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Chapter 2: Problem 65

Using conversion factors, solve each of the following clinical problems: a. A nurse practitioner prepares \(500 . \mathrm{mL}\) of an 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. 2.471 mL

Step by step solution

01

Determine the infusion time for the IV saline solution

Given: Volume, V = 500 mL Rate, R = 80 mL/h The formula to find the infusion time (T) is given by \[T = \frac{V}{R}\]Substitute the given values:\[T = \frac{500 \ \mathrm{mL}}{80 \ \mathrm{mL/h}}\]Calculate the result:\[T = 6.25 \ \text{hours}\]
02

Convert child's weight from pounds to kilograms

Given: Weight, W = 72.6 lbs The conversion factor is 1 lb = 0.453592 kg.Using the conversion factor:\[W = 72.6 \ \text{lbs} \times 0.453592 \ \text{kg/lb}\]Calculate the result:\[W \approx 32.95 \ \text{kg}\]
03

Calculate the required dose of Medrol

Given: Dose per kg, D = 1.5 mg/kg Child's weight, W = 32.95 kg.The formula for the required dose (Total Dose) is:\[ \text{Total Dose} = D \times W\]Substitute the given values:\[ \text{Total Dose} = 1.5 \ \text{mg/kg} \times 32.95 \ \text{kg}\]Calculate the result:\[ \text{Total Dose} \approx 49.425 \ \text{mg}\]
04

Convert the required dose into milliliters of Medrol

Given: Total Dose = 49.425 mg Concentration of Medrol = 20 mg/mL.The formula to convert the dose into volume (V) is given by:\[V = \frac{\text{Total Dose}}{\text{Concentration}}\]Substitute the given values:\[V = \frac{49.425 \ \text{mg}}{20 \ \text{mg/mL}}\]Calculate the result:\[V \approx 2.471 \ \text{mL}\]

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Key Concepts

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

Infusion Time Calculation
When calculating the infusion time for an IV there is a simple process to follow. The formula to use is \( T = \frac{V}{R} \) where \( T \) is the time in hours, \( V \) is the volume in milliliters, and \( R \) is the rate in milliliters per hour.
If a nurse needs to deliver 500 mL of normal saline at a rate of 80 mL/h, just substitute the given values into the formula:
\( T = \frac{500 \text{ mL}}{80 \text{ mL/h}} \)
After performing the division, we get:
The infusion time is 6.25 hours.
This means it would take 6 hours and 15 minutes to administer the entire volume of saline.
Body Weight Conversion
Often in medical dosage calculations, you'll need to convert a patient's weight from pounds (lbs) to kilograms (kg). The conversion factor is :
  • 1 lb = 0.453592 kg
Let's go through an example. Suppose a child weighs 72.6 lbs and you need to find out their weight in kilograms:
\( \text{Weight in kg} = 72.6 \text{ lbs} \times 0.453592 \text{ kg/lb} \)
Doing the multiplication:
\( \text{Weight in kg} \) is approximately 32.95 kg.
This conversion is crucial for accurate medication dosage.
Medication Dosage
Calculating the correct dosage of medication based on body weight is vital. Let's say Medrol must be administered at a dosage of 1.5 mg per kg of body weight.
If the child's body weight is 32.95 kg, here's how you find the total dose required:
\( \text{Total Dose} = \text{Dose per kg} \times \text{Weight in kg} \)
Substitute the values:
\( \text{Total Dose} = 1.5 \text{ mg/kg} \times 32.95 \text{ kg} \)
After multiplying:
The total dose is approximately 49.425 mg.
Accurate dosage ensures effective treatment and avoids potential overdosing.
Unit Conversions
Unit conversion is another essential skill in medical calculations. Often, medications come in different concentrations, for example, 20 mg/mL for Medrol. To convert the total dose into milliliters, you can use the following formula:
\( \text{Volume} = \frac{\text{Total Dose}}{\text{Concentration}} \)
If you need to administer 49.425 mg of Medrol with a concentration of 20 mg/mL:
Substitute the values:
\( \text{Volume} = \frac{49.425 \text{ mg}}{20 \text{ mg/mL}} \)
Do the division:
The volume is approximately 2.471 mL.
Understanding how to switch between units ensures accurate medication administration.

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Most popular questions from this chapter

On a typical day, medical personnel may encounter several situations involving measurement. State the name and type of measurement indicated by the units in each of the following: a. During open-heart surgery, the temperature of a patient is lowered to \(29^{\circ} \mathrm{C}\) b. The circulation time of a red blood cell through the body is \(20 \mathrm{~s}\) c. A patient with a persistent cough is given \(10 . \mathrm{mL}\) of cough syrup. d. The amount of iron in the red blood cells of the body is \(2.5 \mathrm{~g}\).

Solve each of the following problems using one or more conversion factors: a. Wine is \(12 \%\) alcohol by volume. How many milliliters of alcohol are in a 0.750-L bottle of wine? b. Blueberry high-fiber muffins contain \(51 \%\) dietary fiber by mass. If a package with a net weight of 12 oz contains six muffins, how many grams of fiber are in each muffin? c. A jar of crunchy peanut butter contains \(1.43 \mathrm{~kg}\) of peanut butter. If you use \(8.0 \%\) of the peanut butter for a sandwich, how many ounces of peanut butter did you take out of the container? d. In a candy factory, the nutty chocolate bars contain \(22.0 \%\) pecans by mass. If \(5.0 \mathrm{~kg}\) of pecans were used for candy last Tuesday, how many pounds of nutty chocolate bars were made?

When three students use the same meterstick to measure the length of a paper clip, they obtain results of \(5.8 \mathrm{~cm}, 5.75 \mathrm{~cm}\), and \(5.76 \mathrm{~cm} .\) If the meterstick has millimeter markings, what are some reasons for the different values? (2.3)

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. One liter is 1.06 qt. b. At the store, oranges are \(\$ 1.29\) per lb. c. One deciliter contains \(100 \mathrm{~mL}\). d. An 18 -carat gold ring contains \(75 \%\) gold by mass.

Consider the following solids. The solids \(\mathbf{A}, \mathbf{B},\) and \(\mathbf{C}\) represent iron \(\left(\mathrm{D}=7.87 \mathrm{~g} / \mathrm{cm}^{3}\right),\) platinum \(\left(\mathrm{D}=21.5 \mathrm{~g} / \mathrm{cm}^{3}\right),\) and titanium \(\left(\mathrm{D}=4.51 \mathrm{~g} / \mathrm{cm}^{3}\right)\). If each has a mass of \(10.0 \mathrm{~g}\), what is the identity of each solid? (2.7)
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