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The problem states that a prescription balance has a sensitivity requirement of 6.5 mg, and you need to weigh 20 mg of a substance with an error not exceeding 2%.

### Step-by-step Solution:

1. **Determine the acceptable error:**  
   Since the error must not exceed 2% of the target weight (20 mg):
   \[
   \text{Maximum error} = 20 \, \text{mg} \times 0.02 = 0.4 \, \text{mg}.
   \]

2. **Check the balance sensitivity:**  
   The sensitivity of the balance is 6.5 mg. This means the smallest change in weight that the balance can detect is 6.5 mg, which is much larger than the acceptable error of 0.4 mg.

3. **Conclude on direct weighing:**  
   Since the balance's sensitivity (6.5 mg) is greater than the maximum allowable error (0.4 mg), you **cannot** weigh 20 mg directly on this balance with an error less than or equal to 2%.

4. **Alternative approach – Dilution method:**  
   To achieve the required accuracy, you would need to use a method involving dilution. Here's how:
   - Weigh a larger quantity that the balance can measure accurately, such as 200 mg, because the sensitivity of the balance is more appropriate for larger weights.
   - Dissolve or dilute this 200 mg into a known volume (say, 200 mL).
   - Then, extract a fraction of this dilution to obtain the desired 20 mg. For instance, extracting 20 mL from this 200 mL solution would give you 20 mg of the substance.

This method ensures that the final 20 mg measurement is more accurate, despite the balance's limitations.

### Would you like further details or have any questions?

### Related Questions:
1. How does the balance's sensitivity affect the weighing accuracy for small quantities?
2. What are the common methods for measuring small quantities accurately when using less sensitive balances?
3. Why is the dilution method an effective approach in such scenarios?
4. What is the impact of using a balance with a lower sensitivity on weighing small amounts?
5. How to prepare and use dilutions to accurately measure substances in pharmaceutical compounding?

### Tip:
When dealing with a balance that has a high sensitivity requirement, always consider measuring a larger quantity and using dilutions or aliquots to achieve the desired smaller amount accurately.

A prescription balance has a sensitivity requirement of 6.5 mg. Explain how you would weigh 20 mg of a substance with an error not >2%.

Learn how to weigh 20 mg of a substance with an error not exceeding 2% on a balance with a sensitivity requirement of 6.5 mg. Explore methods like error calculation and the dilution approach to achieve precision.

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