Fuzzy math problem

[BenJammin]

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I know you guys hate it when someone asks you how to do math problems but this question is just driving me crazy.

You are given an unlimited supply of potassium chloride injection that is concentrated in 2 mEq per milliliter. AA, a patient in your hospital, has been given a solution that is concentrated in 3.5 mEq of potassium chloride per 100 milliliters. Dr Pat wants you to increase the concentration in the bag to 6 mEq per 100 milliliters and right now there is 850 milliliters of fluid remaining in the bag. How many milliliters of potassium chloride should be added to the bag in order to provide the concentration requested by the doctor?

This can't be just a simple algebra problem because the total amount in the bag will increase no matter what you add but I don't know how to compensate for the volume of the potassium chloride. Anybody have an idea how to do this?

 

[PharmDstudent]

I know you guys hate it when someone asks you how to do math problems but this question is just driving me crazy.



This can't be just a simple algebra problem because the total amount in the bag will increase no matter what you add but I don't know how to compensate for the volume of the potassium chloride. Anybody have an idea how to do this?

If the bag is already hanging on the patient, then you get the patient a new bag. You would never add KCl to a bag that's hanging on a patient... per our host hospital's guidelines. 😉

 

[iFarm]

If the bag is already hanging on the patient, then you get the patient a new bag. You would never add KCl to a bag that's hanging on a patient... per our host hospital's guidelines. 😉

Okay, but what if you find yourself in some tiny village in Africa, and you can't waste ANY electrolytes because the shipment from the UN/WHO/etc doesn't come in for another week and you've got 6 other patients that need KCl as well.

What?... it could happen...

 

[PharmDstudent]

Okay, but what if you find yourself in some tiny village in Africa, and you can't waste ANY electrolytes because the shipment from the UN/WHO/etc doesn't come in for another week and you've got 6 other patients that need KCl as well.

What?... it could happen...

Sure, but if you add it while it's hanging, then you may add (dump) all of the KCl next to the port. 😱

 

[iFarm]

Sure, but if you add it while it's hanging, then you may add (dump) all of the KCl next to the port. 😱

Oh, i see. I thought you were referring to the additional risk of error due to the extra calculations.

OP... make sure to invert that bag a few times...

 

[amox]

2mEq/mL solution available

3.5mEq/100mL previously prepared (total 850mL)

6mEq/100mL Concentration needed

6mEq-3.5mEq = 2.5mEq needed per 100mL

850mL/100mL = 8.5 Factor

2.5mEq * 8.5 = 21.25 mEq needs to be added to the bag(850mL) to make 6mEq/100ml

Since concentration is 2mEq/mL ---> 21.25/2 = 10.625 mL needs to be added to the 850mL

Now yes the volume will change which will change the concentration.
However, 6mEq*8.5 = 51mEq in the bag.

51mEq/850mL (Not adding the volume from KCL) = 0.06mEq/mL
51mEq/860.625mL (Adding the volume from KCL) = 0.0593 mEq/mL

Generally this is insignificant and not calculated in. From what I've seen in practice if the solution doesn't change the concentration by 5% its okay. To check this ((0.06-0.593)/0.06)*100 = 1.16667%

Solved with higher math than algebra below. (Won't show work)

For exact calculation you need to add 1/3 extra mL of the solution. to get 6mEq/100mL

1/3 mL would be 0.666667 mEq add this mEq to the 51 total in the bag.

51.666667 mEq in the 850 mL bag. Then this adds 0.33333 mL volume, therefore you take the 860.625 + 0.33333 to get = 861.29166667 When you divide this out

51.666667/861.29166667 you get 6mEq/100mL

Now the math for that gets tricky, and I love calculus 🙂

 

[Cutubaman]

Algebra is all you need. I'm a 3rd year pharmacy student at UNC, but my undergraduate major was math. It's kind of my thing. Here's how I got the answer. It's all about proportions.

3.5mEq/100mL = x/850mL ------ x=29.75mEq ------ so 29.75mEq/850mL

Now we know that for every mL you add, you're adding 2mEq, therefore:
29.75mEq + 2x = 6mEq/100mL
850mL + x

where x = the number of mL needed. Cross multiply and you get:

2975 +200x = 5100 + 6x ------ x = 10.95mL

To check:
29.75mEq + (2*10.95)mEq
850mL + 10.95mL

which divides out to be 0.05999mEq/mL, which essentially rounds to the desired concentration of 0.06mEq/mL or 6mEq/100mL as stated in the problem.

The name of the game is proportions. You add 2 mEq KCl to the numerator as you add 1 mL of solution to the denominator. Adding both at the same time allows you to account for the fluid volume that you're adding.

 

[naseuy]

If the volume that you're adding 10% or greater than the volume of the IV bag, we would withdraw that volume from the bag before injecting the drug.