A certain antibiotic is supplied in liquid form as 50.0 mg in 5.00 mL. How many mL are required for a dosage of 500. mg of the antibiotic?
The correct answer and explanation is :
To determine how many milliliters (mL) of the antibiotic are required for a dosage of 500 mg, we use a proportion based on the given concentration.
Given Data:
- Concentration: 50.0 mg per 5.00 mL
- Required dosage: 500 mg
Step-by-Step Solution:
We set up a proportion:
[
\frac{50.0 \text{ mg}}{5.00 \text{ mL}} = \frac{500 \text{ mg}}{x \text{ mL}}
]
Now, solve for ( x ):
[
x = \frac{500 \text{ mg} \times 5.00 \text{ mL}}{50.0 \text{ mg}}
]
[
x = \frac{2500}{50}
]
[
x = 50.0 \text{ mL}
]
Answer:
50.0 mL of the antibiotic is required for a 500 mg dosage.
Explanation:
This calculation is based on a direct proportion since the relationship between milligrams (mg) and milliliters (mL) is linear. Since 50.0 mg is dissolved in 5.00 mL, increasing the dosage to 500 mg requires scaling up the volume proportionally. By multiplying 500 mg by the volume corresponding to 50 mg (5.00 mL), and then dividing by 50 mg, we maintain the same concentration and ensure accurate dosing.
This approach is crucial in medical applications to ensure patients receive the correct amount of medication. Errors in dosage calculations can lead to underdosing (ineffective treatment) or overdosing (potential toxicity). Thus, healthcare professionals must be proficient in unit conversions and proportions when administering liquid medications.
Always double-check calculations in clinical settings and use dimensional analysis if needed.