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Dilution math question

by Holly
(Akron, Pa.)

An order for 1.2L of a 10% oral solution is needed. In stock you have only 12% solution. Which of the following mixtures will yield the volume and strength needed to fill this order?


A. 800ml of 12% + 400ml of sterilized water
B. 1000ml of sterilized water + 200ml of 12%
C. 600ml of 12% + 600ml of sterilized water
D. 200ml of sterilized water + 1000ml of 12%

I can't understand what I am doing wrong with this problem. I have done many dilution problems but this one is difficult for me.

Thank You for helping me . I will look at some of the other problems to see if I can help someone else.

Comments for Dilution math question

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Dilution Question
by: Brad Wojcik, Pharm D

Hi Holly, Let's assume this is a w/v problem. It doesn't say, but the answer will be the same and it will be easier to explain. Step 1) Determine how many g of AI you need in the final solution. 10% w/v is the same as 10% g/mL. 1.2 L (1000 ml/L)(10%g/mL) (1/100%) = 120 g. (remember, to add the % sign, multiply by 100%, to remover the % sign divide by 100%) Ok, so we need 120 g of AI. Now we go shopping for our 120 g. We look on the shelf and we have a 12% solution. How many mL of this do we need.
120 g(100 mL/12g) =1000 mL. So we need 1000 mL of the 12% and 200 mL of sterile water. I changed the 12%w/v to 12g/100 mL and flipped it upside down. You can flip any ratio if you need to.

Solution for Understanding Question
by: Anonymous


Patient Need:
1200mL X 0.1 = 120 of active ingredient per 1.2L.

Pharmaceutical On Hand:
12/100% of active ingredient per 100mL.

Physician orders to Dispense:
1000mL of 12/100% of active ingredient qsad 200mL NS.

//Explanation:

solutions; are
dry weight/100mL or
(Active Ingredient/Total Volume = Active Ingredient% per 100% of Total Volume)

volume/100mL or
(Active Ingredient/Total Volume = Active Ingredient% per 100% of Total Volume)

If you dilute 10% (need) of Active Ingredient into 1.2L you get ( dry weight or volume / 1.2L = 10/100% per 100mL ) or ( X:1200mL=10:100%) -dry weight or volume is 120.

If you dilute 12% (have) of Active Ingredient into 1L you get ( dry weight or volume / 1L = 12/100% per 100mL ) or ( X:1000mL=12:100%)
-dry weight or volume is 120.

Dispense 1000mL of a 12% Active Ingredient then add 200mL of Sterile water to compensate for the order for 1.2L of a 10% Active Ingredient Solution that is needed.

Another view
by: Anonymous

Simply use "C1 V1 = C2 V2"
C is concentration, V is volume (sometimes called "quantity"), and this says the mass or amount of substance in the 2 solutions is constant.

What we are given is the desired (final) concentration and volume, and the initial (stock) concentration.

What we are looking for is the initial volume, V1, that is, of the stock solution to use.

So, according to the formula,
12% X V1 = 10% X 1200 mL

Solve for V1 by dividing both sides of equation by 12%:

V1 = (10 X 1200)/12
= 1000 mL
That is, 1000 mL of the stock solution provides the amount of drug required.

But to make the total volume of 1200 mL (the 1.2 L), you have to add 200 mL of water to the 1000 mL of stock solution.

Hence, D is the answer.

alligation
by: Anonymous

this is not a dilution it is an alligation.

Answer is D
by: Anonymous

This problem can be solved with both allegation and dilution.

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