calculations question

[kov82]

How many milliliters of sterile water for injection should be added to a vial containing 5 µg/mL of a drug to prepare a solution containing 1.5 µg/mL of the drug?

could you please show how you would come up with the answer? thanks!

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[trap]

well you're missing information - the amount of the original drug solution you started with (or the total volume you want to end up with would also work too)

Easiest way is alligation.

5 ug/dL (original solution) --------------------------------------------- (= 1.5 - 0)
-------------------------------------1.5 ug/dL (desired concentration)
0 ug/dL (sterile water) ------------------------------------------------- ( = 5 - 1.5)

You need 1.5 parts of the original solution per every 3.5 parts of sterile water.
So 3 parts original solution to 7 parts sterile water. If you had 3 mL to start, you'd add 7 mL to get 10 mL total of the diluted amount

 

[trap]

The longer way is alegbreic, but can be done that way too

Assume the starting volume is 3 mL (we should end up with the same answer in the end that way!)

3 mL of 5 ug/dL solution + x mL of sterile water = 3+x mL of 1.5 ug/dL solution

On the left side, the drug amount is 3 mL (5 ug/dL) (1 dL/100 mL) = 15/100 = 0.15

On the right side, the drug amount is (1.5 ug/dL) (3+x mL) (1 dL/100 mL) = 0.015 (3+x)

0.15 = 0.015 (3+x)
3+x = 10
x=7

 

[kov82]

The book answer was 2.33, a pharm tech helped solve it

[5/(x+1) ] = 1.5

x= 2.33

thanks though

 

[RUSK17]

All 3 answers are correct and different ways to approaching the same problem.

The difference is the first two replies made up the volume of 3mL to help you visualize the problem. The problem only calls for 1mL, so if you divide their numbers appropriately, you still get 2.33 mL.