Question

Read the dosage information or label given for the following problems. Express body weight conversion to the nearest tenth where indicated and dosages to the nearest tenth. Furadantin oral suspension \(25 \mathrm{mg}\) p.o. qoh is ordered for a child weighing 37.4 lb. Recommended dosage is \(5-7 \mathrm{mg} / \mathrm{kg} / 24\) hr divided qoh. Available: Furadantin oral suspension \(25 \mathrm{mg}\) per \(5 \mathrm{~mL}\). a. What is the child's weight in kilograms to the nearest tenth? b. What is the dosage range for this child? c. Is the dosage ordered safe? (Prove mathematically.) d. How many milliliters must be given per dosage to administer the ordered dosage? Calculate the dose if the order is safe.

Short answer

Weight: 17.0 kg, Dosage safe at 100 mg/24 hr, 5 mL per dose.

Step-by-step solution

Convert Weight to Kilograms

To convert the child's weight from pounds to kilograms, use the conversion factor: \( 1 \text{ lb} = 0.453592 \text{ kg} \). Thus, the child's weight in kilograms is \( 37.4 \text{ lb} \times 0.453592 \text{ kg/lb} = 16.9645698 \text{ kg} \). When rounded to the nearest tenth, the child's weight is \( 17.0 \text{ kg} \).

Calculate Dosage Range

Using the weight in kilograms, calculate the minimum and maximum dosage using the range \(5-7 \text{ mg/kg/24 hr}\). Calculate the total dosage per day: \(\text{Minimum dosage} = 5 \text{ mg} \times 17.0 \text{ kg} = 85 \text{ mg/24 hr}\)\(\text{Maximum dosage} = 7 \text{ mg} \times 17.0 \text{ kg} = 119 \text{ mg/24 hr}\)Therefore, the safe dosage range is \(85-119 \text{ mg/24 hr}\).

Determine Dose Safety

The order is for \(25 \text{ mg} \) every 6 hours (qoh, q6h). In 24 hours, this equates to \(4 \times 25 \text{ mg} = 100 \text{ mg/24 hr}\). This falls within the safe range of \(85-119 \text{ mg/24 hr}\), so the ordered dose is safe.

Calculate Milliliters per Dose

Since the suspension contains \(25 \text{ mg} \) per \(5 \text{ mL}\), the amount to administer is calculated by the proportion:\(\frac{25 \text{ mg}}{5 \text{ mL}} = rac{25 \text{ mg}}{x \text{ mL}} \)Solving for \(x\): \(x = 5 \text{ mL} \).The amount given per dosage is \(5 \text{ mL} \).

Key concepts

Body Weight Conversion

Before calculating the exact dosage of medication for a child, it is crucial to convert the child's weight from pounds (lb) to kilograms (kg). This conversion is essential because most medication dosages are calculated based on kilograms. The conversion factor to remember is:

• 1 lb = 0.453592 kg

To convert, multiply the child's weight in pounds by the conversion factor. For instance, a child weighing 37.4 lb would be converted by multiplying by 0.453592, which gives approximately 16.964 kg. Always round this number to the nearest tenth to make it practical for dosage calculations, resulting in a weight of 17.0 kg.
This conversion ensures accuracy and safety in medication administration.

Safe Dosage Range

After converting the weight to kilograms, the next critical step is to determine the safe dosage range for the medication in question. Each medication has a recommended dosage range expressed in milligrams per kilogram per day (mg/kg/day). This range ensures that the dose is effective yet not harmful.

• Typically, the range will be given as a minimum and maximum dose.

To calculate the safe dosage for a child weighing 17.0 kg:

• Minimum dosage: 5 mg/kg x 17.0 kg = 85 mg/day
• Maximum dosage: 7 mg/kg x 17.0 kg = 119 mg/day

Thus, the safe dosage range for this child is between 85 mg and 119 mg per 24 hours. This ensures that the child receives enough medication for therapeutic effects without exceeding a limit that could cause adverse reactions.

Medication Administration

Once you have determined the safe dosage range, compare it with the prescribed dosage to ensure it falls within the safe limits. This helps prevent overdose or underdose situations that could either make the medication ineffective or dangerous.
For this exercise, the prescription is 25 mg every six hours (q6h). This means a total of 4 doses per 24-hour period:

• Total dosage per day = 4 doses x 25 mg = 100 mg/day

The calculated total (100 mg) lies within the previously determined safe range of 85 mg to 119 mg. Thus, this shows that the prescribed dosage is safe and effective for the child's weight.

Unit Conversion in Healthcare

Converting between different units accurately is a fundamental skill in healthcare. It ensures that the correct dosage of medication is administered. In this scenario, the Furadantin oral suspension is available at 25 mg per 5 mL.
To determine how many milliliters (mL) to administer per dose, use:

• The provided formula: 25 mg medication is contained in 5 mL of suspension.

So, if the child needs 25 mg as per the prescription, they should be administered the suspension accordingly. The calculation becomes straightforward:

• Since 25 mg corresponds directly to 5 mL, administer 5 mL per dose.

This straightforward method ensures the child receives the exact dosage needed every six hours as prescribed, maintaining effective therapeutic levels without the risk of inaccuracy inherent in converting measurements.