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a_zed24

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Hello there,

I'm having a hard time understanding the following problem taken from the textbook "Ansel's Pharmaceutical Dosage Forms and Drugs Delivery Systems, 9th edition":

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Preservation of Syrups
Syrups can be preserved by (a) storage at low temperature, (b) adding preservatives such as glycerin, benzoic acid, sodium benzoate, methyl paraben, or alcohol in the formulation, or (c) by the maintenance of a high concentration of sucrose as a part of the formulation. High sucrose concentrations will usually protect an oral liquid dosage form from growth of most microorganisms. A problem arises, however, when pharmacists must add other ingredients to syrups that can result in a decrease in the sucrose concentration.
This may cause a loss of the preservative effectiveness of the sucrose. This can be overcome,
however, by calculating the quantity of a preservative (such as alcohol) to add to the formula to maintain the preservative effectiveness of the final product.

EXAMPLE
Rx Active drug 5 mL volume occupied
Other drug solids 3 mL volume occupied
Glycerin 15 mL
Sucrose 25 g
Ethanol 95% q.s.
Purifi ed water q.s. 100 mL
How much alcohol would be required to preserve this prescription?
We will use the free-water method to calculate the quantity of alcohol required.

Simple syrup contains 85 g sucrose per 100 mL of solution, which weighs 131.3 g (specific gravity,
1.313). It takes 46.3 mL of water to prepare the solution (131.3 − 85 = 46.3), and the sucrose
occupies a volume of (100 − 46.3 = 53.7) 53.7 mL.

1. Because this solution is preserved, 85 g of sucrose preserves 46.3 mL of water, and 1 g of sucrose preserves
0.54 mL of water. With 25 g of sucrose present, the amount of water preserved is 25 × 0.54 = 13.5 mL
2. Because 85 g of sucrose occupies a volume of 53.7 mL, 1 g of sucrose will occupy a volume of 0.63 mL.
The volume occupied by the sucrose in this prescription is 25 × 0.63 = 15.75 mL
3. The active drug and other solids occupy 8 mL (5 + 3) volume.
4. Each mL of glycerin can preserve an equivalent quantity of volume (2 × 15 = 30), so 30 mL would be preserved.
5. The volume taken care of so far is 13.5 + 15.75 + 8 + 30 = 67.25 mL. The quantity of free water
remaining is 100 − 67.25 = 32.75 mL
6. Because it requires about 18% alcohol to preserve the water, 0.18 × 32.75 = 5.9 mL of alcohol (100%) would be required.
7. If 95% ethanol is used, 5.9/0.95 = 6.21 mL would be required.
To prepare the prescription, about 6.21 mL of 95% ethanol can be added with suffi cient purifi ed water to make 100 mL of the fi nal solution.

I understand all the process except for two points:
1) Why does the glycerin preserve twice its volume? The book says "each ml of glycerin preseves an equivalent volume". What's this equivalent volume?
2) Why does it take 18% alcohol to preserve water? From where does this value come from?

Thank you very much in advance!
 
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