Question

a client receives a new prescription for heparin 900 units/hour per infusion pump. the pharmacy delivers a 500 ml iv bag labeled 0.9% sodium chloride with heparin 25,000 units. how many milliliters per hour should the nurse program the pump?
a 9
b 18
c 4.5
d 20

Explanation:

Step1: Set up the proportion

We know that 25,000 units are in 500 mL, and we need to find out how many mL (let's call it \( x \)) correspond to 900 units per hour. So we set up the proportion: \(\frac{25000 \text{ units}}{500 \text{ mL}} = \frac{900 \text{ units}}{x \text{ mL}}\)

Step2: Cross - multiply and solve for \( x \)

Cross - multiplying gives us \( 25000x = 900\times500 \). First, calculate \( 900\times500 = 450000 \). Then, solve for \( x \) by dividing both sides of the equation by 25000: \( x=\frac{450000}{25000}=18 \). Wait, no, wait, let's check again. Wait, the formula for IV infusion rate when we have units is: Rate (mL/hour)=\(\frac{\text{Desired units per hour}\times\text{Volume (mL)}}{\text{Available units}}\). So Desired units per hour is 900, Volume is 500 mL, Available units is 25000. So Rate=\(\frac{900\times500}{25000}=\frac{450000}{25000} = 18\)? Wait, no, that can't be right. Wait, no, wait, 25000 units in 500 mL, so per mL, there are \( \frac{25000}{500}=50 \) units per mL. Then, to get 900 units per hour, we need \( \frac{900}{50}=18 \) mL per hour? Wait, but let's recalculate. Wait, 25,000 units in 500 mL. So the concentration is 25000 units / 500 mL = 50 units/mL. The client needs 900 units per hour. So the volume per hour is (900 units/hour) / (50 units/mL) = 18 mL/hour. Wait, but let's check the options. Option B is 18. But wait, maybe I made a mistake. Wait, no, let's do it again. The formula for infusion rate when you have a drug in a solution is:

\( \text{Rate (mL/h)}=\frac{\text{Ordered dose (units/h)}}{\text{Concentration (units/mL)}} \)

Concentration is \( \frac{25000 \text{ units}}{500 \text{ mL}} = 50 \text{ units/mL} \)

Ordered dose is 900 units/h.

So \( \text{Rate}=\frac{900}{50}=18 \text{ mL/h} \)

Answer:

B. 18