Hi, this is Cathy with Level Up RN. In this video, I will be going over a dosage calculation problem that involves both reconstitution and dilution. I'll be working through this problem on my whiteboard using three different methods, including dimensional analysis, ratio and proportion, and the formula method. You can find all the information that I'll be covering in this video in our Level Up RN dosage calculation workbook. If you are in nursing school, then you know how important it is to master dosage calculations, and our workbook will help you do just that. In a nutshell, our workbook contains all different types of dosage calculation problems that you are likely to encounter in nursing school, and we demonstrate how to solve each problem using multiple methods so you can pick the way that makes the most sense to you.
All right. In this problem, we are going to reconstitute and dilute a medication. So it's kind of like the grand finale of this topic. So with this order, we have azithromycin 500 milligrams IV daily ordered. Instructions state to reconstitute with 4.8 milliliters of sterile water for a concentration of 100 milligrams per milliliter. Then we need to dilute the dose in normal saline to achieve a concentration of 2 milligrams per ml. And then we need to make sure we are rounding our answers for C, D, and E to the nearest whole number. So a lot of information there. We're not going to panic. We're just going to see what's being asked, and only consider the information we need to answer the question at hand.
So question A is, how much sterile water will be added to the vial for reconstitution? So no math is required for this question, right? Because it says here, "Reconstitute with 4.8 milliliters of sterile water." So the answer to part A is just 4.8 milliliters. That's how much we are adding to the vial to reconstitute it. And then what is the concentration of the vial after reconstitution? Again, we were told that in the question. So it says, "Reconstitute with 4.8 milliliters of sterile water for a concentration of 100 milligrams per ml." So after reconstitution, our concentration is going to be 100 milligrams per ml. Again, I just pulled that out of there. No math required.
C. How many milliliters will be withdrawn from the vial to dilute with normal saline? So we do need to use math for this part. And we can calculate this using dimensional analysis, ratio and proportion, or the formula method. So let's first do-- so this is part C. Let's first solve this with dimensional analysis. So I'm going to start by writing down what is ordered, which is 500 milligrams. I'm going to make sure my units of measure match up between what's ordered and what's available, the available concentration, and they do. They're both in milligrams. So I'm just going to take the ordered dose times the available concentration, which is 100-- oops. I'm going to make sure we put our milliliters on top here and our milligrams on bottom because we want our milligrams to cross off, and we want to be left with milliliters. So calculate this out, and it is 5 milliliters. That's how much we need to pull out of the vial.
We can also use ratio and proportion to do this. So our vial after reconstitution has this concentration. And we want 500 milligrams, and we don't know how many milliliters that will take. So we're just comparing the known ratio to the unknown value. All right. We're going to cross-multiply here. So 100 X equals 1 times 500. X equals 500 divided by 100. So X equals 5 ml. And that's how we would solve it with ratio and proportion.
We can also do the formula method. So if you recall, the formula method has desired over have times the vehicle. So our desired dose is our ordered dose, so that's 500 milligrams. And what we have is 100 milligrams in 1 ml of solution. So we do this math. Again, we end up with 5 mls. So that's what we are pulling out of the vial. And it says round to the nearest whole number. We're already there. So we're good to go on round B.
Now let's look at Part D. Part D is asking us, what is the total volume needed to achieve a 2 milligram per milliliter concentration? So we can work this part of the problem out using dimensional analysis and ratio and proportion, but not the formula method. So this is part D, with dimensional analysis. If I take my ordered dose, which is 500 milligrams, and multiply this times the desired concentration, so 1 milliliter over 2 milligrams, making sure I put my milliliters on top and milligrams on bottom, such that my milligrams will cross off, then I end up with 250 milliliters. And that is the total volume I need to make sure my dose is in, in order to achieve that concentration.
I can also do this part of the problem with ratio and proportion. So if I take my desired concentration on one side of the equation and put my ordered dose on the other with an X for the unknown milliliters, then I can cross multiply. So 2 X equals 500. X equals 500 divided by 2. X will equal 250 ml. So same answer as we have here. Just a different way to work it out. So that's already rounded to the nearest whole number, so we're good to go for part D.
Then part E asks us, how much diluent should be added to achieve that concentration? So we need a final volume of 250 mls, but when we pulled the medication out of the vial, it was in 5 mls. So we actually only need to add 245 mls to this 5 mls to get that final concentration. So we need to add 245 mls to the 5 mls to get that 250 ml volume that we are looking for. And that is how you would solve this type of problem.
