Pharmacy math problem?

Question

The problem states: "You are to reconstitute a powder that is 5g. The label states that the powder volume is 8.6ml and the resultant solution will be 50mg/ml. What is the dilutent volume?" Can anyone please help with this one? I can't seem to brain around it and it has me struck with a dumb. Thanks to all who can help.

Answer 1

50 mg = 0.05 g

5 g / ( 0.05 g / ml )= 100 ml = Total volume of the solution

100 ml - 8.6 ml = 91.4 ml = dilutent volume

Answer 2

Here's one way to solve this problem.  Set up an equivalence ratio:

1 mg = 1/1000 g ----> 50 mg = 50/1000 g = 0.50 g.  Now you can plug 0.50 g into the ratio instead of 50 mg, since the powder's original mass was given in grams:

5 g /(8.6 ml + x ml) = 0.05 g /1 ml

Cross-multiply and then solve for x:

5 g∙ml = 0.43 g∙ml + 0.05 g∙x ml

4.57 g∙ml = 0.05 g∙x ml

4.57 g∙ml/0.05 g = x ml

91.4 ml = x ml

So the volume of dilutant that should be added is 91.4 ml.