In preparing capsules of Cyanocobalamine, 500 mg of drug was diluted to 10 g with Lactose; 1.00 g of this mix was diluted to 10 g with Lactose; 1.00 g of this second mix was further diluted to 12 g with Lactose; 300 mg of this mix was filled into a No.3 empty gelatin capsule. How much Cyanocobalamine is there in each capsule?单项选择题
A
a. 125 mg
B
b. 125 mcg
C
c. 12.5 mcg
D
d. 1.25 mcg
E
e. 125 g

Question

In preparing capsules of Cyanocobalamine, 500 mg of drug was diluted to 10 g with Lactose; 1.00 g of this mix was diluted to 10 g with Lactose; 1.00 g of this second mix was further diluted to 12 g with Lactose; 300 mg of this mix was filled into a No.3 empty gelatin capsule. How much Cyanocobalamine is there in each capsule?单项选择题

A

a. 125 mg

B

b. 125 mcg

C

c. 12.5 mcg

D

d. 1.25 mcg

E

e. 125 g

BlackTom AI · Accepted Answer

Serial dilutions multiply concentration fractions: start by tracking how many milligrams of Cyanocobalamine are present per gram at each dilution, then convert to the amount in a 300 mg fill.

1) Relevant concepts
- Concentration by weight (mg of drug per g of mixture).
- Serial dilution: amount of drug in a fixed mass is conserved when that fixed mass is diluted; concentration changes by the dilution factor.
- Unit conversions: 1 g = 1000 mg; 1 mg = 1000 mcg.

2) Step-by-step reasoning and intermediate calculations
- First dilution: 500 mg drug diluted to 10 g total.
  Concentration = 500 mg / 10 g = 50 mg per g.
- Second dilution: 1.00 g of the first mix (which contains 50 mg) is diluted to 10 g.
  Amount of drug taken = 50 mg (in that 1 g). After diluting to 10 g, concentration = 50 mg / 10 g = 5 mg per g.
- Third dilution: 1.00 g of the second mix (which contains 5 mg) is diluted to 12 g.
  Amount of drug taken = 5 mg. After diluting to 12 g, concentration = 5 mg / 12 g = 0.416666... mg per g.
- Capsule fill: 300 mg = 0.300 g of the final mix is filled.
  Drug per capsule = concentration (mg/g) × mass (g) = 0.416666... mg/g × 0.300 g = 0.125 mg.
- Convert to micrograms: 0.125 mg × 1000 mcg/mg = 125 mcg.

3) Why the correct answer is correct
Each dilution step reduces concentration by the ratio of final mass to the portion taken; following those ratios (10, then 10, then 12) yields a final concentration that, when multiplied by 0.300 g, gives 0.125 mg = 125 mcg. The arithmetic above shows this directly.

4) Why other options are incorrect
- a. 125 mg is 1000× too large (would correspond to 100% of the initial 500 mg concentrated into a single capsule).
- c. 12.5 mcg is 10× too small (would follow if a decimal error occurred).
- d. 1.25 mcg is 100× too small.
- e. 125 g is nonsensical given initial quantities (units and magnitude wrong).