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Question 101Question →

A nurse is caring for a client with cardiogenic shock who weighs 85 kg85 \text{ kg}. The healthcare provider prescribes a continuous intravenous (IV) infusion of dopamine at 5 mcg/kg/min5 \text{ mcg/kg/min}. The pharmacy provides an IV bag containing 400 mg400 \text{ mg} of dopamine mixed in 250 mL250 \text{ mL} of 5%5\% Dextrose in Water (D5W). At what rate should the nurse set the IV infusion pump in mL/hr\text{mL/hr}? (Record your answer to the nearest tenth.)

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Answer: 15.9

Answer

The nurse should set the infusion pump to 15.9 mL/hr.
The correct answer is derived by calculating the weight-based dose per minute, converting it to an hourly rate, matching the units to the supplied concentration (mcg to mg), and dividing by the concentration of the dopamine bag. Finally, the value is rounded to the nearest tenth.

Step-by-Step Solution

1
Calculate the required dose per minute based on the client's weight.
85 kg×5 mcg/kg/min=425 mcg/min85 \text{ kg} \times 5 \text{ mcg/kg/min} = 425 \text{ mcg/min}
The prescription is weight-based, requiring the nurse to multiply the ordered rate by the client's weight in kg.
2
Convert the per-minute dose to a per-hour dose.
425 mcg/min×60 min/hr=25,500 mcg/hr425 \text{ mcg/min} \times 60 \text{ min/hr} = 25,500 \text{ mcg/hr}
Infusion pumps are programmed in mL per hour, so the minute dosage must be converted to an hourly rate.
3
Convert the required hourly dose from micrograms (mcg) to milligrams (mg).
25,500 mcg/hr÷1000 mcg/mg=25.5 mg/hr25,500 \text{ mcg/hr} \div 1000 \text{ mcg/mg} = 25.5 \text{ mg/hr}
The supplied medication concentration is provided in mg, so the hourly dose must match these units.
4
Calculate the concentration of the supplied IV fluid.
400 mg÷250 mL=1.6 mg/mL400 \text{ mg} \div 250 \text{ mL} = 1.6 \text{ mg/mL}
Determining the concentration simplifies the final volume calculation.
5
Calculate the final infusion rate and round to the nearest tenth.
25.5 mg/hr÷1.6 mg/mL=15.9375 mL/hr25.5 \text{ mg/hr} \div 1.6 \text{ mg/mL} = 15.9375 \text{ mL/hr}, which rounds to 15.9 mL/hr15.9 \text{ mL/hr}
Dividing the required hourly dose by the concentration yields the final pump setting.

Key Concept

Weight-based continuous IV infusion rate calculation (mcg/kg/min to mL/hr)
Question 102Question →

A client admitted with cardiogenic shock weighs 198 lbs198\text{ lbs}. The provider initially orders a continuous intravenous (IV) infusion of dopamine at 4 mcg/kg/min4\text{ mcg/kg/min}. The pharmacy dispenses a premixed IV bag containing 800 mg800\text{ mg} of dopamine in 250 mL250\text{ mL} of 5% Dextrose5\%\text{ Dextrose} in water (D5WD_5W). Two hours later, the client's mean arterial pressure (MAP) remains at 55 mmHg55\text{ mmHg}, and the provider increases the dopamine infusion order to 7 mcg/kg/min7\text{ mcg/kg/min}. At what rate in mL/hr\text{mL/hr} should the nurse set the infusion pump to deliver the newly ordered dose? (Record your answer rounding to the nearest tenth. Do not include units in your answer.)

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Answer: 11.8

Answer

11.8
To calculate the new IV pump rate, first convert the client's weight to kilograms (198 lbs÷2.2=90 kg198\text{ lbs} \div 2.2 = 90\text{ kg}). Next, identify the correct active dose to administer, which is the newly ordered 7 mcg/kg/min7\text{ mcg/kg/min}. Calculate the hourly dose required: 7 mcg/kg/min×90 kg=630 mcg/min7\text{ mcg/kg/min} \times 90\text{ kg} = 630\text{ mcg/min}, then multiply by 60 minutes60\text{ minutes} to determine the hourly requirement of 37,800 mcg/hr37,800\text{ mcg/hr}. Convert this value to milligrams (37.8 mg/hr37.8\text{ mg/hr}) so it matches the supplied medication's unit of measurement. Determine the IV bag concentration by dividing the total drug amount by the total volume: 800 mg÷250 mL=3.2 mg/mL800\text{ mg} \div 250\text{ mL} = 3.2\text{ mg/mL}. Finally, divide the required hourly dose by the concentration: 37.8 mg/hr÷3.2 mg/mL=11.8125 mL/hr37.8\text{ mg/hr} \div 3.2\text{ mg/mL} = 11.8125\text{ mL/hr}. According to the rounding instructions, this rounds to 11.8 mL/hr11.8\text{ mL/hr}.

Step-by-Step Solution

1
Convert the client's weight from pounds to kilograms.
198÷2.2=90 kg198 \div 2.2 = 90\text{ kg}
Weight-based medication dosing requires the weight to be in kilograms.
2
Determine the active prescribed dose.
7 mcg/kg/min7\text{ mcg/kg/min}
The provider increased the dose from the initial 4 mcg/kg/min4\text{ mcg/kg/min} due to the client's hypotensive state.
3
Calculate the required dose per minute.
7 mcg/kg/min×90 kg=630 mcg/min7\text{ mcg/kg/min} \times 90\text{ kg} = 630\text{ mcg/min}
This establishes the total micrograms of dopamine the client needs every minute.
4
Convert the minute dose to an hourly dose.
630 mcg/min×60 min/hr=37,800 mcg/hr630\text{ mcg/min} \times 60\text{ min/hr} = 37,800\text{ mcg/hr}
Intravenous infusion pumps are programmed in milliliters per hour, so the time unit must be converted.
5
Convert micrograms to milligrams.
37,800 mcg÷1,000 mcg/mg=37.8 mg/hr37,800\text{ mcg} \div 1,000\text{ mcg/mg} = 37.8\text{ mg/hr}
The medication supplied by the pharmacy is measured in milligrams, so the units must match.
6
Calculate the concentration of the supplied IV bag.
800 mg÷250 mL=3.2 mg/mL800\text{ mg} \div 250\text{ mL} = 3.2\text{ mg/mL}
This determines exactly how many milligrams of dopamine are in each milliliter of fluid.
7
Calculate the final infusion rate in mL/hr.
37.8 mg/hr÷3.2 mg/mL=11.8125 mL/hr37.8\text{ mg/hr} \div 3.2\text{ mg/mL} = 11.8125\text{ mL/hr}
Dividing the required hourly dose by the fluid concentration provides the correct pump rate.
8
Round the final answer to the nearest tenth.
11.811.8
The question explicitly specifies rounding to the nearest tenth.

Key Concept

Weight-based continuous IV infusion calculation with dose titration.
Question 103Question →

A nurse is caring for a client with a deep vein thrombosis who is receiving a continuous intravenous heparin infusion. The client weighs 198 lb.

The hospital's weight-based heparin protocol includes the following instructions:

aPTT (seconds)Bolus DoseContinuous Infusion Adjustment
< 3580 units/kgIncrease by 4 units/kg/hr
35 - 4540 units/kgIncrease by 2 units/kg/hr
46 - 70NoneNo change
71 - 90NoneDecrease by 2 units/kg/hr
> 90Hold infusion for 1 hourDecrease by 3 units/kg/hr

The client's current heparin infusion is infusing at a rate of 15 units/kg/hr. The most recent aPTT result is 42 seconds. The available intravenous solution contains heparin 25,000 units in 250 mL of 5% dextrose in water (D5W).

What should the nurse set the new continuous intravenous infusion pump rate to, in mL/hr?

(Record your answer to the nearest tenth. Do not use a trailing zero.)

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Answer: 15.3

Answer

15.3
The correct pump setting is 15.3 mL/hr. First, the client's weight must be converted to kilograms: 198 lb / 2.2 = 90 kg. According to the protocol, an aPTT of 42 seconds falls into the 35-45 seconds tier, which dictates an increase of the continuous infusion by 2 units/kg/hr. The current running rate is 15 units/kg/hr, meaning the new ordered rate becomes 17 units/kg/hr (15 + 2). The total hourly dose is calculated by multiplying the new rate by the client's weight: 17 units/kg/hr * 90 kg = 1530 units/hr. The available concentration is 25,000 units in 250 mL, which simplifies to 100 units/mL. To find the final intravenous pump rate, divide the hourly dose by the concentration: 1530 units/hr / 100 units/mL = 15.3 mL/hr. This meets the rounding requirement of the nearest tenth.

Step-by-Step Solution

1
Convert the client's weight from pounds (lb) to kilograms (kg).
198 lb / 2.2 = 90 kg
Weight-based medication dosing requires the client's weight in kilograms to ensure accurate administration.
2
Determine the necessary infusion rate adjustment based on the aPTT result.
Increase by 2 units/kg/hr
The client's aPTT is 42 seconds, which falls into the 35-45 seconds protocol parameter requiring a specific upward titration.
3
Calculate the new weight-based hourly dose.
15 units/kg/hr + 2 units/kg/hr = 17 units/kg/hr
The current rate must be increased by the protocol-determined amount to achieve therapeutic coagulation levels.
4
Calculate the total units required per hour.
17 units/kg/hr * 90 kg = 1530 units/hr
Multiplying the new weight-based dose by the client's weight provides the absolute total units of heparin required each hour.
5
Calculate the volume of the infusion needed per hour.
1530 units/hr / 100 units/mL = 15.3 mL/hr
Dividing the required hourly dose by the concentration of the available solution (25,000 units / 250 mL = 100 units/mL) provides the final pump setting.

Key Concept

Weight-Based Continuous Intravenous Medication Titration
Question 104Question →

A client admitted with cardiogenic shock requires hemodynamic support. The healthcare provider orders an intravenous infusion of dopamine at a rate of 5 mcg/kg/min5 \text{ mcg/kg/min}. The client's admission weight is 176 lbs176 \text{ lbs}. The pharmacy dispenses a premixed bag containing 400 mg400 \text{ mg} of dopamine in 250 mL250 \text{ mL} of 0.9%0.9\% sodium chloride. At how many mL/hr\text{mL/hr} should the nurse program the infusion pump? (Record answer as a whole number.)

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Answer: 15

Answer

15
To find the correct infusion rate, first convert the client's weight to kilograms (176÷2.2=80 kg176 \div 2.2 = 80 \text{ kg}). Calculate the dose per minute: 80 kg×5 mcg=400 mcg/min80 \text{ kg} \times 5 \text{ mcg} = 400 \text{ mcg/min}. Convert to an hourly dose: 400 mcg/min×60 min=24,000 mcg/hr400 \text{ mcg/min} \times 60 \text{ min} = 24,000 \text{ mcg/hr}. Find the concentration of the IV bag: 400 mg400 \text{ mg} is 400,000 mcg400,000 \text{ mcg}; 400,000 mcg÷250 mL=1,600 mcg/mL400,000 \text{ mcg} \div 250 \text{ mL} = 1,600 \text{ mcg/mL}. Finally, divide the hourly dose by the concentration to determine the pump rate: 24,000 mcg÷1,600 mcg/mL=15 mL/hr24,000 \text{ mcg} \div 1,600 \text{ mcg/mL} = 15 \text{ mL/hr}.

Step-by-Step Solution

1
Convert the client's weight from pounds to kilograms.
176 lbs÷2.2 lbs/kg=80 kg176 \text{ lbs} \div 2.2 \text{ lbs/kg} = 80 \text{ kg}
The prescribed dose is weight-based in kg, so the weight must be converted first.
2
Calculate the total dose required per minute.
5 mcg/kg/min×80 kg=400 mcg/min5 \text{ mcg/kg/min} \times 80 \text{ kg} = 400 \text{ mcg/min}
This establishes the exact amount of medication the client needs every minute.
3
Convert the minute dose to an hourly dose.
400 mcg/min×60 min/hr=24,000 mcg/hr400 \text{ mcg/min} \times 60 \text{ min/hr} = 24,000 \text{ mcg/hr}
Infusion pumps are programmed in mL/hr, so the dose must be expressed per hour.
4
Determine the concentration of the available medication in mcg/mL.
400 mg=400,000 mcg400 \text{ mg} = 400,000 \text{ mcg}. Then, 400,000 mcg÷250 mL=1,600 mcg/mL400,000 \text{ mcg} \div 250 \text{ mL} = 1,600 \text{ mcg/mL}
The dose is in mcg, so the medication concentration must also be in mcg to calculate the volume.
5
Calculate the final infusion rate in mL/hr.
24,000 mcg/hr÷1,600 mcg/mL=15 mL/hr24,000 \text{ mcg/hr} \div 1,600 \text{ mcg/mL} = 15 \text{ mL/hr}
Dividing the hourly dose by the concentration yields the volume needed per hour.

Key Concept

Weight-based continuous intravenous infusion calculations (mcg/kg/min to mL/hr)
Question 105Question →

A client diagnosed with a deep vein thrombosis is prescribed a continuous intravenous infusion of heparin. The client's current weight is 198 lb198\text{ lb}. The provider's prescription requires an initial infusion rate of 18 units/kg/hr18\text{ units/kg/hr}. The available medication is a 250 mL250\text{ mL} intravenous bag containing 25,000 units25,000\text{ units} of heparin sodium. At what rate in mL/hr\text{mL/hr} should the nurse program the infusion pump? Record your answer using one decimal place.

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Answer: 16.2

Answer

16.2
To determine the correct infusion pump rate, the nurse must accurately convert the client's weight into kilograms, calculate the total hourly unit requirement based on that weight, and divide by the medication's concentration (100 units/mL100\text{ units/mL}) to find the correct volume per hour.

Step-by-Step Solution

1
Convert weight from pounds to kilograms.
198÷2.2=90 kg198 \div 2.2 = 90\text{ kg}
The medication protocol requires a weight-based dose in kilograms, but the client's weight is provided in pounds.
2
Calculate the hourly heparin dose.
90 kg×18 units/kg/hr=1,620 units/hr90\text{ kg} \times 18\text{ units/kg/hr} = 1,620\text{ units/hr}
Multiplying the client's weight by the ordered unit rate per kilogram determines the total units needed every hour.
3
Calculate the volume needed per hour based on the supplied concentration.
1,620 units/hr÷(25,000 units/250 mL)=16.2 mL/hr1,620\text{ units/hr} \div (25,000\text{ units} / 250\text{ mL}) = 16.2\text{ mL/hr}
Dividing the required units per hour by the concentration of the IV bag (100 units/mL100\text{ units/mL}) yields the correct pump setting.

Key Concept

Weight-based continuous intravenous infusion calculations
Question 106Question →

A nurse is preparing to administer a continuous intravenous (IV) infusion of heparin for a client diagnosed with a pulmonary embolism. The healthcare provider's prescription is for 18 units/kg/hr18 \text{ units/kg/hr}. The client's admission weight is 198 lb198 \text{ lb}. The available IV fluid is heparin 25,000 units25,000 \text{ units} in 250 mL250 \text{ mL} of 0.45%0.45\% sodium chloride.

At what rate in mL/hr\text{mL/hr} should the nurse set the IV infusion pump? (Record your answer using one decimal place.)

Show answer & explanation

Answer: 16.2

Answer

16.2
To determine the correct IV pump rate, first convert the client's weight to kilograms (198 lb÷2.2=90 kg198 \text{ lb} \div 2.2 = 90 \text{ kg}). Next, calculate the hourly heparin dose by multiplying the weight by the prescribed rate (90 kg×18 units/kg/hr=1,620 units/hr90 \text{ kg} \times 18 \text{ units/kg/hr} = 1,620 \text{ units/hr}). Finally, divide the hourly dose by the concentration of the IV solution (25,000 units÷250 mL=100 units/mL25,000 \text{ units} \div 250 \text{ mL} = 100 \text{ units/mL}). The final rate is 1,620 units/hr÷100 units/mL=16.2 mL/hr1,620 \text{ units/hr} \div 100 \text{ units/mL} = 16.2 \text{ mL/hr}.

Step-by-Step Solution

1
Convert the client's weight from pounds (lb) to kilograms (kg).
198 lb÷2.2=90 kg198 \text{ lb} \div 2.2 = 90 \text{ kg}
The medication is prescribed based on the client's weight in kilograms, so a conversion is necessary before calculating the dose.
2
Calculate the hourly dose of heparin required in units.
90 kg×18 units/kg/hr=1,620 units/hr90 \text{ kg} \times 18 \text{ units/kg/hr} = 1,620 \text{ units/hr}
Multiplying the weight by the weight-based prescription provides the total amount of medication needed per hour.
3
Determine the concentration of the supplied IV heparin solution.
25,000 units÷250 mL=100 units/mL25,000 \text{ units} \div 250 \text{ mL} = 100 \text{ units/mL}
Finding the concentration per milliliter is required to convert the hourly dose from units into a volume (mL).
4
Calculate the infusion pump rate in mL/hr.
1,620 units/hr÷100 units/mL=16.2 mL/hr1,620 \text{ units/hr} \div 100 \text{ units/mL} = 16.2 \text{ mL/hr}
Dividing the required hourly dose by the concentration provides the volume to be infused over one hour.

Key Concept

Weight-based intravenous continuous infusion calculation
Question 107Question →

To ensure medication safety, a nurse is performing an independent double-check of a milrinone infusion for a client with acute decompensated heart failure. The client weighs 80 kg80 \text{ kg}. The infusion pump is currently delivering the medication at a rate of 15 mL/hr15 \text{ mL/hr}. The available medication is a premixed bag containing 20 mg20 \text{ mg} of milrinone in 100 mL100 \text{ mL} of 0.9% sodium chloride.

Calculate the dose the client is receiving in mcg/kg/min\text{mcg/kg/min}. Record your answer to the nearest hundredth.

Show answer & explanation

Answer: 0.63

Answer

0.63
To determine the weight-based dosage from a known infusion rate, multiple conversions must occur. First, the concentration of the milrinone solution is 0.2 mg/mL0.2 \text{ mg/mL}, which converts to 200 mcg/mL200 \text{ mcg/mL}. At a rate of 15 mL/hr15 \text{ mL/hr}, the client receives 3,000 mcg/hr3,000 \text{ mcg/hr}. Dividing by 60 min/hr60 \text{ min/hr} reveals the client receives 50 mcg/min50 \text{ mcg/min}. Finally, dividing the total minute dose by the client's 80 kg80 \text{ kg} weight yields 0.625 mcg/kg/min0.625 \text{ mcg/kg/min}. Standard rounding rules require rounding 0.6250.625 up to 0.630.63.

Step-by-Step Solution

1
Determine the concentration of milrinone in mg/mL.
20 mg÷100 mL=0.2 mg/mL20 \text{ mg} \div 100 \text{ mL} = 0.2 \text{ mg/mL}
Establishing the concentration is the first step to finding out how much medication is in each milliliter of fluid.
2
Convert the concentration from milligrams (mg) to micrograms (mcg).
0.2 mg/mL×1,000 mcg/mg=200 mcg/mL0.2 \text{ mg/mL} \times 1,000 \text{ mcg/mg} = 200 \text{ mcg/mL}
The final requested unit is in micrograms, so the concentration must be converted appropriately.
3
Calculate the total dose delivered per hour.
15 mL/hr×200 mcg/mL=3,000 mcg/hr15 \text{ mL/hr} \times 200 \text{ mcg/mL} = 3,000 \text{ mcg/hr}
Multiplying the pump rate by the concentration yields the total hourly dose.
4
Calculate the total dose delivered per minute.
3,000 mcg/hr÷60 min/hr=50 mcg/min3,000 \text{ mcg/hr} \div 60 \text{ min/hr} = 50 \text{ mcg/min}
The final requested unit is per minute, requiring conversion from the hourly dose.
5
Calculate the weight-based dose.
50 mcg/min÷80 kg=0.625 mcg/kg/min50 \text{ mcg/min} \div 80 \text{ kg} = 0.625 \text{ mcg/kg/min}
Dividing the total minute dose by the client's weight provides the exact dose being administered.
6
Round the calculated dose to the nearest hundredth.
0.630.63
The question specifies rounding to two decimal places (the nearest hundredth).

Key Concept

Weight-based reverse dosage calculation for continuous intravenous infusions.
Question 108Question →

A nurse in the intensive care unit is caring for a client with a hypertensive emergency. The client weighs 198 lb198\text{ lb}. The client is currently receiving a continuous intravenous (IV) infusion of nitroprusside at 14 mL/hr14\text{ mL/hr}. The IV solution contains 50 mg50\text{ mg} of nitroprusside in 250 mL250\text{ mL} of 5%5\% dextrose in water (D5WD_5W). Based on the client's current blood pressure of 185/110 mm Hg185/110\text{ mm Hg}, the healthcare provider prescribes an increase in the nitroprusside infusion rate by 0.5 mcg/kg/min0.5\text{ mcg/kg/min}. What is the new infusion rate in mL/hr\text{mL/hr} that the nurse should set on the IV pump? Record your answer using one decimal place.

Show answer & explanation

Answer: 27.5

Answer

27.5
To determine the new infusion rate, calculate the volume required for the prescribed increase and add it to the current baseline rate. First, convert the weight: 198 lb÷2.2=90 kg198\text{ lb} \div 2.2 = 90\text{ kg}. Calculate the increase per minute: 0.5 mcg/kg/min×90 kg=45 mcg/min0.5\text{ mcg/kg/min} \times 90\text{ kg} = 45\text{ mcg/min}. Convert to an hourly dose: 45 mcg/min×60 min/hr=2700 mcg/hr45\text{ mcg/min} \times 60\text{ min/hr} = 2700\text{ mcg/hr}. Next, determine the concentration of the available solution: 50 mg=50,000 mcg50\text{ mg} = 50,000\text{ mcg}; 50,000 mcg÷250 mL=200 mcg/mL50,000\text{ mcg} \div 250\text{ mL} = 200\text{ mcg/mL}. Divide the hourly dose increase by the concentration: 2700 mcg/hr÷200 mcg/mL=13.5 mL/hr2700\text{ mcg/hr} \div 200\text{ mcg/mL} = 13.5\text{ mL/hr}. Finally, add this volume increase to the current rate: 14 mL/hr+13.5 mL/hr=27.5 mL/hr14\text{ mL/hr} + 13.5\text{ mL/hr} = 27.5\text{ mL/hr}.

Step-by-Step Solution

1
Convert the client's weight to kilograms.
90 kg
The prescribed dose increase is weight-based (mcg/kg/min), so weight must be in kg.
2
Calculate the total mcg/min required for the rate increase.
45 mcg/min
Multiplies the prescribed dose increase (0.5 mcg/kg/min) by the patient's weight (90 kg).
3
Convert the required dose increase from mcg/min to mcg/hr.
2700 mcg/hr
The IV infusion pump is programmed in mL/hr, so the dose must be standardized to an hourly rate.
4
Determine the concentration of the IV solution in mcg/mL.
200 mcg/mL
Converts 50 mg to 50,000 mcg, then divides by the total volume (250 mL) to find the amount of drug per mL.
5
Calculate the additional infusion rate (mL/hr) required for the increase.
13.5 mL/hr
Divides the required hourly dose increase (2700 mcg/hr) by the drug concentration (200 mcg/mL).
6
Calculate the new total infusion rate.
27.5 mL/hr
Adds the required increase (13.5 mL/hr) to the current continuous infusion rate (14 mL/hr).

Key Concept

Complex weight-based IV medication titration and dosage calculation
Question 109Question →

A nurse is caring for a client with a pulmonary embolism who weighs 85.4 kg85.4\text{ kg}. The client is receiving a continuous intravenous heparin infusion. The current infusion rate is 14 units/kg/hr14\text{ units/kg/hr}. The heparin is supplied as 25,000 units25,000\text{ units} in 250 mL250\text{ mL} of 5% dextrose in water.

The client's morning activated partial thromboplastin time (aPTT) is 39 seconds39\text{ seconds}. According to the hospital's weight-based heparin protocol, for an aPTT between 3636 and 44 seconds44\text{ seconds}, the nurse must administer an intravenous bolus of 40 units/kg40\text{ units/kg} and increase the continuous infusion rate by 2 units/kg/hr2\text{ units/kg/hr}.

Calculate the client's new continuous infusion pump rate in mL/hr\text{mL/hr}. (Record your answer using one decimal place.)

Show answer & explanation

Answer: 13.7

Answer

13.7
To safely titrate a heparin infusion based on a protocol, the nurse must first determine the new dose by adding the prescribed increase to the current rate (14 + 2 = 16 units/kg/hr). Next, calculate the total hourly dose using the client's weight (16 units/kg/hr * 85.4 kg = 1366.4 units/hr). The concentration of the IV bag is 100 units/mL (25,000 units / 250 mL). Finally, divide the total hourly units by the concentration to find the pump rate in mL/hr (1366.4 / 100 = 13.664), which rounds to 13.7 mL/hr.

Step-by-Step Solution

1
Determine the new prescribed heparin dose per hour.
14 units/kg/hr + 2 units/kg/hr = 16 units/kg/hr
The protocol requires increasing the continuous infusion rate by 2 units/kg/hr based on the subtherapeutic aPTT result.
2
Calculate the total required units of heparin per hour.
16 units/kg/hr * 85.4 kg = 1366.4 units/hr
The infusion is weight-based, so the per-kg dose must be multiplied by the client's weight.
3
Determine the concentration of the supplied heparin solution.
25,000 units / 250 mL = 100 units/mL
This establishes how many units of medication are in each mL of the IV fluid.
4
Calculate the final infusion pump rate.
1366.4 units/hr / 100 units/mL = 13.664 mL/hr
Dividing the total hourly units by the concentration yields the fluid volume needed per hour.
5
Round the calculated rate to one decimal place.
13.7 mL/hr
The question explicitly requires rounding to one decimal place.

Key Concept

Weight-based heparin protocol titration and IV pump rate calculation
Estimated Time:2m 0s
Question 110Question →

An adult client admitted with acute decompensated heart failure requires inotropic support. The healthcare provider prescribes a continuous intravenous dobutamine infusion at a dose of 5 mcg/kg/min5\text{ mcg/kg/min}. The client's current weight is 80 kg80\text{ kg}. The medication is supplied as a pre-mixed bag containing 500 mg500\text{ mg} of dobutamine in 250 mL250\text{ mL} of 5%5\% dextrose in water. Calculate the required infusion rate in mL/hr\text{mL/hr}. Record your answer as a whole number.

Show answer & explanation

Answer: 12

Answer

12
The correct infusion rate is 12 mL/hr. The patient requires 400 mcg of dobutamine per minute (80 kg * 5 mcg/kg/min). Over one hour (60 minutes), this equals 24,000 mcg, or 24 mg. Because the IV bag contains a concentration of 2 mg per 1 mL (500 mg / 250 mL), delivering 24 mg requires an infusion rate of 12 mL/hr.

Step-by-Step Solution

1
Calculate the total dose required per minute.
80 kg×5 mcg/kg/min=400 mcg/min80\text{ kg} \times 5\text{ mcg/kg/min} = 400\text{ mcg/min}
Weight-based dosing requires determining the individualized dose based on the client's current weight.
2
Convert the dose from per minute to per hour.
400 mcg/min×60 min/hr=24,000 mcg/hr400\text{ mcg/min} \times 60\text{ min/hr} = 24,000\text{ mcg/hr}
IV infusion pumps are programmed in mL per hour, so the medication dose must be standardized to an hourly rate.
3
Convert the hourly dose from micrograms to milligrams.
24,000 mcg/hr÷1000 mcg/mg=24 mg/hr24,000\text{ mcg/hr} \div 1000\text{ mcg/mg} = 24\text{ mg/hr}
The supplied medication is measured in milligrams, so the requested dose must match the provided unit of measurement.
4
Calculate the concentration of the supplied medication.
500 mg÷250 mL=2 mg/mL500\text{ mg} \div 250\text{ mL} = 2\text{ mg/mL}
Determining the amount of medication in each milliliter is required to calculate the final infusion rate.
5
Calculate the required infusion rate in mL/hr.
24 mg/hr÷2 mg/mL=12 mL/hr24\text{ mg/hr} \div 2\text{ mg/mL} = 12\text{ mL/hr}
Dividing the required hourly dose by the concentration yields the fluid volume needed per hour.

Key Concept

Weight-based intravenous medication dosage calculation
Question 111Question →

A client weighing 192 lbs192 \text{ lbs} is receiving treatment for a stable ventricular tachycardia. The healthcare provider prescribes a continuous intravenous infusion of amiodarone at 0.5 mg/min0.5 \text{ mg/min}. The pharmacy supplies an amiodarone infusion bag containing 900 mg900 \text{ mg} in 500 mL500 \text{ mL} of 5% dextrose5\% \text{ dextrose} in water (D5WD_5W). At what rate, in mL/hr\text{mL/hr}, should the nurse set the infusion pump? Record your answer using one decimal place.

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Answer: 16.7

Answer

16.7
The correct infusion rate of 16.7 mL/hr16.7 \text{ mL/hr} is calculated by first recognizing that the client's weight is not needed for a non-weight-based dose. Convert the per-minute dose to an hourly dose (0.5 mg/min×60=30 mg/hr0.5 \text{ mg/min} \times 60 = 30 \text{ mg/hr}). Then, determine the concentration of the IV fluid (900 mg÷500 mL=1.8 mg/mL900 \text{ mg} \div 500 \text{ mL} = 1.8 \text{ mg/mL}). Finally, divide the hourly dose by the concentration to find the correct pump rate (30÷1.8=16.666...30 \div 1.8 = 16.666...) and round to one decimal place.

Step-by-Step Solution

1
Determine the required medication dose per hour.
0.5 mg/min×60 min/hr=30 mg/hr0.5 \text{ mg/min} \times 60 \text{ min/hr} = 30 \text{ mg/hr}
The infusion pump operates in mL/hr, so the prescribed mg/min dose must be converted to an hourly rate. The client's weight is extraneous data.
2
Calculate the concentration of the supplied medication.
900 mg÷500 mL=1.8 mg/mL900 \text{ mg} \div 500 \text{ mL} = 1.8 \text{ mg/mL}
Finding the concentration allows you to convert the required hourly dose from milligrams to milliliters.
3
Calculate the infusion rate in mL/hr.
30 mg/hr÷1.8 mg/mL=16.666... mL/hr30 \text{ mg/hr} \div 1.8 \text{ mg/mL} = 16.666... \text{ mL/hr}
Dividing the desired hourly dose by the concentration provides the volume of fluid to be infused per hour.
4
Round the final calculation to one decimal place.
16.716.7
Clinical calculations must follow precise rounding rules as instructed in the question stem.

Key Concept

Continuous IV Infusion Calculation and Extraneous Data Identification
Question 112Question →

A client admitted with decompensated heart failure weighing 198 lb198\text{ lb} is prescribed a continuous intravenous infusion of milrinone at 0.5 \mug/kg/min0.5\text{ \mu g/kg/min}. The pharmacy dispenses a premixed bag containing 20 mg20\text{ mg} of milrinone in 100 mL100\text{ mL} of 0.9%0.9\% sodium chloride. The nurse should set the infusion pump to deliver how many mL/hr\text{mL/hr}? (Round the answer to the nearest tenth.)

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Answer: 13.5

Answer

13.5
To determine the correct infusion rate, a multi-step calculation is required. First, the client's weight is converted to kilograms (198÷2.2=90 kg198 \div 2.2 = 90\text{ kg}). Second, the hourly dose is calculated by multiplying the weight-based dose by the client's weight and then by 6060 minutes (0.5×90×60=2,700 \mug/hr0.5 \times 90 \times 60 = 2,700\text{ \mu g/hr}). Third, the concentration of the IV bag is converted to matching units (20 mg=20,000 \mug20\text{ mg} = 20,000\text{ \mu g}; 20,000÷100 mL=200 \mug/mL20,000 \div 100\text{ mL} = 200\text{ \mu g/mL}). Finally, the hourly dose is divided by the concentration (2,700÷2002,700 \div 200) to yield the correct pump setting of 13.5 mL/hr13.5\text{ mL/hr}.

Step-by-Step Solution

1
Convert the client's weight from lb to kg.
198 lb÷2.2 lb/kg=90 kg198\text{ lb} \div 2.2\text{ lb/kg} = 90\text{ kg}
The medication dosage is prescribed based on the client's weight in kilograms.
2
Calculate the prescribed dose per minute.
0.5 \mug/kg/min×90 kg=45 \mug/min0.5\text{ \mu g/kg/min} \times 90\text{ kg} = 45\text{ \mu g/min}
This determines the exact amount of milrinone the client needs every minute.
3
Convert the dose per minute to the dose per hour.
45 \mug/min×60 min/hr=2,700 \mug/hr45\text{ \mu g/min} \times 60\text{ min/hr} = 2,700\text{ \mu g/hr}
Intravenous pumps are typically programmed in milliliters per hour (mL/hr), so the hourly dose is required.
4
Determine the concentration of the supplied milrinone solution in \mug/mL\text{\mu g/mL}.
20 mg×1,000 \mug/mg=20,000 \mug20\text{ mg} \times 1,000\text{ \mu g/mg} = 20,000\text{ \mu g}. Then, 20,000 \mug÷100 mL=200 \mug/mL20,000\text{ \mu g} \div 100\text{ mL} = 200\text{ \mu g/mL}
To calculate the volume needed, the medication dose units (micrograms) must match the concentration units.
5
Calculate the infusion rate in mL/hr\text{mL/hr}.
2,700 \mug/hr÷200 \mug/mL=13.5 mL/hr2,700\text{ \mu g/hr} \div 200\text{ \mu g/mL} = 13.5\text{ mL/hr}
Dividing the hourly dose by the concentration yields the fluid volume that needs to be delivered per hour.

Key Concept

Weight-based continuous intravenous infusion rate calculation requiring multiple unit conversions
Estimated Time:3m 0s
Question 113Question →

An intensive care nurse assumes care for a client admitted with acute decompensated heart failure. The client, who weighs 176 lb, has a continuous intravenous line infusing dopamine. The medication bag is labeled: dopamine 400 mg in 250 mL of 5% dextrose in water. The smart pump displays a current infusion rate of 15 mL/hr. Based on this data, what dosage of dopamine is the client receiving in mcg/kg/min? Record your answer as a whole number.

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Answer: 5

Answer

5
To determine the exact mcg/kg/min dose from a known mL/hr rate, the nurse must work backward through standard infusion calculations. First, convert the weight to kilograms (176 ÷ 2.2 = 80 kg) and find the bag's concentration in mcg/mL (400,000 mcg ÷ 250 mL = 1,600 mcg/mL). Next, determine the hourly dose in mcg by multiplying the volume rate by the concentration (15 mL/hr × 1,600 mcg/mL = 24,000 mcg/hr). Convert this to a per-minute dose by dividing by 60 (24,000 ÷ 60 = 400 mcg/min). Finally, divide by the client's weight in kg to find the exact dose being delivered (400 ÷ 80 = 5 mcg/kg/min).

Step-by-Step Solution

1
Convert the client's weight from pounds to kilograms.
176 lb ÷ 2.2 lb/kg = 80 kg
Weight-based dosing requires the client's weight to be expressed in kilograms.
2
Determine the concentration of the dopamine solution in mcg/mL.
400 mg = 400,000 mcg. Then, 400,000 mcg ÷ 250 mL = 1,600 mcg/mL.
The final requested unit is in micrograms (mcg), so the total medication amount must be converted from milligrams to micrograms before determining the per-mL concentration.
3
Calculate the total amount of dopamine infusing per hour.
15 mL/hr × 1,600 mcg/mL = 24,000 mcg/hr
Multiplying the current pump volume rate by the concentration yields the total hourly dose.
4
Convert the hourly dose to a per-minute dose.
24,000 mcg/hr ÷ 60 min/hr = 400 mcg/min
The requested administration rate is per minute, necessitating the division of the hourly rate by 60.
5
Calculate the final dose in mcg/kg/min.
400 mcg/min ÷ 80 kg = 5 mcg/kg/min
Dividing the total minute dose by the client's weight in kilograms provides the precise weight-based dosage currently being delivered.

Key Concept

Weight-based continuous intravenous infusion calculation (reverse calculation from mL/hr to mcg/kg/min)
Question 114Question →

A client who is hemodynamically unstable is admitted to the critical care unit. The client's body weight is recorded as 187 lbs187\text{ lbs}. The healthcare provider prescribes a continuous intravenous infusion of norepinephrine at 0.05 mcg/kg/min0.05\text{ mcg/kg/min}. The pharmacy dispenses an intravenous solution containing norepinephrine 4 mg4\text{ mg} in 250 mL250\text{ mL} of 0.9% Sodium Chloride0.9\%\text{ Sodium Chloride}. At what rate should the nurse program the infusion pump? Record your answer in mL/hr\text{mL/hr} and round to the nearest tenth.

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Answer: 15.9

Answer

15.9
To accurately program the infusion pump for a weight-based continuous drip, dimensional analysis is used to bridge the ordered dose (0.05 mcg/kg/min0.05\text{ mcg/kg/min}) to the pump setting (mL/hr\text{mL/hr}). The weight is first converted to 85 kg85\text{ kg}. The hourly dose required is 255 mcg/hr255\text{ mcg/hr}. Because the bag contains 4 mg4\text{ mg} (4000 mcg4000\text{ mcg}) in 250 mL250\text{ mL}, the concentration is 16 mcg/mL16\text{ mcg/mL}. Dividing the hourly dose by the concentration yields 15.937515.9375, which rounds appropriately to 15.915.9.

Step-by-Step Solution

1
Convert weight from pounds to kilograms.
187 lbs÷2.2 lbs/kg=85 kg187\text{ lbs} \div 2.2\text{ lbs/kg} = 85\text{ kg}
Weight-based dosing requires the client's weight in kilograms.
2
Calculate the total dose prescribed per minute.
0.05 mcg/kg/min×85 kg=4.25 mcg/min0.05\text{ mcg/kg/min} \times 85\text{ kg} = 4.25\text{ mcg/min}
This establishes the exact amount of medication the client needs every minute.
3
Calculate the total dose required per hour.
4.25 mcg/min×60 min/hr=255 mcg/hr4.25\text{ mcg/min} \times 60\text{ min/hr} = 255\text{ mcg/hr}
Infusion pumps are programmed in mL per hour, so the dose must reflect an hourly rate.
4
Determine the medication concentration in mcg/mL.
4 mg=4000 mcg4\text{ mg} = 4000\text{ mcg}; 4000 mcg÷250 mL=16 mcg/mL4000\text{ mcg} \div 250\text{ mL} = 16\text{ mcg/mL}
The prescribed dose is in micrograms, so the available medication must be converted to match.
5
Calculate the final infusion rate and round to the nearest tenth.
255 mcg/hr÷16 mcg/mL=15.9375 mL/hr255\text{ mcg/hr} \div 16\text{ mcg/mL} = 15.9375\text{ mL/hr}, which rounds to 15.9 mL/hr15.9\text{ mL/hr}.
Dividing the hourly dose by the concentration yields the volume required per hour.

Key Concept

Weight-based complex continuous intravenous infusions.
Question 115Question →

A nurse is caring for a client in the intensive care unit who is experiencing severe hypotension and weighs 87 kg87\text{ kg}. The healthcare provider prescribes a continuous intravenous (IV) infusion of norepinephrine at 0.05 mcg/kg/min0.05\text{ mcg/kg/min}. The pharmacy dispenses norepinephrine 4 mg4\text{ mg} in 250 mL250\text{ mL} of 5%5\% dextrose in water (D5W\text{D}_5\text{W}). At what rate should the nurse set the IV infusion pump in mL/hr\text{mL/hr}? (Round the answer to the nearest tenth. Do not use a trailing zero.)

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Answer: 16.3

Answer

16.3
The correct infusion rate is calculated by first determining the total hourly dose required for the client's specific weight (0.05 mcg/kg/min×87 kg×60 min/hr=261 mcg/hr0.05\text{ mcg/kg/min} \times 87\text{ kg} \times 60\text{ min/hr} = 261\text{ mcg/hr}). Next, the concentration of the IV bag is found by converting milligrams to micrograms (4 mg=4000 mcg4\text{ mg} = 4000\text{ mcg}) and dividing by the total volume (4000 mcg/250 mL=16 mcg/mL4000\text{ mcg} / 250\text{ mL} = 16\text{ mcg/mL}). Finally, dividing the hourly dose by the concentration gives the pump rate (261 mcg/hr÷16 mcg/mL=16.3125 mL/hr261\text{ mcg/hr} \div 16\text{ mcg/mL} = 16.3125\text{ mL/hr}), which rounds to 16.316.3.

Step-by-Step Solution

1
Calculate the prescribed dose per minute based on the client's weight.
0.05 mcg/kg/min×87 kg=4.35 mcg/min0.05\text{ mcg/kg/min} \times 87\text{ kg} = 4.35\text{ mcg/min}
The prescription is weight-based, so the total microgram dose per minute must be determined first.
2
Convert the prescribed dose per minute to the prescribed dose per hour.
4.35 mcg/min×60 min/hr=261 mcg/hr4.35\text{ mcg/min} \times 60\text{ min/hr} = 261\text{ mcg/hr}
IV infusion pumps deliver medication at an hourly rate (mL/hr\text{mL/hr}), requiring the dose to be converted from minutes to hours.
3
Determine the concentration of the dispensed IV solution in mcg/mL\text{mcg/mL}.
4 mg×1000 mcg/mg=4000 mcg4\text{ mg} \times 1000\text{ mcg/mg} = 4000\text{ mcg}. Then, 4000 mcg/250 mL=16 mcg/mL4000\text{ mcg} / 250\text{ mL} = 16\text{ mcg/mL}.
The prescribed dose is in micrograms, so the medication supplied in milligrams must be converted to match the units before calculating the volume.
4
Calculate the final infusion rate in mL/hr\text{mL/hr} and round to the nearest tenth.
261 mcg/hr÷16 mcg/mL=16.3125 mL/hr261\text{ mcg/hr} \div 16\text{ mcg/mL} = 16.3125\text{ mL/hr}. Rounded to the nearest tenth is 16.316.3.
Dividing the required hourly dose by the concentration yields the exact volume needed per hour. Rounding to the nearest tenth is standard for critical care infusions.

Key Concept

Weight-based continuous intravenous (IV) medication calculation and infusion pump programming.

Alternative Method

Dimensional analysis can be used to solve this in a single equation: X mL/hr=(250 mL/4 mg)×(1 mg/1000 mcg)×(0.05 mcg/1 kg×1 min)×(87 kg/1)×(60 min/1 hr)=16.3125 mL/hrX\text{ mL/hr} = (250\text{ mL} / 4\text{ mg}) \times (1\text{ mg} / 1000\text{ mcg}) \times (0.05\text{ mcg} / 1\text{ kg} \times 1\text{ min}) \times (87\text{ kg} / 1) \times (60\text{ min} / 1\text{ hr}) = 16.3125\text{ mL/hr}.
Estimated Time:2m 0s
Question 116Question →

A nurse is caring for a client with acute decompensated heart failure who has a prescription for a continuous IV infusion of milrinone at 0.375 mcg/kg/min0.375 \text{ mcg/kg/min}. The client weighs 209 lbs209 \text{ lbs}. The pharmacy provides milrinone 20 mg20 \text{ mg} in 100 mL100 \text{ mL} of 0.9% NaCl0.9\% \text{ NaCl}. The nurse should set the IV infusion pump to deliver how many mL/hr\text{mL/hr}? (Round the final answer to the nearest tenth.)

Show answer & explanation

Answer: 10.7

Answer

10.7
The correct infusion rate is determined by a multi-step calculation: first, converting the client's weight to kg (209÷2.2=95 kg209 \div 2.2 = 95 \text{ kg}); second, calculating the hourly dose in micrograms (95×0.375×60=2137.5 mcg/hr95 \times 0.375 \times 60 = 2137.5 \text{ mcg/hr}); third, determining the concentration of the IV bag in mcg/mL (20,000÷100=200 mcg/mL20,000 \div 100 = 200 \text{ mcg/mL}); and finally, dividing the required hourly dose by the concentration (2137.5÷200=10.68752137.5 \div 200 = 10.6875). Rounding 10.687510.6875 to the nearest tenth gives 10.7 mL/hr10.7 \text{ mL/hr}.

Step-by-Step Solution

1
Convert weight from pounds to kilograms
95 kg95 \text{ kg}
The prescription is weight-based in kg, so the client's weight must be converted first (209÷2.2209 \div 2.2).
2
Calculate the total mcg required per minute
35.625 mcg/min35.625 \text{ mcg/min}
Multiply the prescribed dose (0.375 mcg/kg/min0.375 \text{ mcg/kg/min}) by the client's weight (95 kg95 \text{ kg}).
3
Calculate the total mcg required per hour
2137.5 mcg/hr2137.5 \text{ mcg/hr}
IV pumps are programmed in mL/hr, so the per-minute dose must be multiplied by 60 minutes.
4
Determine the concentration of the IV solution in mcg/mL
200 mcg/mL200 \text{ mcg/mL}
Convert 20 mg20 \text{ mg} to 20,000 mcg20,000 \text{ mcg}, then divide by 100 mL100 \text{ mL} to match the units of the required dose.
5
Calculate the final infusion rate in mL/hr
10.6875 mL/hr10.6875 \text{ mL/hr}
Divide the total hourly dose (2137.5 mcg/hr2137.5 \text{ mcg/hr}) by the concentration (200 mcg/mL200 \text{ mcg/mL}).
6
Round the final answer to the nearest tenth
10.710.7
Rounding instructions require the answer to one decimal place.

Key Concept

Weight-based continuous IV infusion calculation
Question 117Question →

An intensive care nurse is managing a male patient diagnosed with cardiogenic shock. The patient's body weight is recorded as 198 lb198 \text{ lb}. The medical team orders an intravenous infusion of dopamine at a rate of 5 mcg/kg/min5 \text{ mcg/kg/min} to support cardiac output. The available medication from the pharmacy is a premixed bag containing 400 mg400 \text{ mg} of dopamine dissolved in 250 mL250 \text{ mL} of 5%5\% dextrose in water (D5W).

Determine the appropriate infusion pump setting in mL/hr\text{mL/hr} to deliver the prescribed dose. Round the final answer to the nearest tenth.

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Answer: 16.9

Answer

16.9
To safely program the infusion pump, the nurse must systematically convert the patient's weight to kilograms, find the total dose required per minute, convert that value to milligrams per hour, and finally divide it by the concentration of the dopamine bag (mg/mL). This mathematically yields the exact fluid volume required per hour.

Step-by-Step Solution

1
Convert the patient's weight from pounds to kilograms.
198 lb÷2.2 lb/kg=90 kg198 \text{ lb} \div 2.2 \text{ lb/kg} = 90 \text{ kg}
Weight-based critical care drug dosing requires the patient's weight to be expressed in metric units (kilograms).
2
Calculate the total required dose per minute.
5 mcg/kg/min×90 kg=450 mcg/min5 \text{ mcg/kg/min} \times 90 \text{ kg} = 450 \text{ mcg/min}
This establishes the exact amount of medication the patient must receive every minute based on their specific body mass.
3
Convert the per-minute dose in micrograms to an hourly dose in milligrams.
450 mcg/min×60 min/hr=27,000 mcg/hr450 \text{ mcg/min} \times 60 \text{ min/hr} = 27,000 \text{ mcg/hr}. Then, 27,000 mcg÷1,000 mcg/mg=27 mg/hr27,000 \text{ mcg} \div 1,000 \text{ mcg/mg} = 27 \text{ mg/hr}
Since the infusion pump is programmed in mL/hr and the drug concentration is usually calculated in mg/mL, unifying these units simplifies the final calculation step.
4
Determine the concentration of the available medication bag.
400 mg÷250 mL=1.6 mg/mL400 \text{ mg} \div 250 \text{ mL} = 1.6 \text{ mg/mL}
This identifies how many milligrams of dopamine are present in a single milliliter of the IV fluid.
5
Calculate the final infusion rate and round to the nearest tenth.
27 mg/hr÷1.6 mg/mL=16.875 mL/hr27 \text{ mg/hr} \div 1.6 \text{ mg/mL} = 16.875 \text{ mL/hr}. Rounded to the nearest tenth, this yields 16.9 mL/hr16.9 \text{ mL/hr}.
Dividing the total required hourly dose by the fluid concentration provides the volume that the infusion pump must deliver per hour.

Key Concept

Weight-Based Continuous IV Medication Calculations
Question 118Question →

A nurse is preparing to administer amoxicillin oral suspension to a pediatric client diagnosed with acute otitis media. The prescription states: amoxicillin 45 mg/kg/day45 \text{ mg/kg/day} orally, divided into equal doses to be administered every 1212 hours. The client's weight is 44 lb44 \text{ lb}. The pharmacy provides amoxicillin suspension with a concentration of 400 mg/5 mL400 \text{ mg}/5 \text{ mL}. How many mL should the nurse administer per dose? (Record your answer using one decimal place.)

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Answer: 5.6

Answer

5.6
The correct volume is determined by first converting the child's weight to kilograms (44 lb÷2.2=20 kg44 \text{ lb} \div 2.2 = 20 \text{ kg}). The total daily dose is calculated by multiplying the weight by the prescribed dosage (20 kg×45 mg/kg/day=900 mg/day20 \text{ kg} \times 45 \text{ mg/kg/day} = 900 \text{ mg/day}). Because the medication is ordered every 1212 hours, the daily dose is divided by 22 to find the individual dose (900 mg÷2=450 mg/dose900 \text{ mg} \div 2 = 450 \text{ mg/dose}). Finally, the liquid volume is calculated using the available concentration: 450 mg400 mg×5 mL=5.625 mL\frac{450 \text{ mg}}{400 \text{ mg}} \times 5 \text{ mL} = 5.625 \text{ mL}. Rounding to the nearest tenth yields 5.6 mL5.6 \text{ mL}.

Step-by-Step Solution

1
Convert the client's weight from pounds to kilograms
44 lb÷2.2 lb/kg=20 kg44 \text{ lb} \div 2.2 \text{ lb/kg} = 20 \text{ kg}
The prescribed medication dose is weight-based in kilograms, so an accurate conversion is the necessary first step.
2
Calculate the total daily dose
20 kg×45 mg/kg/day=900 mg/day20 \text{ kg} \times 45 \text{ mg/kg/day} = 900 \text{ mg/day}
This determines the total amount of active medication the client needs to receive over a 24-hour period.
3
Calculate the amount per individual dose
900 mg/day÷2 doses=450 mg/dose900 \text{ mg/day} \div 2 \text{ doses} = 450 \text{ mg/dose}
Because the medication is ordered to be given every 12 hours, the total daily dose must be divided into 2 equal administrations.
4
Calculate the liquid volume needed per dose
450 mg400 mg×5 mL=5.625 mL\frac{450 \text{ mg}}{400 \text{ mg}} \times 5 \text{ mL} = 5.625 \text{ mL}
This dimensional analysis determines how many milliliters of the supplied concentration contain the required 450 mg.
5
Round the final answer
5.6 mL5.6 \text{ mL}
Standard clinical calculation rules and the question instructions require rounding to the nearest tenth (one decimal place).

Key Concept

Pediatric weight-based dosage calculation and liquid medication administration
Question 119Question →

A client presenting with a hypertensive emergency requires a continuous intravenous (IV) infusion of sodium nitroprusside. The client weighs 187 lb187\text{ lb}. The healthcare provider prescribes the infusion to begin at a rate of 3 mcg/kg/min3\text{ mcg/kg/min}. The pharmacy dispenses a premixed bag containing 50 mg50\text{ mg} of sodium nitroprusside in 250 mL250\text{ mL} of 5%5\% dextrose in water (D5WD5W). At what rate in mL/hr\text{mL/hr} should the nurse set the IV infusion pump? (Record your answer to the nearest tenth.)

Show answer & explanation

Answer: 76.5

Answer

76.5
The correct rate is exactly 76.5 mL/hr76.5\text{ mL/hr}. This is achieved by systematically aligning the units of measurement: changing weight to kg\text{kg}, converting the dose interval from minutes to hours, converting the supplied drug mass from mg\text{mg} to mcg\text{mcg}, and then dividing the hourly requirement by the concentration.

Step-by-Step Solution

1
Convert weight from pounds to kilograms.
187 lb÷2.2 lb/kg=85 kg187\text{ lb} \div 2.2\text{ lb/kg} = 85\text{ kg}
Weight-based dosing algorithms require the client's weight to be in metric units.
2
Calculate the prescribed medication dose per minute.
85 kg×3 mcg/kg/min=255 mcg/min85\text{ kg} \times 3\text{ mcg/kg/min} = 255\text{ mcg/min}
This establishes the exact amount of active drug the client must receive every minute based on the provider's prescription.
3
Convert the minute dose to an hourly dose.
255 mcg/min×60 min/hr=15,300 mcg/hr255\text{ mcg/min} \times 60\text{ min/hr} = 15,300\text{ mcg/hr}
Standard IV infusion pumps are programmed to deliver fluids at an hourly rate (mL/hr\text{mL/hr}), so the required drug amount must match this timeframe.
4
Determine the concentration of the supplied medication in mcg/mL\text{mcg/mL}.
50 mg×1,000 mcg/mg=50,000 mcg50\text{ mg} \times 1,000\text{ mcg/mg} = 50,000\text{ mcg}; then 50,000 mcg÷250 mL=200 mcg/mL50,000\text{ mcg} \div 250\text{ mL} = 200\text{ mcg/mL}
To calculate the volume required, the units of the supplied medication must be identical to the units of the prescribed dose (micrograms).
5
Calculate the final infusion pump rate in mL/hr\text{mL/hr}.
15,300 mcg/hr÷200 mcg/mL=76.5 mL/hr15,300\text{ mcg/hr} \div 200\text{ mcg/mL} = 76.5\text{ mL/hr}
Dividing the total required hourly dose by the concentration per milliliter provides the final fluid volume to be infused over one hour.

Key Concept

Weight-Based Continuous IV Medication Dosing
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