The adult dosage of diphenhydramine, an antihistamine, is 50.0 mg.

The adult dosage of diphenhydramine, an antihistamine, is 50.0 mg. A 21 lb child should only receive 20.0% of the adult dose. Calculate this dose in milligrams. Enter the dose numerically – NO UNITS (provided): mg Use your answer to solve the next part: liquid diphenhydramine comes in a concentration of 12.5 mg per 5.00 mL. How many milliliters of diphenhydramine should be administered to the child? Enter the dose numerically – NO UNITS (provided): mL Pay attention to significant figures.

The Correct Answer and Explanation is:

Correct Answers:

Milligrams for child: 10.0
Milliliters to administer: 4.00

Step-by-Step Explanation:

This problem involves a two-part dosage calculation using proportions and significant figures. Let’s go through each step in detail.

Part 1: Calculating the Child’s Dose in Milligrams

Given:

Adult dose of diphenhydramine = 50.0 mg
Child should receive 20.0% of adult dose

Calculation: Child’s dose=20.0%×50.0 mg=(20.0100)×50.0 mg=0.200×50.0=10.0 mg\text{Child’s dose} = 20.0\% \times 50.0\, \text{mg} = \left( \frac{20.0}{100} \right) \times 50.0\, \text{mg} = 0.200 \times 50.0 = 10.0\, \text{mg}Child’s dose=20.0%×50.0mg=(10020.0)×50.0mg=0.200×50.0=10.0mg

Significant Figures:

The percentage (20.0%) has 3 significant figures
The adult dose (50.0 mg) also has 3 significant figures
Final answer: 10.0 mg (3 significant figures)

Part 2: Converting the Milligram Dose to Milliliters

Given:

Concentration: 12.5 mg per 5.00 mL
Dose needed: 10.0 mg

We use a proportion to find the volume: 12.5 mg5.00 mL=10.0 mgx mL\frac{12.5\, \text{mg}}{5.00\, \text{mL}} = \frac{10.0\, \text{mg}}{x\, \text{mL}}5.00mL12.5mg=xmL10.0mg

Cross-multiplying: 12.5x=10.0×5.00=50.0⇒x=50.012.5=4.00 mL12.5x = 10.0 \times 5.00 = 50.0 \Rightarrow x = \frac{50.0}{12.5} = 4.00\, \text{mL}12.5x=10.0×5.00=50.0⇒x=12.550.0=4.00mL