10 mL of a 1% w/v of Aminacrine HCl is diluted to 1 litre and then 10 mL of this dilution is further diluted to 1 litre. What will be the concentration in mg/litre of the final solution?

Question

BlackTom AI · Accepted Answer

1. Relevant knowledge points and concepts
1% w/v means 1 g of solute per 100 mL of solution. Serial dilution factors multiply. Concentration can be tracked either by mass in the aliquot or by multiplying the initial concentration by the product of dilution factors. Convert grams to milligrams (1 g = 1000 mg) when final units are mg/L.

2. Step-by-step reasoning
Start concentration: 1% w/v = 1 g / 100 mL.
Express per litre: (1 g / 100 mL) × (1000 mL / 1 L) = 10 g/L = 10,000 mg/L.

Method A (mass-tracking):
- Take 10 mL of the stock. Mass of Aminacrine HCl in 10 mL = (1 g / 100 mL) × 10 mL = 0.1 g = 100 mg.
- Dilute this 10 mL to 1 L (1000 mL). Concentration after first dilution = 100 mg / 1 L = 100 mg/L.
- Take 10 mL of that 100 mg/L solution. Mass in 10 mL = 100 mg/L × 0.01 L = 1 mg.
- Dilute this to 1 L. Final concentration = 1 mg / 1 L = 1 mg/L.

Method B (dilution-factor):
- Each dilution is 10 mL → 1000 mL, a factor of 10/1000 = 1/100 (i.e., 1:100 dilution).
- Two such dilutions give overall factor (1/100) × (1/100) = 1/10,000.
- Initial concentration in mg/L = 10,000 mg/L. Final = 10,000 mg/L × (1/10,000) = 1 mg/L.

3. Intermediate calculations shown
- 1% w/v → 1 g/100 mL = 10 g/L = 10,000 mg/L.
- First aliquot mass: (1 g/100 mL)×10 mL = 0.1 g = 100 mg.
- First dilution: 100 mg / 1000 mL = 100 mg/L.
- Second aliquot mass: 100 mg/L × 0.01 L = 1 mg.
- Final dilution: 1 mg / 1 L = 1 mg/L.

4. Why the correct answer is correct
Both mass-tracking and dilution-factor methods give the same result: after two 1:100 dilutions of a 10,000 mg/L stock, the concentration is 1 mg/L.

5. Why other options are incorrect (brief)
- 10 mg/L would be obtained by a single 1:1000 total dilution of 10,000 mg/L (not the two 1:100 steps performed).
- 50, 75, 100 mg/L do not match the serial dilution arithmetic from the given volumes and starting concentration.

6. Conclusion
The final concentration is 1 mg/L, which matches the provided correct answer (a. 1 mg/L).

10 mL of a 1% w/v of Aminacrine HCl is diluted to 1 litre and then 10 mL of this dilution is further diluted to 1 litre. What will be the concentration in mg/litre of the final solution?单项选择题

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