Write an equality and two conversion factors for each of the following medications:
a. 10 mg of Atarax per 5 mL of Atarax syrup

Verified step by step guidance

1. Step 1: Start by writing the equality that relates the given quantities of Atarax. The problem states that 10 mg of Atarax is equivalent to 5 mL of Atarax syrup. Therefore, the equality is: $10 \mathrm{mg} = 5 \mathrm{mL}$.
2. Step 2: To create the first conversion factor, divide both sides of the equality by 10 mg. This gives: $1 \mathrm{mL} = \frac{5}{10} \mathrm{mg}$. Simplify the fraction to get: $1 \mathrm{mL} = 0.5 \mathrm{mg}$.
3. Step 3: To create the second conversion factor, divide both sides of the equality by 5 mL. This gives: $1 \mathrm{mg} = \frac{10}{5} \mathrm{mL}$. Simplify the fraction to get: $1 \mathrm{mg} = 2 \mathrm{mL}$.
4. Step 4: Verify that both conversion factors are consistent with the original equality. For example, multiplying $10 \mathrm{mg}$ by $0.5 \mathrm{mL}/\mathrm{mg}$ should yield $5 \mathrm{mL}$, confirming the accuracy.
5. Step 5: Use these conversion factors in dimensional analysis to convert between milligrams and milliliters of Atarax syrup as needed in future calculations.

Key Concepts

Medication Dosage

Medication dosage refers to the specific amount of a drug that is administered to achieve the desired therapeutic effect. In this case, 10 mg of Atarax indicates the quantity of the active ingredient in the syrup, which is crucial for ensuring safe and effective treatment.

Conversion Factors

Conversion factors are ratios used to convert one unit of measurement to another. For medications, these factors help healthcare professionals accurately calculate dosages based on different units, such as milligrams to milliliters, ensuring proper administration of the drug.

Syrup Formulation

Syrup formulation refers to the specific composition of a liquid medication, which includes the active ingredient and other components like sweeteners and preservatives. Understanding the formulation is essential for determining how the medication is dosed and administered, particularly in pediatric or geriatric populations.