Final answer:
The nurse needs to administer approximately 6.944 mL of the atropine solution to provide the prescribed 3mg dose of atropine. This is calculated by converting grains to mg and then dividing the prescribed dose by the concentration in mg/mL.
Step-by-step explanation:
The student has asked about the calculation of the volume of atropine to be administered intravenously, based on a prescribed dose and available concentration. The prescription requires a dose of 3mg of atropine. The on-hand atropine solution has a concentration of grain (1)/(150) in milliliters (mL). In this scenario, one needs to convert the grains into milligrams (mg) to proceed with the calculation.
Firstly, it is important to note that 1 grain is approximately equal to 64.79891 milligrams. Therefore, atropine gr (1)/(150) can be converted to mg/ml by multiplying 1/150 by the mg equivalent of one grain:
gr (1)/(150) * 64.79891 mg/gr ≈ 0.432 mg/mL
Next, to find the amount of solution needed to deliver a 3mg dose, use the formula:
Dose (mg) = Volume (mL) × Concentration (mg/mL)
Isolate the volume (mL):
Volume (mL) = Dose (mg) / Concentration (mg/mL)
Substitute the values:
Volume (mL) = 3mg / 0.432 mg/mL ≈ 6.944 mL
The nurse needs to administer approximately 6.944 mL of the atropine solution to provide the prescribed 3mg dose of atropine.