Question

an iv infusion of terbutaline sulfate 5 mg in 500 ml of d₅w, infusing at a rate of 30 mcg/min, is prescribed for a client in premature labor. how many ml/hr should the nurse set the infusion pump?

a 60.

b 180.

c 120.

d 90.

Explanation:

Step1: Convert mg to mcg

We know that \( 1\space mg = 1000\space mcg \), so \( 5\space mg = 5\times1000 = 5000\space mcg \).

Step2: Find the rate in mcg/hr

The infusion rate is \( 30\space mcg/min \). To find the rate per hour, we multiply by 60 (since there are 60 minutes in an hour): \( 30\space mcg/min\times60\space min/hr = 1800\space mcg/hr \).

Step3: Set up a proportion to find mL/hr

Let \( x \) be the volume in mL/hr. We know that \( 5000\space mcg \) is in \( 500\space mL \), and \( 1800\space mcg \) is in \( x\space mL \). So we set up the proportion:

$$ \frac{5000\space mcg}{500\space mL}=\frac{1800\space mcg}{x\space mL} $$

Cross - multiplying gives \( 5000x = 500\times1800 \).

Step4: Solve for x

First, calculate \( 500\times1800 = 900000 \). Then, \( x=\frac{900000}{5000}=180 \)? Wait, no, wait. Wait, maybe I made a mistake. Wait, let's re - do step 3. Wait, the formula for infusion rate (mL/hr) is \( \frac{\text{Rate (mcg/min)}\times60\space min/hr\times\text{Volume (mL)}}{\text{Drug amount (mcg)}} \)

So, \( \text{Rate (mL/hr)}=\frac{30\space mcg/min\times60\space min/hr\times500\space mL}{5000\space mcg} \)

First, calculate the numerator: \( 30\times60\times500 = 30\times30000 = 900000 \)

Then divide by 5000: \( \frac{900000}{5000}=180 \)? But wait, the option D is 90. Wait, no, maybe I messed up the drug amount. Wait, the drug is 5 mg in 500 mL. 5 mg is 5000 mcg. The infusion rate is 30 mcg/min. Let's use the formula:

\( \text{mL/hr}=\frac{\text{mcg/min}\times60\space min/hr\times\text{mL}}{\text{mcg in solution}} \)

So, \( \text{mL/hr}=\frac{30\times60\times500}{5000} \)

\( 30\times60 = 1800 \); \( 1800\times500 = 900000 \); \( 900000\div5000 = 180 \). But the option B is 180. Wait, but the marked option is D. Wait, maybe I made a mistake in the problem interpretation. Wait, let's check again.

Wait, the problem is: 5 mg in 500 mL, infusing at 30 mcg/min. Let's convert 5 mg to mcg: 5 mg = 5000 mcg.

The concentration is \( \frac{5000\space mcg}{500\space mL}=10\space mcg/mL \)

The rate in mcg/min is 30 mcg/min. To find mL/min, we divide by the concentration: \( \frac{30\space mcg/min}{10\space mcg/mL}=3\space mL/min \)

Then, to find mL/hr, we multiply by 60: \( 3\space mL/min\times60\space min/hr = 180\space mL/hr \)

Wait, so the correct answer should be B. 180.

Answer:

B. 180