A patient is to receive magnesium sulfate 2 grams per hour at 50 mL/hour rate of infusion.
How much magnesium sulfate must be added to 1000 mL normal saline to provide the ordered infusion?
A.
10g
B.
20 g
C.
30 g
D.
40 g
The Correct Answer and Explanation is:
To determine how much magnesium sulfate must be added to 1000 mL of normal saline to provide a continuous infusion of 2 grams per hour at a rate of 50 mL per hour, follow these steps:
- Calculate the Total Amount of Magnesium Sulfate Needed per Hour:The order is for a magnesium sulfate infusion rate of 2 grams per hour. Therefore, the total amount of magnesium sulfate needed per hour is 2 grams.
- Determine the Concentration of Magnesium Sulfate in the Infusion:The infusion rate is 50 mL per hour. To find out how much magnesium sulfate is required in each 50 mL of the solution, we need to calculate the concentration that will deliver 2 grams per hour.Let CCC be the concentration of magnesium sulfate in grams per mL. We use the formula:Total amount per hour=Infusion rate×Concentration\text{Total amount per hour} = \text{Infusion rate} \times \text{Concentration}Total amount per hour=Infusion rate×ConcentrationSubstituting the values:2 grams=50 mL/hour×C2 \text{ grams} = 50 \text{ mL/hour} \times C2 grams=50 mL/hour×CSolving for CCC:C=2 grams50 mL=0.04 grams/mLC = \frac{2 \text{ grams}}{50 \text{ mL}} = 0.04 \text{ grams/mL}C=50 mL2 grams=0.04 grams/mL
- Calculate the Total Amount of Magnesium Sulfate Needed for 1000 mL:To prepare a 1000 mL solution at a concentration of 0.04 grams per mL, we need:Total amount=Concentration×Volume\text{Total amount} = \text{Concentration} \times \text{Volume}Total amount=Concentration×VolumeSubstituting the values:Total amount=0.04 grams/mL×1000 mL=40 grams\text{Total amount} = 0.04 \text{ grams/mL} \times 1000 \text{ mL} = 40 \text{ grams}Total amount=0.04 grams/mL×1000 mL=40 grams
So, 40 grams of magnesium sulfate must be added to 1000 mL of normal saline to achieve the desired infusion rate of 2 grams per hour at 50 mL/hour.
Correct Answer: D. 40 g