You are required to prepare 200 g of Sodium Benzoate 5% w/w in sorbolene cream from existing supplies of Sodium Benzoate 10% w/w (in sorbolene cream) and sorbolene cream. How much Sodium Benzoate 10% w/w cream is required?

Question

BlackTom AI · Accepted Answer

Using conservation of the active ingredient (mass of sodium benzoate) and simple dilution/alligation.

1) Relevant knowledge points and concepts
- Weight/weight percent (w/w) expresses grams of active per 100 g of formulation.
- Total mass of active must be conserved when mixing two preparations.
- If you mix a 10% w/w source with a 0% w/w diluent (plain sorbolene), the grams of active come only from the 10% source.
- Alligation or direct mass-balance calculations can be used.

2) Step-by-step reasoning
Let x = grams of 10% w/w sodium benzoate cream required. The rest (200 − x) g will be plain sorbolene cream (0% active). Calculate grams of sodium benzoate needed in the final 200 g of 5% w/w cream:
- Required active = 5% of 200 g = 0.05 × 200 = 10 g.

3) Calculations (intermediate steps)
- Active supplied by x grams of 10% cream = 0.10 × x grams.
- Set supply = requirement: 0.10 x = 10
- Solve: x = 10 / 0.10 = 100 g.

Alternatively, alligation: difference between source and desired (10 − 5 = 5) equals parts of diluent; difference between desired and diluent (5 − 0 = 5) equals parts of source → equal parts source and diluent → 200 g total → 100 g each.

4) Why the correct answer is correct
With 100 g of 10% cream you supply 0.10 × 100 = 10 g sodium benzoate. Mixed with 100 g plain sorbolene to make 200 g, this 10 g corresponds to 10/200 = 0.05 = 5% w/w, which meets the specification exactly.

5) Why other options are incorrect (briefly)
- 10 g → supplies 1 g active (far too little).
- 25 g → supplies 2.5 g active.
- 50 g → supplies 5 g active (would give 2.5% in 200 g, not 5%).
- 66 g → supplies 6.6 g active (≈3.3% in 200 g), all insufficient except 100 g.

6) Conclusion
Therefore 100 g of the 10% w/w sodium benzoate cream is required. This matches the provided correct answer: 100 g.

You are required to prepare 200 g of Sodium Benzoate 5% w/w in sorbolene cream from existing supplies of Sodium Benzoate 10% w/w (in sorbolene cream) and sorbolene cream. How much Sodium Benzoate 10% w/w cream is required?单项选择题

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