A saturated solution of a drug contains 120 g of the drug in a total volume of 100 mL. The density of this solution is approximately 1.5 g per mL. Express the concentration of the solution in terms of the % w/w.

Question

BlackTom AI · Accepted Answer

Percent weight/weight (% w/w) is defined as grams of solute per 100 grams of total solution. Use the solution density to convert the given solution volume to its mass, then compute the percent.

1) Relevant concepts:
- Density = mass/volume, so mass = volume × density.
- % w/w = (mass of solute / mass of solution) × 100 (units: g solute per 100 g solution).

2) Step-by-step reasoning and calculations:
- Given: solute (drug) mass = 120 g, solution volume = 100 mL, density = 1.5 g/mL.
- Compute mass of 100 mL of solution: mass_solution = volume × density = 100 mL × 1.5 g/mL.
- Intermediate step: 100 × 1.5 = 150, so mass_solution = 150 g.
- Now compute % w/w: % w/w = (mass_solute / mass_solution) × 100 = (120 g / 150 g) × 100.

3) Arithmetic shown:
- 120 / 150 = 0.8
- 0.8 × 100 = 80

4) Why this answer is correct:
- The calculation directly applies the definitions. There are 120 g of drug in a total of 150 g of solution, which corresponds to 80 g of drug per 100 g of solution, i.e., 80% w/w.

5) Why the other options are incorrect:
- 170%: implies more grams of solute than grams of solution (impossible here, would mean >150 g solute in 150 g solution).
- 60%: would correspond to 90 g solute in 150 g solution (120 g is greater than this).
- 15%: corresponds to only 22.5 g solute in 150 g solution (far too small).
- 100%: would mean solute mass equals solution mass (150 g), but solute is only 120 g.

6) Conclusion:
The correct % w/w concentration is 80%, which matches the provided answer (c. 80%).

A saturated solution of a drug contains 120 g of the drug in a total volume of 100 mL. The density of this solution is approximately 1.5 g per mL. Express the concentration of the solution in terms of the % w/w.单项选择题

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