Chapter 10: Advanced Intravenous Calculations
Get the Test Bank for Mulholland’s The Nurse, The Math, The Meds, 5th Edition by Susan Turner, a valuable tool for excelling in nursing calculations and medication management.
ESSAY
1. Directions: Calculate the IV medication and infusion rates. Use a calculator for safe dose range calculations, multiplication, and long division as desired. Verify results using DE-style equations where requested. If the order is unsafe, do not proceed with the math. Label answers.
Ordered: medicated IV at 4 mcgper kg per min.
Patient’s weight: 50 kg.
a. Information requested: Micrograms per minute orderedCalculator result:
b. Information requested: Micrograms per hour orderedCalculator result:
c. Information requested: Milligrams per hour orderedCalculator result:
ANS:
a. 200 mcg per minute (4 50)
b. 12,000 mcg per hour (200 60)
c. 12 mg per hour (12,000 ÷ 1000)
2. Directions: Calculate the IV medication and infusion rates. Use a calculator for safe dose range calculations, multiplication, and long division as desired. Verify results using DE-style equations where requested. If the order is unsafe, do not proceed with the math. Label answers.
An IV of 1000 mL of D5W contains 400 mg of dopamine HCl.
a. What is the concentration in milligrams per milliliter? (Remember: per indicates division.) Show the data you would enter on a calculator or use a DA equation.
b. What is the concentration in micrograms per milliliter? (Move the decimal point carefully.) Show the data you would enter on a calculator or use a DA equation.
ANS:
a.
b. 1.6 1000 = 1600 mcg per mL
3. Directions: Calculate the IV medication and infusion rates. Use a calculator for safe dose range calculations, multiplication, and long division as desired. Verify results using DE-style equations where requested. If the order is unsafe, do not proceed with the math. Label answers.
Ordered: aminophylline IV infusion, for a patient with asthma. Infusing: aminophylline at 33 mL per hr
Available: IV of 500 mL of D5W with the contents of the vial shown here
Patient’s weight: 110 kg
The nurse has withdrawn 20 mL of D5W and added the medication to make a total volume of 500 mL.
How many milligrams of aminophylline is the patient receiving per hour? a. DA equation:
b. Evaluation:
ANS:
a.
b. Equation is balanced. Only mg per hour remain. Note: The equation is solved using the total mL (500 mL) not 20 mL.
4. Directions: Calculate the IV medication and infusion rates. Use a calculator for safe dose range calculations, multiplication, and long division as desired. Verify results using DE-style equations where requested. If the order is unsafe, do not proceed with the math. Label answers.
Ordered: dopamine infusion at 3 mcg per kg per min, for a patient in shock.
Available: dopamine 200 mg per 250 mL D5W.
Patient’s weight: 60 kg
a. Information requested: Micrograms per hour orderedCalculator result:
b. Information requested: Milligrams per hour orderedCalculator result:
Milliliters per hour to be administered on infusion pump
c. DA equation:
d. Evaluation:
ANS:
a. 10,800 mcg per hr (3 60 60)
b. 10.800 mg per hr (10.800) (10.800 1000) c.
d. Equation is balanced. Only mL per hour remain. A shortcut can be used by entering the
5. Directions: Calculate the IV medication and infusion rates. Use a calculator for safe dose range calculations, multiplication, and long division as desired. Verify results using DE-style equations where requested. If the order is unsafe, do not proceed with the math. Label answers.
Ordered: dobutamine 2.5 mcg per kg per min
Available: 500 mL D5W
Patient’s weight: 80 kg
a. Information requested: Micrograms per minute orderedCalculator result:
b. Information requested: Micrograms per hour orderedCalculator result:
c. Information requested: Milligrams per minute orderedCalculator result:
d. Milligrams per hour ordered (Use in final flow rate equation.)Calculator result:
Milliliters per hour to be administered on infusion pump:
e. DA equation:
f. Evaluation:
ANS:
a. 200 mcg (2.5 80)
b. 12,000 mcg (200 60)
c. 0.2 mg (0.200) (200 1000)
d. 12 mg (12.000) (0.2 60)
e.
f. Equation is balanced. Only mL per hour remain.
6. Directions: Calculate the IV medication and infusion rates. Use a calculator for safe dose range calculations, multiplication, and long division as desired. Verify results using DE-style equations where requested. If the order is unsafe, do not proceed with the math. Label answers.
Ordered: Lasix 25 mg direct IV, for a patient with pulmonary edema. SDR: Up to 20 mg per min
For pulmonary edema, push over several minutes.
The nurse plans to administer the medication over a 5-minute period. Available:
Total number of milliliters for the prepared injection to the nearest tenth of a milliliter: a. Estimated dose:
b. DA equation:
c. Evaluation:
d. Total minutes for injection:
Total seconds for injection:
e. Total number of calibrations occupied by the dose:
Number of calibrations per second to be pushed: f. DA equation:
g. Evaluation:
ANS:
a. Estimate: Give less than 4 mL.
b.
c. Equation is balanced. Estimate supports answer.
d. 5 minutes; 300 seconds (5 60)
e. 25 calibrations
g. Only calibrations per second remain. Inject volume of 2.5 mL at a rate of 1 calibration every 12 seconds.
7. Directions: Calculate the IV medication and infusion rates. Use a calculator for safe dose range calculations, multiplication, and long division as desired. Verify results using DE-style equations where requested. If the order is unsafe, do not proceed with the math. Label answers.
Ordered: meperidine 30-mg IV push, for a patient with complaints of pain. Drug reference: Inject over 1 minute. Available:
Total number of milliliters for the prepared injection to nearest tenth of a milliliter: a. Estimate:
b. DA equation:
c. Evaluation:
d. Total minutes for injection:
Total seconds for injection:
e. Total number of calibrations occupied by dose:
Number of calibrations per second to be pushed: f. DA equation:
g. Evaluation:
ANS:
a. Estimate: Give less than 1 mL.
b.
c. Equation is balanced. Estimate supports answer.
d. 1 minute; 60 seconds
e. 6 calibrations
f.
g. Inject volume of 0.6 mL at a rate of 1 calibration every 10 seconds.
8. Directions: Calculate the IV medication and infusion rates. Use a calculator for safe dose range calculations, multiplication, and long division as desired. Verify results using DE-style equations where requested. If the order is unsafe, do not proceed with the math. Label answers.
Ordered: magnesium sulfate 2.5 g per hr IV infusion, for a patient with toxemia
Existing infusion rate when nurse arrives on shift: 75 mL per hr Available: magnesium sulfate (refer to label) diluted in 500 mL D5W
a. Number of milliequivalents per milliliter stated on label:
b. Number of milligrams per milliliter stated in fine print on right side of label:
c. Total number of grams of magnesium sulfate in 50-mL vial:
Number of grams per hour infusing on the infusion pump:
d. DA equation:
e. Evaluation:
Ordered infusion rate:
f. DA equation:
g. Evaluation:
h. Decision:
ANS:
a. 4 mEq mL
b. 500 mg per mL
c. 25 g
d.
e. Equation is balanced. Only g per hour remains. f.
g. Equation is balanced. Existing flow rate is too rapid.
h. Flow rate needs to be reduced to 50 mL per hr. Contact prescriber promptly for rate of adjustment. Assess and monitor patient. Document.
9. Directions: Calculate the IV medication and infusion rates. Use a calculator for safe dose range calculations, multiplication, and long division as desired. Verify results using DE-style equations where requested. If the order is unsafe, do not proceed with the math. Label answers.
Ordered: oxytocin drip, 1 milliunit per min Infusing: oxytocin drip at 6 mL per hr Available:
a. How many units of Pitocin are contained in 1 mL, according to label?
b. How many milliunits equal 1 unit? How many milliunits equal 10 units? (Recall the meaning of the prefix “milli”.)
c. One mL of Pitocin has been placed in 1000 mL of D5W. What is the concentration of milliunits per milliliter in the IV solution?
DA equation:
d. How many milliunits per hour are being infused?
DA equation: e. Evaluation:
f. How many milliunits per minute are infusing?
DA equation: g. Evaluation:
h. Is the existing flow rate correct? (Do the milliunits per minute being infused match the order?) If not, what flow rate should be set?
i. DA equation:
j. Evaluation:
ANS:
a. 10 units
b. 1000 milliunits = 1 unit; 10,000 milliunits = 10 units (1000 10) c.
d.
e. Equation is balanced. Only milliunits per hour remain. f.
g. Equation is balanced. Only mU per minute remain.
h. Yes. Flow rate is correct.
i. N/A
j. Continue the infusion at 6 mL per hour. Note: Be sure to insert commas when working with large numbers.
10. Directions: Calculate the IV medication and infusion rates. Use a calculator for safe dose range calculations, multiplication, and long division as desired. Verify results using DE-style equations where requested. If the order is unsafe, do not proceed with the math. Label answers.
Diltiazem hydrochloride IV maintenance drip infusion has been ordered for a patient diagnosed with atrial flutter, who was treated on admission with a bolus IV dose to lower the ventricular pulse rate.
Order: Titrate the diltiazem HC1 at 5-15 mg per hr to maintain a ventricular pulse rate 
90 beats per minute (bpm). Increase by increments of 5 mg per hr
Available: diltiazem hydrochloride 100 mg per 100 mL NS
a. With what IV dose in mg per hr will the nurse initiate the infusion?
b. Estimated initial flow rate on an EID:
c. DA equation for flow rate:
d. Evaluation:
The patient’s ventricular pulse rate is 100 bpm at the end of the first hour.
e. IV dose in mg per hr to be administered:
f. Estimated flow rate:
g. DA equation for flow rate:
h. Evaluation:
ANS:
a. 5 mg per hr. Note: When titrating medications, the initial dose must be the lowest dose in the range.
b. 5 mL per hr (100 mg per 100 mL = 1:1)c.
d. Equation is balanced. Only mL per hour remain.
e. 10 mg per hr. Note: The drug is to be titrated in 5 mg per hr increments.f. 10 mL per hr
g. 
h. Equation is balanced. Only mL per hr remain.
11. Directions: Calculate the IV medication and infusion rates. Use a calculator for safe dose range calculations, multiplication, and long division as desired. Verify results using DE-style equations where requested. If the order is unsafe, do not proceed with the math. Label answers.
Ordered: A medicated IV infusion at 3 mg per minute. Available: Drug Y 1500 mg in 1000 mL of D5NS.
a. How many mg per hr will be administered?
b. How many mg per mL will be in the IV?
DA:
Evaluation:
ANS:
a. 180 mg per hr
12. Directions: Calculate the IV medication and infusion rates. Use a calculator for safe dose range calculations, multiplication, and long division as desired. Verify results using DE-style equations where requested. If the order is unsafe, do not proceed with the math. Label answers.
Ordered: A medicated IV infusion at 0.5 mg per minute. Available: Drug Y 500 mg in 100 mL. LRS.
a. What will the flow rate be in mL per hr?
b. DA:
c. Evaluation:
ANS:
c. Equation is balanced, only mL/hr remains.
13. Directions: Calculate the IV medication and infusion rates. Use a calculator for safe dose range calculations, multiplication, and long division as desired. Verify results using DE-style equations where requested. If the order is unsafe, do not proceed with the math. Label answers.
Ordered: A medicated IV infusion at 1 mg per minute. Available: Drug Y 250 mg in 250 mL of D5W.
a. What will the flow rate be in mL per hour?
b. DA:
c. Evaluation:
ANS:
a. Estimate: 1 mg per mL of D5W 60 mg per hr and 60 mL per hr b. DA:
c. Estimate supports answer.
14. Directions: Calculate the IV medication and infusion rates. Use a calculator for safe dose range calculations, multiplication, and long division as desired. Verify results using DE-style equations where requested. If the order is unsafe, do not proceed with the math. Label answers.
Ordered: A medicated IV infusion with drug Y at 2 mg per minute. Available: Drug Y 1 g in 1000 mL of NS.
a. What will the flow rate be in mL per hr?
b. DA:
c. Evaluation
ANS:
a. 120 mL per hr
c. Equation balanced, only mL per hour remains.
15. Directions: Calculate the IV medication and infusion rates. Use a calculator for safe dose range calculations, multiplication, and long division as desired. Verify results using DE-style equations where requested. If the order is unsafe, do not proceed with the math. Label answers.
Ordered: A medicated IV at 2 mcg per kg per minute
Patient’s weight: 60 kg
a. Micrograms per minute ordered:
b. Micrograms per hour ordered:
c. Milligrams per hour ordered:
ANS:
a. 2 mcg 60 kg =120 mcg per minute
b. 120 60 min = 7200 mcg per hr
c. 7200 ÷ 1000 mcg = 7.2 mg per hr
16. Directions: Calculate the IV medication and infusion rates. Use a calculator for safe dose range calculations, multiplication, and long division as desired. Verify results using DE-style equations where requested. If the order is unsafe, do not proceed with the math. Label answers.
Ordered: A medicated IV at 6 mcg per kg per minute
Patient’s weight: 176 lb
a. Estimated wt. in kg:
b. Actual wt. in kg:
c. mcg per hour ordered
d. mg per hour ordered
ANS:
a. Estimated wt. in kg: 176 ÷ 2 = 88
b. Actual wt. in kg: 176 ÷ 2.2 = 80
c. mcg per hour ordered 6 80 60 min = 28,800 mcg per hr
d. mg per hr ordered: 28,800 ÷ 1000 = 28.8 mg per hr
17. Directions: Calculate the IV medication and infusion rates. Use a calculator for safe dose range calculations, multiplication, and long division as desired. Verify results using DE-style equations where requested. If the order is unsafe, do not proceed with the math. Label answers.
Ordered: A medicated IV at 3 mcg per kg per minute. Available IV: D5W 1000 mL with 500 mg of Drug Y. Patient weight: 50 kg
a. What flow rate will you set in mL per hr to the nearest tenth of a mL?
DA:
b. Evaluation:
ANS:
a. Flow rate: 18 mL per hr
DA:
b. Evaluation: Equation verified twice with calculator.
18. Directions: Calculate the IV medication and infusion rates. Use a calculator for safe dose range calculations, multiplication, and long division as desired. Verify results using DE-style equations where requested. If the order is unsafe, do not proceed with the math. Label answers.
Ordered: Dobutamine hydrochloride IV infusion 0.5 mcg per kg per minute, for a patient with cardiac decompensation.
Patient weight: 70 kg.
Available dobutamine: 250 mg in 500 mL
a. How many mg per mL of drug are contained in the IV?
b. How many mcg per mL of drug are contained in the IV?
c. What flow rate will you set in mL per hr to the nearest tenth of a mL?
DA:
d. Evaluation:
ANS:
a.
b. 0.5 X 1000 = 500 mcg/mL
c. 4.2 mL per hr
DA:
d. Evaluation: Equation verified twice with calculator.
19. Directions: Calculate the IV medication and infusion rates. Use a calculator for safe dose range calculations, multiplication, and long division as desired. Verify results using DE-style equations where requested. If the order is unsafe, do not proceed with the math. Label answers.
Ordered: Dopamine infusion at 10 mcg per kg per minute. Available: Dopamine 400 mg premixed in 500 mL of D5W. Patient weight: 60 kg (45 mL per hr)
a. How many mg per mL are contained in the solution?
b. How many mcg per mL are contained in the solution?
c. How many mL per hr will the flow rate be set?
DA:
d. Evaluation:
ANS:
a. mg per mL:
b. mcg per mL: 0.8 mg = 800 mcg per mL
c. 45 mL per hr
d. Equation balanced, only 1 mL per hour remain. Equation verified twice with calculator.
20. Directions: Calculate the IV medication and infusion rates. Use a calculator for safe dose range calculations, multiplication, and long division as desired. Verify results using DE-style equations where requested. If the order is unsafe, do not proceed with the math. Label answers.
Ordered: Dopamine infusion at 5 mcg per kg per min. Available: Dopamine 200 mg in 250 mL of D5W.
Patient weight: 80 kg
a. How many mcg per mL are contained in the solution?
b. How many mL per hr will the flow rate be set?
DA:
c. Evaluation
ANS:
a. 800 mcg per mL; 0.8 mg per mL
b. 30 mL per hr
DA:
c. Evaluation: Equation verified twice with calculator.
21. Directions: Calculate the IV medication and infusion rates. Use a calculator for safe dose range calculations, multiplication, and long division as desired. Verify results using DE-style equations where requested. If the order is unsafe, do not proceed with the math. Label answers.
(11 to 15)
IV Push (Bolus) Rx Total mL to
and Time For Available Dilution Be Given mL per Minute
a. Morphine sulfate IV 2 Morphine 1 mg per mL mg over 2 minutes sulfate 10 mg of NS
for pain per mL
3 mL syringe
b. Hydromorphone HCl Dilaudid 2 mg 5 mL SW or
(Dilaudid) IV 0.5 mg ampule NS
over 5 minutes for pain 5 mL syringe
c. Naloxone HCl Naloxone Dilute up to 2
(Narcan) 1 mg IV for 400 mcg per mL opioid overdose mL
Rate: Each 0.4 mg or 3 mL syringe
fraction thereof over 15 seconds
d. Furosemide (Lasix) 30 Furosemide 10 May be given mg IV for edema. Give mg per mL undiluted
over 2 minutes 3 mL syringe
e. Phenobarbital sodium Phenobarbital Dilute to 10 120 mg IV for status sodium 120 mgmL with SW
epilepticus. May repeatper 3 mL times 3. Give 60 mg 10 mL syringe per minute
ANS:
IV Push (Bolus) Rx Total mL to
and Time For Available Dilution Be Given mL per Minute
a. Morphine sulfate IV 2 Morphine 1 mg per mL 2.2 mL 1.1 mL per mg over 2 minutes sulfate 10 mg of NS minute for pain per mL
3 mL syringe
b. Hydromorphone HCl Dilaudid 2 mg 5 mL SW or 5 mL 1 mL per minute (Dilaudid) IV 0.5 mg ampule NS
over 5 minutes for pain5 mL syringe
c. Naloxone HCl Naloxone Dilute up to 2 2 mL 2 mL per 3 (Narcan) 1 mg IV for 400 mcg per mL minutes or 0.67
opioid overdose mL mL rounded to Rate: Each 0.4 mg or 0.7 ml 1st and
fraction thereof over 153 mL syringe 2nd minute and
seconds 0.6 mL 3rd
d. Furosemide (Lasix) 30 Furosemide 10 May be given mg IV for edema. Give mg per mL undiluted
minute
3 mL 3 mL over 2
minutes = 1.5
over 2 minutes 3 mL syringe mL per minute
e. Phenobarbital sodium Phenobarbital Dilute to 10 10 mL 10 mL over 2 120 mg IV for status sodium 120 mgmL with SW minutes = 5 mL epilepticus. May repeatper 3 mL per minute times 3. Give 60 mg 10 mL syringe per minute
22. Directions: Calculate the IV medication and infusion rates. Use a calculator for safe dose range calculations, multiplication, and long division as desired. Verify results using DE-style equations where requested. If the order is unsafe, do not proceed with the math. Label answers.
RX: Lanoxin 0.25 mL direct IV Available: Lanoxin (digoxin) 0.5 mg per 2 mL. Dilute to 4 mL SW. Give over 5 minutes.
a. How many mL will be given?
b. How many calibrations will the mL occupy on the syringe?
c. Total minutes to administer:
d. Flow rate in seconds per calibration?
ANS:
a. 4 mL SW
b. 20 calibrations
c. 5 minutes
d.
23. How many grams of dextrose are contained in 1 L of a D5W solution?
ANS:
5 g dextrose per 100 mL 50 g per 1000 mL
24. How many approximate calories of dextrose are contained in 1 L of a D5W solution?
ANS:
50 g dextrose 4 cal per g = approximately 200 calories
25. What is the purpose of a TPN solution?
ANS:
The purpose of a TPN solution is to provide high-calorie IV nutrition to patients unable to ingest fluids and nutrients through the alimentary tract.
26. What are the typical contents of a TPN solution?
ANS:
The typical contents of a TPN solution are amino acids, electrolytes, glucose, vitamins and minerals. Lipid emulsions may be added to the order.
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