Optimizing Morphine Solution for Standard PCA Syringes

How many full 50 mL syringes can the pharmacist make with the given morphine solution?

The pharmacist mixed a morphine solution of 50 mg in 250 mL and wants to create standard PCA syringes with a concentration of 1mg/mL. Using the supplied morphine solution, how many full 50 mL syringes can the pharmacist make of the desired concentration?

Answer:

Using the supplied morphine solution, the pharmacist will be able to create a maximum of 16 complete 50 mL syringes of the necessary concentration (1 mg/mL).

To calculate the number of full 50 mL syringes that can be made with the desired concentration of 1 mg/mL, we need to determine the amount of morphine solution required for each syringe and then divide the total available solution by that amount.

The desired concentration is 1 mg/mL, and the pharmacist has a stock solution of 15 mg/mL. To achieve the desired concentration, we can dilute the stock solution with an appropriate volume of diluent.

First, we need to calculate the amount of the stock solution required for each syringe. Since each syringe has a volume of 50 mL and a concentration of 1 mg/mL, the amount of morphine required is 50 mg.

Next, we need to determine the dilution factor. To achieve a concentration of 1 mg/mL, the stock solution needs to be diluted 15-fold. This means that for every 15 mL of the stock solution, we need to add 1 mL of diluent.

Now, we can calculate the number of syringes by dividing the total available solution (250 mL) by the amount of solution required for each syringe (15 mL).

Number of syringes = Total available solution / Solution required per syringe

Number of syringes = 250 mL / 15 mL = 16.67

Since we cannot have a fraction of a syringe, the pharmacist will be able to make a maximum of 16 full 50 mL syringes of the desired concentration (1 mg/mL) using the available morphine solution.