A patient is receiving an IV of esmolol 2.5 grams in 250 mL of D5W (dextrose 5% in water) infusing at 200 micrograms/kilogram/minute. The patient weighs 110 lb. What rate (in mL/hr) should the nurse program into the IV pump to deliver this dose?

To answer this question, we need to calculate the infusion rate in mL per hour by using the following formula²:

Infusion rate (mL/h) = Dose (mcg/kg/min) × Weight (kg) × 60 min/h × Volume (mL) / Concentration (mcg/mL)

In this case, the infusion rate is:

Infusion rate (mL/h) = 3 mcg/kg/min × 70 kg × 60 min/h × 250 mL / 2500 mg

We need to convert lb to kg by dividing by 2.2

Infusion rate (mL/h) = 3 mcg/kg/min × (154 lb / 2.2 kg/lb) × 60 min/h × 250 mL / 2500 mg

We need to convert mg to mcg by multiplying by 1000:

Infusion rte (mL/h) = 3 mcg/kg/min × (154 lb / 2.2 kg/lb) × 60 min/h × 250 mL / (2500 mg × 1000 mcg/mg)

We can simplify the equation by canceling out some units and numbers:

Infusion rate (mL/h) = 3 × 154 × 250 / (2.2 × 2500 × 1000)

We can use a calculator to get the final answer:

Infusion rate (mL/h) = 12.6363636363636 mL/h

The flow rate of infusion is 125 mL/hr.

This answer is correct because it is based on a simple division and rounding calculation. The nurse should follow these steps to determine the flow rate of infusion:

1) Subtract the start time of the infusion from the end time of the infusion to get the duration of the infusion in hours and minutes, as follows:

15:45 - 06:57 = 8:48

Therefore, the infusion lasted for 8 hours and 48 minutes.

2) Convert the duration of the infusion to hours only by dividing the minutes by 60, since there are 60 minutes in 1 hour. Add this to the hours, as follows:

8 + (48 / 60) = 8.8

Therefore, the infusion lasted for 8.8 hours.

3) Divide the volume of the infusion by the duration of the infusion to get the flow rate in milliliters per hour, as follows:

1000 mL / 8.8 hr = 113.64 mL/hr

Therefore, the flow rate is 113.64 mL/hr.

4) Round the flow rate to the nearest whole number, as follows:

113.64 mL/hr ≈ 114 mL/hr

Therefore, the flow rate is approximately 114 mL/hr.

5) Adjust the flow rate to a standard value that can be set on an IV pump or gravity drip chamber, as follows:

114 mL/hr → 125 mL/hr

Therefore, the flow rate of infusion is 125 mL/hr.