A dosage of 500 mg of ibuprofen is to be delivered to a patient in an IV drip over 180 minutes. It's supplied in a solution that contains 1.6 grams of the drug in [tex]$10 cm^3$[/tex] of the solution. The pump used to deliver the drug uses units of [tex]$cc^{\prime}s$[/tex] (cubic centimeters) per hour. At what rate should the pump be set? Round your answer to the nearest cubic centimeter.
The pump should be set at a rate of $\square$ cc per hour.
Answer (1)
Convert the dosage from mg to grams: 500 m g = 0.5 g .
Calculate the volume of the solution needed: V = 1.6 5 = 3.125 c m 3 .
Convert the delivery time from minutes to hours: 180 min u t es = 3 h o u rs .
Calculate the pump rate and round to the nearest cubic centimeter: P u m p r a t e = 3 3.125 ≈ 1 c m 3 / h o u r . The final answer is 1 .
Explanation
Problem Analysis We are given that a 500 mg dosage of ibuprofen needs to be delivered over 180 minutes. The ibuprofen solution has a concentration of 1.6 grams in 10 c m 3 . We need to find the rate at which the pump should be set in c m 3 /hour.
Convert mg to g First, we need to convert the dosage from milligrams (mg) to grams (g). Since 1 gram = 1000 milligrams, we have: 500 m g = 1000 500 g = 0.5 g
Calculate Volume of Solution Next, we need to determine the volume of the solution required to deliver 0.5 g of ibuprofen. We know that the solution contains 1.6 g of ibuprofen in 10 c m 3 . We can set up a proportion to find the volume V in c m 3 :
10 c m 3 1.6 g = V c m 3 0.5 g Cross-multiplying, we get: 1.6 × V = 0.5 × 10 1.6 V = 5 V = 1.6 5 = 3.125 c m 3
Convert Minutes to Hours Now, we need to convert the delivery time from minutes to hours. Since 1 hour = 60 minutes, we have: 180 min u t es = 60 180 h o u rs = 3 h o u rs
Calculate Pump Rate Finally, we need to calculate the pump rate in c m 3 /hour. The pump rate is the volume of the solution delivered divided by the time it takes to deliver it: P u m p r a t e = 3 h o u rs 3.125 c m 3 = 1.041666... c m 3 / h o u r
Round to Nearest Integer We are asked to round the answer to the nearest cubic centimeter. Therefore, the pump rate should be approximately 1 c m 3 /hour.
Final Answer The pump should be set at a rate of 1 cc per hour.
Examples
IV drips are used to administer medications, fluids, and nutrients directly into a patient's bloodstream over a specific period. Calculating the correct drip rate is crucial for ensuring the patient receives the prescribed dosage safely and effectively. For example, in chemotherapy, precise drug delivery is essential to minimize side effects and maximize the therapeutic effect. Similarly, in pain management, a controlled infusion rate can provide consistent relief while avoiding over-sedation. Understanding these calculations helps healthcare professionals deliver optimal care.
