaminophen:**
   - The mass is calculated using the formula:
   \[
   \text{Mass} = \text{Concentration} \times \text{Volume}
   \]
   - Substituting the values:
   \[
   \text{Mass} = 10 \, \mu g/mL \times 0.130 \, mL = 1.3 \, \mu g
   \]

Thus, the minimum mass of acetaminophen that the system must detect is **1.3 µg**.

Would you like any further details or have questions on the steps?

### 5 Related Questions:
1. How would the calculation change if the concentration was 30 µg/mL instead of 10 µg/mL?
2. What is the significance of using significant digits in this context?
3. How does the volume of the sample affect the detectability of the acetaminophen?
4. How would you calculate the maximum mass the system must detect?
5. How would the result change if the blood sample volume was larger, say 200 µL?

### Tip:
When converting units, always ensure consistency between the units of concentration and volume before performing calculations to avoid errors.

GenAlex Medical, a leading manufacturer of medical laboratory equipment, is designing a new automated system that can detect therapeutic levels of dissolved acetaminophen (10 to 30 μg/mL), using a blood sample that is as small as 130 μL. Calculate the minimum mass in micrograms of acetaminophen that the new system must be able to detect. Be sure your answer has the correct number of significant digits.

Learn how to calculate the minimum mass of acetaminophen that a medical system must detect with a sample volume of 130 µL and a concentration range of 10 to 30 µg/mL. This problem demonstrates unit conversions and the use of significant figures, suitable for students in Grades 9-12.

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