Question

The dosage of quinine when a 145−lb adult takes a 200.−mg tablet is equivalent to _____ μg drug per kg of body weight.

Answer 1

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

Answer 2

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:

1. Sort the given.
2. Identify the unknown.
3. Set up the dimensional analysis. Check that the units cancel except for the desired units.
4. Get the product of the numerators.
5. Get the product of the denominators.
6. 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:

$dose \ in \ \frac{ \mu g }{kg} \ = \frac{200. \ mg}{145 \ lbs} (\frac{1 \ g}{1000 \ mg})(\frac{1,000,000 \ \mu g}{1 \ g})(\frac{2.2 \ lbs}{1 \ kg})$

$dose \ in \ \frac{ \mu g}{kg} \ = 3034.48$

Since the given has 3 significant figures,  the final answer should have 3 significant figures.

Therefore, the equivalent dose is $3.03 \ x \ 10^3 \ \frac{ \mu g}{kg}$/

LEARN MORE

• dimensional analysis https://brainly.com/question/1600704
• unit conversion https://brainly.com/question/1557970
• stoichiometry https://brainly.com/question/12979299

Keywords: dimensional analysis, conversion