How many mL of a 1:400 (w/v) stock solution is needed to make 4 litres of a 1:2000 (w/v) solution?

Question

BlackTom AI · Accepted Answer

Use the dilution equation C1V1 = C2V2 where concentrations are in the same units (here w/v expressed as g per mL). Relevant concept: a 1:400 (w/v) solution contains 1 g solute in 400 mL (so concentration = 1/400 g·mL^-1). A 1:2000 (w/v) solution contains 1 g solute in 2000 mL (concentration = 1/2000 g·mL^-1).

Step-by-step reasoning and calculations:
1. Convert final volume to mL: 4 litres = 4000 mL.
2. Find mass of solute required in the final 1:2000 solution:
   - C_final = 1/2000 g·mL^-1
   - mass_final = C_final × V_final = (1/2000 g·mL^-1) × (4000 mL) = 4000/2000 g = 2 g.
   So the diluted 4 L must contain 2 g of solute.
3. Determine the volume of 1:400 stock that contains 2 g:
   - C_stock = 1/400 g·mL^-1
   - V_stock = mass_final / C_stock = 2 g / (1/400 g·mL^-1) = 2 × 400 mL = 800 mL.
   Alternatively using C1V1 = C2V2: V1 = (C2×V2)/C1 = [(1/2000)×4000]/(1/400) = 2/(1/400) = 800 mL.

Why this is correct: 800 mL of 1:400 stock contains exactly 2 g of solute (800 mL × 1/400 g·mL^-1 = 2 g), and diluting that to 4000 mL yields 2 g in 4000 mL → 1 g per 2000 mL, i.e. 1:2000.

Why the other options are incorrect (quick checks):
- 200 mL of 1:400 → 200 × (1/400) = 0.5 g (too little).
- 400 mL → 1.0 g (too little).
- 600 mL → 1.5 g (too little).
- 1000 mL → 2.5 g (too much).
Only 800 mL gives the required 2 g.

Conclusion: The correct choice is d. 800 mL, matching the provided answer.

How many mL of a 1:400 (w/v) stock solution is needed to make 4 litres of a 1:2000 (w/v) solution?单项选择题

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