Could someone answer this question? Thanks.
Allow me to try:
A physician prescribed 25 capsules, each is 4 mg, of a drug for a special needs patient, knowing that the dose prescribed was considered ‘‘subtherapeutic.’’
The lowest strength commercially available tablets contain 25 mg.
The pharmacist decided to select the minimum required number of 25 mg tablets (which is 4 tablets to get 100 mg of Active Ingredient);
The pharmacist reduced them to a powder with a mortar and pestle;
The pharmacist weighed the powder and got 280 mg;
The pharmacist continued the process using the aliquot method.
The pharmacist called upon her pharmacy student intern to do 3 jobs:
calculate and show your calculations for (a) and (b):
(a) the minimum quantity of lactose (diluent) to use in preparing the crushed tablet-diluent mixture and
(b) the quantity of the mixture to use to fill each capsule.
The prescription balance had a SR of 6 mg and a weighing error of 5% was acceptable.
and
(c) prove that your answer to (b) is correct by demonstrating that each capsule would indeed contain 4 mg of drug.
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Let's find minimum weight that we can weigh on this balance:
6 mg is 5%
x mg is 100%
x = 120 mg.
Given the data, we found we must weigh something that is at least 120 mg, no less.
If we weigh something under 120 mg, we will have error over 5 percent, which is not okay.
Doctor needs: Total need of active ingredient: 25 pills TIMES 4 mg a pill = 100 mg of Active Ingredient.
Pharmacy has: 25 mg a pill, so, use 4 pills to get 100 mg that doctor needs.
4 tablets has total weight of 280 mg.
4 tablets has total Active Ingredient of 100 mg.
4 tablets has total Inactive Ingredient of 280 mg - 100 mg = 180 mg Inactive Ingredient.
Good discovery. Let's continue:
To make a future capsule, we need to weigh 120 mg for each capsule. We can not weigh any powder that is under 120 mg. Any time we weigh under 120 mg, we will have error over 5%, which is not okay.
For each pill, we need at least 120 mg.
For 25 pills, we need at least how much?
To make 25 capsules, we need to a mixture of at least certain weight. What is that?
25 capsules TIMES (120 mg / capsule) = 3000 mg total of mixed powder.
Let's see next issue.
So far, from crushing 4 tablets, we have 280 mg.
We need to add diluent. How much?
3000 mg - 280 mg = 2720 mg of diluent.
Each pill must have exactly 4 mg of Active Ingredient.
In 3000 mg of mixed powder, I will have 100 mg of Active Ingredient, 180 mg of Inactive Ingredient that came from the crushed tablet, 2720 mg of Inactive Ingredient that I would add.
A pill needs 4 mg of Active Ingredient, how much powder should I get from Mixed powder?
Let's see link:
3000 mg of mixed powder has 100 mg of Active Ingredient.
x mg of mixed powder has 4 mg of Active Ingredient?
x = ( 3000 mg TIMES 4 mg ) DIVIDE BY 100 mg = 120 mg of mixed powder.
That means:
120 mg of mixed powder has 4 mg of Active Ingredient.
Can I weigh 120 mg of mixed powder? Yes. Bingo. I can continue.
Steps: go to lab.
Crush 4 tablets, knowing I have 100 mg of Active Ingredient in 280 mg of crushed tablet.
Weigh 2720 mg of diluent.
Mix 280 mg of crushed tablets with 2720 mg of diluent, now I get 3000 of mixed powder.
Weigh 120 mg of mixed powder, somehow, put that inside a capsule, close capsule. Ha Ha, got 1 pill with 4 mg of Active Ingredient.
Repeat the process 24 more times to get total 25 pills:
Weigh 120 mg of mixed powder, somehow, put that inside a capsule, close capsule. Ha Ha, got 1 pill with 4 mg of Active Ingredient.
Weigh 120 mg of mixed powder, somehow, put that inside a capsule, close capsule. Ha Ha, got 1 pill with 4 mg of Active Ingredient.
Weigh 120 mg of mixed powder, somehow, put that inside a capsule, close capsule. Ha Ha, got 1 pill with 4 mg of Active Ingredient.
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Answer a:
(a) the minimum quantity of lactose (diluent) to use in preparing the crushed tablet-diluent mixture is: 2720 mg of lactose.
Answer b:
(b) the quantity of the mixture to use to fill each capsule is: 120 mg.
Answer c:
(c) prove that your answer to (b) is correct by demonstrating that each capsule would indeed contain 4 mg of drug.
Let's trace the Active Ingredient:
Factory promised each pill has 25 mg of Active Ingredient.
I crushed 4 pills, I got 100 mg of Active Ingredient
After I crushed 4 pills, I weighed it: I got 280 mg of crushed tablets now as powder which has 100 mg of Active Ingredient.
I added 2720 mg of Lactose. I got a new mixture of 3000 mg which still has 100 mg of Active Ingredient.
I mixed so well, so well, so well that any spoon of that mixture will have the same drug like the next spoon.
3000 mg can be divided evenly into 25 portions of 120 mg each.
Each portion of 120 mg will have exactly 4 mg of Active Ingredient because I mixed so well, so well that my hand swells.
There, I traced the Active Ingredient so carefully. I did not lose any Active Ingredient. Each portion of 120 mg must absolutely has 4 mg of Active Ingredient. For sure.
If my method does not convince you, for the same method, If I use Active Ingredient as Tiny Metal Balls, I can put 120 mg of mixed powder into water, the lactose will dissolve, I can strain the liquid away and weigh the filter paper and I for sure will find 4 mg of Tiny Metal Balls. Anyone would like to experiment?
Good luck and please come back and help others....Thank you very much in advance.
