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Answer :
The equivalent dosage is 3.03 x 10^3 μg/kg. This problem is solved using dimensional analysis.
FURTHER EXPLANATION
The steps in answering the problem are:
- Sort the given.
- Identify the unknown.
- Set up the dimensional analysis. Check that the units cancel except for the desired units.
- Get the product of the numerators.
- Get the product of the denominators.
- Divide the numerator by the denominator.
The given problem requires conversion of the mass from milligrams (mg) to μg and pounds (lbs) to kilograms (kg). The following conversion factors may be used:
1 g = 1000 mg
1 g = 1,000,000 μg
2.2 lbs. = 1 kg
Using dimensional analysis, the problem may be solved as follows:
[tex]dose \ in \ \frac{ \mu g }{kg} \ = \frac{200. \ mg}{145 \ lbs} (\frac{1 \ g}{1000 \ mg})(\frac{1,000,000 \ \mu g}{1 \ g})(\frac{2.2 \ lbs}{1 \ kg})[/tex]
[tex]dose \ in \ \frac{ \mu g}{kg} \ = 3034.48\\[/tex]
Since the given has 3 significant figures, the final answer should have 3 significant figures.
Therefore, the equivalent dose is [tex]3.03 \ x \ 10^3 \ \frac{ \mu g}{kg}[/tex]/
LEARN MORE
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- unit conversion https://brainly.com/question/1557970
- stoichiometry https://brainly.com/question/12979299
Keywords: dimensional analysis, conversion
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Rewritten by : Barada
Basically, all you have to do to solve this problem is convert units and calculate for their ratio. Convert pounds to kilograms and milligrams to micrograms.
Pounds→kilograms
2.2 lbs → 1 kg
∴, 145 lbs * 1 kg/2.2 lbs = 65.91 kg
milligrams → micrograms
1 mg → 1000 μg
∴, 200 mg * 1000 μg/1 mg = 200,000 μg
The ratio is, therefore,
200,000 μg/65.91 kg = 3,034.44 μg/kg
Pounds→kilograms
2.2 lbs → 1 kg
∴, 145 lbs * 1 kg/2.2 lbs = 65.91 kg
milligrams → micrograms
1 mg → 1000 μg
∴, 200 mg * 1000 μg/1 mg = 200,000 μg
The ratio is, therefore,
200,000 μg/65.91 kg = 3,034.44 μg/kg
