Yet another math question that is blowing my mind...

suzw · May 26, 2014

OK, I'm gonna take a stab at this. Keep in mind, I am first year and have never seen a problem like this, AND I hate dimensional analysis. But I'm usually pretty good at figuring this stuff out, so...

That packet of dry powder takes up 1.8 mL of space. So you add 18.2 mL to it, and there you have it, 20 mL, or 1 million units/ mL. It's the only way the numbers will add up. If you reconstitute it to a total of 10 mL (8.2 + 1.8= 10, right?) then you will obviously have 2 million units in a mL, right? And so on, and so on. So you want 11 million units. You could make it easy and reconstitute it with 18.2 mL for a total of 20 mL, and then draw up 11mL (yay no math required!) Well that's a no yay. How big do you want that shot to be, anyway? Maybe if you really didn't like the patient.... KIDDING. You want that shot to be some amount that you can do in 1 injection, and you can't do that with 11 mL. So your answer is 2.2 mL (out of a 4 mL solution) and it better not be going into the deltoid! (2.2 x 5 million = 11 million, right?)

On the other hand, if you needed only 1 million units, it would be best to reconstitute with 18.2 mL of diluent, and draw up 1 mL for best accuracy.

Does that make any sense? Not sure if I explained it right. Remember, I hate DA. Someone else could probably explain how to set up the problem.

la_chica_suerte85, BSN, RN · May 26, 2014

Like the above poster said, it's IM so you want ideally no more than 2 or so mL for this type of injection. So, you want the least amount possible to start with. Looking at the 2.2 ml = 5 million unit/1 ml concentration gives you 5 million + 5 million + (5 million X 2.2 = 1 million) = 11 million units dose. When I look at these kinds of problems, I just see what can really go with what to give me the ordered dose. 2.2 X 5 is 11 and this is seems reasonable for the situation. None of the other answers give you 11 no matter what you do. Ignore the 20 because it doesn't really have anything to do with the problem the way it is set up.

Esme12, ASN, BSN, RN · May 26, 2014

Basically the above posters are correct..you want to give 11,000,000 units in the LEAST amount of fluid because you are giving an IM injection so your choice is the 5,000,000u/ml option.

It takes 2.2 ml of liquid to mix with the powder that contains the 5,000,000u of antibiotic. Once mixed that Final concentration is 5,000,000u in 1 ml.

No calculation necessary here really they gave you the information.

Add Sterile H2O-----------Concentration
18.2-----------------------1,000,000 Units/mL
8.2------------------------2,000,000 Units/mL
3.2------------------------4,000,000 Units/mL
2.2------------------------5,000,000 Units/mL

When you add the 2.2ml to the 1.8gm pf powder you will have a final 4mls of fluid in the vial with a concentration of 5,000,000u/ml.

Now your question....

Doctor ordered 11 million units IM.

So....you need to give how many mls IM to administer 11,000,000u to your patient.

[TABLE=class: example]

[TR]

[TD][TABLE=class: fraction]

[TR]

[TD=class: numerator]Ordered

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[TR]

[TD=class: denominator] Have [/TD]

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[/TABLE]

[/TD]

[TD] x Volume Per Have [/TD]

[TD] = Y (Liquid Required) [/TD]

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DosageHelp.com - Helping Nursing Students Learn Dosage Calculations - Mass/Liquid For Liquid Questions

suzw · May 26, 2014

la chica, you are basically correct, except the answers are just the dilution tables- the column on the left is the amount of diluent you add to make the concentration pre mL on the right, not the number of mLs to give to make 11 million. I think it is just coincidence that 2.2 x 5= 11 (though I can see people getting this question right without having any idea why).

Let's say they asked you to give 10 million units instead. Yhe answer would still be a 5 million/ mL concentration, but the amount given would be 2 mL. Although, I could argue for the 4 million/mL concentration, but then you would need to give 2.5 mL (if you were giving 10 million units). I'm not a math peron so it's hard for me to tell you how to set it up, but I can tell you how to think about it!