drug calculations progress check

bgxyrnf, MSN, RN · Oct 27, 2016

The maximum concentration of clarithromycin is 2ml/ml.
We have 500mg in a 10ml solution.
What volume of diluent will you need to add to make the solution safe
volume = 500mg/2ml= 250mg is that correct.
And do I have to divide the 250ml with 10 ml diluent

Let's start with some basic terminology and units of measure.

VOLUME

Volume is the 3-dimensional space occupied by something... in the context of medications, that something is a liquid solution of some sort... water, normal saline, lactated Ringer's solution, liquid morphine, a reconstituted powdered medication such as ceftriaxone, Vancomycin, or azithromycin.

In SI (metric) units, volume is measured in liters or some multiple thereof... and in the context of medications, it's generally milliliters which is one thousandth of a liter or (1/1000) liters or 0.001 liters.

A milliliter is the volume of a cube that measures 1 centimeter in each direction (that is, 1 cubic centimeter or 1 cc).

MASS

Mass is essentially how much something weighs. That's not precisely correct but is suitable for this discussion.

(If you care, the difference between mass and weight is that mass is an inherent property of matter while weight is the result of an acceleration acting on mass. The mass of the Apollo 11 lunar module was the same on Earth and on the moon. However, because the acceleration of gravity on the moon is 1/6 that on Earth, it weighed 1/6 as much and hence could be launched from the surface of the moon with much smaller thrusters than would have been necessary to launch it from Earth.)

Mass is measured in grams... and for most medications, in milligrams. A milligram is (1/1000) of a gram. That is, it takes 1000 mg to equal 1 g.

Parenthetically, 1 mL of water has a mass of 1 gram.

CONCENTRATION

Concentration refers to how much of something is dissolved in something else. The thing being dissolved is known as the solute; the thing in which it is dissolved is known as the solvent; and the combination of the solute and the solvent together is known as a solution.

In chemistry, concentration is generally described in terms of how many particles of solute are dissolved in a given volume of solvent (remember the infamous mole?). Here, though, we don't really care about how many, we care about how much they weigh (since that's what we can measure and what the docs are ordering).

Concentration is described in mass per unit volume. That is, the weight of the solute divided by the volume of the solution. In terms of units, it will be a unit of mass (g or mg) over a unit of volume (L or mL).

Note that the concentration is the mass of solute divided by the volume of the solution, not the volume of the solvent. Fortunately, for our purposes, we can assume that the volume of the solvent and the volume of the solution are the same. They're really not but for the small amounts of solute that we work with, they are sufficient close to just call them the same.

To get a sense of concentration, pour two cups of the same coffee. Into one put 1 packet of sweetener and into the other put 5 packets of sweetener. As sipping each will reveal, the latter solution is much more concentrated than the former. The concentration of a sip (that is, a tiny volume) is the same as the concentration of the whole cup... or the concentration of an espresso cup filled from the original cup. Assuming your coffee cup is 300 mL, the concentration would be (5 packs) divided by (300 mL) or (5 packs)/(300 mL) or 0.017 packs/mL

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Now to your problem:

You are given a concentration of medication... that is, a mass of medication in a volume of solution.

How much medication? 500 mg (strictly speaking, the mass is not "how much" but rather the weight of "how much" but it doesn't matter in the context of these problems)

What's the volume of the solution? 10 mL

That is, the concentration is (500 mg) divided by (10 mL)... (500 mg)/(10 mL) = 50 mg/mL

Each milliliter of the solution contains 50 mg of medication.

However, your problem statement says that the maximum safe concentration is 2 mg/mL so your solution is much too concentrated and needs to be diluted.

So, into what volume of solvent should the 500 mg of med be dissolved to obtain the safe concentration (2 mg/mL)?

Mathematically speaking: (500 mg) divided by (what volume) equals (2 mg/mL)

That is, (500 mg)/x = (2 mg/mL)... or... (500 mg) = (2 mg/mL)(x)... or... (500 mg)/(2 mg/mL) = (x)

Since this solves for the total volume, you simply need to subtract your starting volume in order to ascertain the volume of diluent to add.

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I promise you, if you really want to understand what you're doing, really learn what the terminology means and be meticulous with your units of measure. (This coming from someone who has literally never made a mistake on a 'med math' problem in school nor in practice at the bedside.)