SOLUTION: thank you in advance need help with pharmacy math...PLEASE SHOW WORK STEP BY STEP. Question: What volume of 24% citric acid is needed to prepare eight 3 ounce bottles of 10% cit

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Question 844665: thank you in advance need help with pharmacy math...PLEASE SHOW WORK STEP BY STEP.
Question: What volume of 24% citric acid is needed to prepare eight 3 ounce bottles of 10% citric acid solution?
Answer by josgarithmetic(39616) About Me  (Show Source):
You can put this solution on YOUR website!
"ounce"?

ASSUMING this is for weight or "mass", then the amount of solution wanted is 8*3=24 "ounces". If you want volumes, then you must use the densities of water and the 24% citric acid.

From a handbook:
24%___________~1.0972, sp.gr., nearly same as density g/ml.
10%___________1.0392

1 fluid ounce = 29.5735 ml.


Actually, IF IF IF IF you have the percents as w/v, then the solution is simpler than needing account using densities.

Let x = volume of the 24% W/V Citric Acid, and you want 24 FLUID OUNCES ( not "ounces") of 10% W/V, and y = volume of water to add, then your equations are:
highlight_green%28%2824x%29%2F24=10%29 and highlight_green%28x%2By=24%29.
The solution of the problem is highlight%28x=2.4%29 FLUID OUNCES of 24% citric acid and highlight%28y=21.6%29 fluid ounces water.