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Chapter 2: Problem 73

Using conversion factors, solve each of the following clinical problems: a. A nurse practitioner prepares \(500 . \mathrm{mL}\) of an \(\mathrm{IV}\) of normal saline solution to be delivered at a rate of \(80 . \mathrm{mL} / \mathrm{h}\). What is the infusion time, in hours, to deliver \(500 . \mathrm{mL}\) ? b. A nurse practitioner orders Medrol to be given \(1.5 \mathrm{mg} / \mathrm{kg}\) of body weight. Medrol is an anti-inflammatory administered as an intramuscular injection. If a child weighs \(72.6 \mathrm{lb}\) and the available stock of Medrol is \(20 . \mathrm{mg} / \mathrm{mL}\), how many milliliters does the nurse administer to the child?

Short Answer

Expert verified
a. 6.25 hours. b. 2.47 mL.

Step by step solution

01

Identify the knowns and unknowns for part (a)

Given: Volume of saline solution = 500 mL, Rate of infusion = 80 mL/h. Need to find: Time (in hours) to deliver the solution.
02

Set up the conversion factor for part (a)

The infusion rate converts volume to time. Use the relation: \[ \text{Time} = \frac{\text{Volume}}{\text{Rate}} \]
03

Calculate the infusion time for part (a)

\[ \text{Time} = \frac{500 \text{ mL}}{80 \text{ mL/h}} = 6.25 \text{ hours} \]
04

Identify the knowns and unknowns for part (b)

Given: Dosage needed = 1.5 mg/kg, Child's weight = 72.6 lb, Medrol stock concentration = 20 mg/mL. Need to find: Volume of Medrol to be administered (in mL).
05

Convert weight from pounds to kilograms for part (b)

1 lb = 0.453592 kg. Convert the child's weight: \[ 72.6 \text{ lb} \times 0.453592 \text{ kg/lb} = 32.93 \text{ kg} \]
06

Calculate the required dosage in mg for part (b)

Dosage required = 1.5 mg/kg. Using the child's weight: \[ 1.5 \text{ mg/kg} \times 32.93 \text{ kg} = 49.395 \text{ mg} \]
07

Calculate the volume of Medrol needed for part (b)

Given concentration is 20 mg/mL. Find the volume: \[ \text{Volume} = \frac{\text{Dose}}{\text{Concentration}} = \frac{49.395 \text{ mg}}{20 \text{ mg/mL}} = 2.46975 \text{ mL} \]. This can be rounded to 2.47 mL for practical purposes.

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Key Concepts

These are the key concepts you need to understand to accurately answer the question.

Conversion Factors
Conversion factors are mathematical tools used to convert a quantity from one unit to another. They are essential in medical dosage calculations to translate between various units, ensuring patients receive the correct dosage. For example, to convert a child's weight from pounds to kilograms, we use the conversion factor where 1 pound equals 0.453592 kilograms. If a child weighs 72.6 pounds, the weight in kilograms becomes: \[72.6 \text{ lb} \times 0.453592 \text{ kg/lb} = 32.93 \text{ kg}\] Using conversion factors correctly ensures all calculations are accurate and trustworthy.
Infusion Rate Calculation
When administering intravenous (IV) fluids, calculating the infusion rate is crucial. The infusion rate tells us how quickly a fluid is delivered to a patient. For instance, if a nurse needs to deliver 500 mL of saline at 80 mL per hour, the total infusion time can be calculated using the formula: \[\text{Time} = \frac{\text{Volume}}{\text{Rate}}\] Plugging in the given values: \[\text{Time} = \frac{500 \text{ mL}}{80 \text{ mL/h}} = 6.25 \text{ hours}\] This ensures the nurse knows exactly how long the IV will run.
Dosage Calculation
Dosage calculation is critical for determining the right amount of medication based on a patient's weight or other factors. In the case of Medrol, an anti-inflammatory drug, the amount needed depends on body weight, with the given dosage being 1.5 mg per kilogram. To find the total dosage for a child weighing 32.93 kilograms: \[1.5 \text{ mg/kg} \times 32.93 \text{ kg} = 49.395 \text{ mg}\] This calculation ensures the child gets the precise amount of medication needed.
Unit Conversion
Unit conversion is often needed in medical dosage calculations to express quantities in the correct units. For example, converting the required dosage from milligrams to the volume in milliliters, given the concentration of the medication. If Medrol is available at a concentration of 20 mg/mL, the volume required for a dose of 49.395 mg is: \[\text{Volume} = \frac{\text{Dose}}{\text{Concentration}} = \frac{49.395 \text{ mg}}{20 \text{ mg/mL}} = 2.47 \text{ mL}\] These conversions ensure the medication is administered accurately and safely.

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Most popular questions from this chapter

Write an equality and two conversion factors for each of the following medications in stock: a. \(2.5 \mathrm{mg}\) of Coumadin per 1 tablet of Coumadin b. \(100 \mathrm{mg}\) of Clozapine per 1 tablet of Clozapine c. \(1.5 \mathrm{~g}\) of Cefuroxime per \(1 \mathrm{~mL}\) of Cefuroxime

In which of the following pairs do both numbers contain the same number of significant figures? a. \(0.00575 \mathrm{~g}\) and \(5.75 \times 10^{-3} \mathrm{~g}\) b. \(405 \mathrm{~K}\) and \(405.0 \mathrm{~K}\) c. \(150000 \mathrm{~s}\) and \(1.50 \times 10^{4} \mathrm{~s}\) d. \(3.8 \times 10^{-2} \mathrm{~L}\) and \(3.0 \times 10^{5} \mathrm{~L}\)

Suppose you have two \(100-\mathrm{mL}\) graduated cylinders. In each cylinder, there is \(40.0 \mathrm{~mL}\) of water. You also have two cubes: one is lead, and the other is aluminum. Each cube measures \(2.0 \mathrm{~cm}\) on each side. After you carefully lower each cube into the water of its own cylinder, what will the new water level be in each of the cylinders?

Write the numerical value for each of the following prefixes: a. giga b. micro c. mega d. nano

Write the equality and two conversion factors, and identify the numbers as exact or give the number of significant figures for each of the following: a. A calcium supplement contains \(630 \mathrm{mg}\) of calcium per tablet. b. The Daily Value (DV) for vitamin \(\mathrm{C}\) is \(60 \mathrm{mg}\). c. The label on a bottle reads \(50 \mathrm{mg}\) of atenolol per tablet. d. A low-dose aspirin contains \(81 \mathrm{mg}\) of aspirin per tablet.
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