How many mL of Glycerin would be needed to prepare 500 g of an ointment containing 5% w/w Glycerin ?
Note: Density of Glycerin = 1.25g per mL

Question

BlackTom AI · Accepted Answer

5% w/w means 5 grams of glycerin in every 100 grams of ointment.

1. Relevant knowledge points and concepts
- "w/w" (weight/weight) concentration gives mass of solute per mass of final product (not volume).  
- Density (ρ) relates mass and volume: ρ = mass / volume, so volume = mass / ρ.  
- Units must be consistent (grams and mL with density in g/mL).

2. Complete reasoning process step by step
- Determine mass of glycerin required for 500 g of ointment using the w/w percentage.  
  mass_glycerin = (percent / 100) × total_mass_ointment.

3. Calculations with intermediate steps
- percent = 5, total_mass = 500 g.  
  mass_glycerin = (5 / 100) × 500 g = 0.05 × 500 g = 25 g.
- Convert this mass to volume using density (1.25 g/mL):  
  volume_glycerin = mass_glycerin / density = 25 g / (1.25 g/mL) = 20 mL.

4. Why the correct answer is correct
- The concentration specification is weight/weight, so you must compute the mass of glycerin (25 g) first. Using the glycerin density to convert that required mass to volume gives 20 mL. This directly matches the calculation above and meets the 5% w/w requirement for a 500 g ointment.

5. Why the other multiple-choice options are incorrect
- 22.5 mL would be 22.5 mL × 1.25 g/mL = 28.125 g glycerin (too high).  
- 17.5 mL → 21.875 g (too low).  
- 18 mL → 22.5 g (too low).  
- 25 mL → 31.25 g (too high).  
All of these give masses that do not equal the required 25 g.

6. Conclusion
- The required volume of glycerin is 20 mL, which confirms the provided correct answer (a. 20 mL).

How many mL of Glycerin would be needed to prepare 500 g of an ointment containing 5% w/w Glycerin ? Note: Density of Glycerin = 1.25g per mLSingle choice

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