Question #9a02f

The idea here is that you need to make sure that the four vials of stock solution have enough morphine sulfate to ensure the amount needed for your target solution.

Now, your solution is #"3.0% m/v"#, which basically means that it contains #"3.0 g"# of morphine sulfate for every #"100 mL"# of solution.

This is equivalent to saying that #"100 mL"# of the target solution must contain

#3.0 color(red)(cancel(color(black)("g solute"))) * (10^3"mg")/(1color(red)(cancel(color(black)("g")))) = "3000 mg solute"#

The total amount of morphine sulfate present in the target solution will be

#250 color(red)(cancel(color(black)("mL solution"))) * "3000 mg solute"/(100color(red)(cancel(color(black)("mL solution")))) = "7500 mg solute"#

Now, each vial of stock solution will contain a total amount of

#50 color(red)(cancel(color(black)("mL solution"))) * "50 mg solute"/(1color(red)(cancel(color(black)("mL solution")))) = "2500 mg solute"#

This means that in order to get the total amount of morphine sulfate needed for your target solution, you must use

#7500 color(red)(cancel(color(black)("mg solute"))) * "1 vial stock"/(2500color(red)(cancel(color(black)("mg solute")))) = "3 vials stock"#

Therefore, you can say that you do have enough stock solution to prepare your target solution.

More specifically, you would mix #3# vials of stock solution, the equivalent of #3 xx "50 mL"#, and add enough water to make the total volume of the solution equal to #"250 mL"#.