What is the final percentage strength of a drug if 500 mL of a 20% (v/v) solution is diluted to 1500 mL?

Rationale

The final percentage strength of the drug is 6.67%.

To find the final concentration after dilution, we can use the dilution formula, which states that the initial concentration multiplied by the initial volume equals the final concentration multiplied by the final volume. Here, we have 500 mL of a 20% solution diluted to 1500 mL, resulting in a final concentration of 6.67%.

A (1.77%) YOUR ANSWER

This percentage is too low and does not reflect the proper calculation of the dilution. Using the dilution formula, the final concentration is calculated as 20% × (500 mL / 1500 mL), which results in a higher concentration than 1.77%.

B (3.23%) YOUR ANSWER

This option also results from an incorrect calculation. The final concentration cannot be 3.23%, as the dilution calculation shows a concentration of 6.67%. The error may stem from misapplying the dilution formula or miscalculating the ratio of volumes.

C (6.67%) CORRECT

This is the correct calculation, as the dilution factor is applied correctly. By multiplying the initial concentration (20%) by the ratio of the initial volume (500 mL) to the final volume (1500 mL), we arrive at a final strength of 6.67%.

D (8.95%) YOUR ANSWER

This choice is incorrect as well. It suggests a higher concentration than what is calculated using the dilution formula. The final percentage strength must be 6.67%, so 8.95% does not accurately reflect the dilution of the original solution.

Conclusion

In summary, when diluting a solution, the final concentration can be determined using the dilution formula, which helps to maintain the ratio of the original and final volumes. In this case, diluting 500 mL of a 20% solution to a total volume of 1500 mL results in a final concentration of 6.67%. The other options reflect miscalculations or misunderstandings of the dilution process.

What is the final percentage strength of a drug if 500 mL of a 20% (v/v) solution is diluted to 1500 mL?

The final percentage strength of the drug is 6.67%.

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