## Pharmacy Tech MathDilution Math Examples

Dilution Question from the Facebook page:

You have on hand a 14% (w/v) topical antiseptic solution. You receive an order for 1 L of a 1:4000 solution. How much of what is on hand is needed to fill this order?

Here is one way to solve this problem using Algebra.

Why not just use proportions math?
Using proportions math is too confusing when solving Dilution problems. It is possible, but using an Alligation or an Algebra formula is faster and more simple. If you want to see a video of the problem above using alligation,

Let's do another one:

Question from Heather in California:

A Pharmacy Tech has been given 300mL of a 15% hydrochloric acid solution. The pharmacist asks the technician to dilute the solution to 1000mL with sterile water and to label the final solution. What percent should appear on the label?

The easiest way to solve this is with the formula:
C1 x V1 = C2 x V2
C - Concentration
V - Volume

1) First, plug in your known factors:

### (.15)(300mL) = ( X )(1000mL)

(Concentration 2 is unknown = "X")

↓   ↓   ↓

2) Do the multiplication:

### (.15)(300) = ( X )(1000)

45         =   1000X

↓   ↓   ↓

3) Do the Division to isolate X:

 45 1000x = 1000 1000

↓   ↓  ↓

4) Now you have the concentration of the larger volume.

.045 = X

4.5% = X

This is the easiest way to solve this problem. Thanks for the question Heather.

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