Final answer:
To calculate the infusion pump rate for a 2000 mg lidocaine solution at 4 mg per minute, convert the rate to mg per hour, then use a proportion to find the corresponding volume in ml. The nurse should set the pump to deliver 120 ml/hour.
Step-by-step explanation:
To calculate the infusion pump rate in ml/hour for a prescription of a continuous infusion of dextrose 5% in water (D5W) 1000 ml with lidocaine (Xylocaine) 2 grams at a rate of 4 mg per minute, we must first determine how many milligrams of lidocaine are in the entire 1000 ml solution. As there are 2 grams of lidocaine in the solution and 1 gram is equivalent to 1000 mg, there is a total of 2000 mg of lidocaine in the 1000 ml of D5W.
Next, we establish that the prescribed rate is 4 mg per minute. To find out how many milligrams are administered in one hour, we multiply 4 mg by 60 minutes (the number of minutes in an hour): 4 mg/min * 60 min/hour = 240 mg/hour.
Then, we calculate the number of milliliters of the D5W solution that contain 240 mg of lidocaine. Since the entire 1000 ml solution contains 2000 mg, and we need 240 mg, we set up a proportion: (2000 mg / 1000 ml) = (240 mg / x ml). Solving for x gives us x = (240 mg * 1000 ml) / 2000 mg, which simplifies to x = 120 ml/hour.
Therefore, the nurse should program the infusion pump to deliver 120 ml/hour.