confusing math problem

[quote=smurfy;2437889

A patient's IV is hanging with 250mg of XYZ in 500ml of NS. The rate is 120ml/hr. What dose of XYZ is the patient recieving in mcg/min?

Here's how I would think about a problem like this:

How much medication is going into the patient?

• The medication is dissolved in normal saline. If I know how fast the normal saline is flowing and I know how much medication is in a given volume of normal saline then I know the answer to my question.
  
• How fast is normal saline flowing?
  • Every hour, 120 ml of solution has flowed
    
  • Every 1/2 hour, 60 ml of solution has flowed (120/2)
    
  • Every 1/4 hour, 30 ml of solution has flowed (120/4)
    
  • Every 1/10 hour, 12 ml has flowed (120/10)
    
  • Every 1/60 hour, 2 ml has flowed (120/60)
    • How many minutes in an hour? 60. What's 1/60 of an hour? 1 minute.
      
    • So the flow rate is 120 ml/hr or 2 ml/min

  [*]How much medicine in the normal saline?

  • The problem statement tells us: 250 mg of medicine dissolved in 500 ml of normal saline.
    • So, if there's 250 mg of medicine in 500 ml, how much medicine is in 50 ml? 25 mg
      
    • How much in 10 ml? 5 mg
      
    • How much in 5 ml? 2.5 mg
      
    • How much in 1 ml? 0.5 mg

    [*]So, each ml of normal saline solution contains 0.5 mg of medication.

  [*]Since I know how much medication is in each milliliter of solution (0.5 mg) and I know how many milliliters of solution flow every minute (2 ml), I know how much medication is flowing every minute:

  • 2 ml NS/min x 0.5 mg XYZ/ml NS = 1 mg XYZ/min
    • This equation is translated into English as: "Every minute, 2 ml of NS flows. Each ml of that NS solution contains 0.5 mg of XYZ. Therefore, there is 1 mg of XYZ flowing into the patient every minute"

  [*]Since the question asked you the amount in micrograms, you just need to convert the flow from milligrams per minute to micrograms per minute.

  • There are 1000 milligrams in each microgram, or each milligram is 0.001 micrograms.
    
  • 1 mg/min x 1000 mcg/mg = 1000 mcg/min

I'm providing this to you just to show you how to think about these problems. You don't really need to memorize formulas, you just need to understand the very basic elements of solution chemistry.

There, I said that nasty "C" word. Now everything I said is going to be disregarded