Calculate the dilution factors (A-D) at each step when performing the dilution series below: [table]
[Stock] | 1500ug/mL | 1000ug/mL | 750ug/mL | 500ug/mL Dilution factor | A | B | C | D [Target] | 1000ug/mL | 750ug/mL | 500ug/mL | 250ug/mL
[/table] Match the correct value to each dilution factor
1: C ____
2: A ____
3: B ____
4: D ____

Question

BlackTom AI · Accepted Answer

To tackle this matching question, I will first restate the setup and then work through each step to determine the dilution factors.

Understanding the setup:
- The stock concentrations given are 1500 ug/mL, 1000 ug/mL, 750 ug/mL, and 500 ug/mL, labeled as A–D under the Dilution factor column.
- The targets are 1000 ug/mL, 750 ug/mL, 500 ug/mL, and 250 ug/mL.
- Each dilution factor (A, B, C, D) corresponds to a transition from the preceding stock concentration to the next target concentration: A is 1500 -> 1000, B is 1000 -> 750, C is 750 -> 500, D is 500 -> 250.

Method for finding the dilution factor (DF):
- The dilution factor DF for a step from C1 to C2 is defined as DF = C1 / C2. This reflects how many-fold the concentration is reduced in that step.
- Alternatively, you can think of it as the multiplier by which the concentration decreases, so higher DF means a larger reduction.

Now compute each step’s DF using DF = C1 / C2:
- Step A (1500 → 1000): DF = 1500 / 1000 = 1.5. That means after the first dilution, the concentration is reduced by a factor of 1.5.
- Step B (1000 → 750): DF = 1000 / 750 ≈ 1.333..., which rounds to 1.33. This is the fold reduction from 1000 to 750.
- Step C (750 → 500): DF = 750 / 500 = 1.5. The third step reduces concentration by a factor of 1.5.
- Step D (500 → 250): DF = 500 / 250 = 2. This final step halves the concentration, i.e., a 2-fold reduction.

With these DFs identified, match them to the prompts:
- 1: C ____ → C corresponds to 1.5 (since DF for 750 → 500 is 1.5).
- 2: A ____ → A corresponds to 1.5 (since DF for 1500 → 1000 is 1.5).
- 3: B ____ → B corresponds to 1.33 (since DF for 1000 → 750 is 1.33).
- 4: D ____ → D corresponds to 2 (since DF for 500 → 250 is 2).

Key notes on the other options (to avoid common pitfalls):
- Values like 0.66 or 0.75 would be used if you were listing DF as the ratio of the final concentration to the initial (C2/C1) rather than C1/C2; in this problem the intended convention matches C1/C2, so those smaller numbers do not fit the required DFs for these steps.
- The 1.33 value is a repeating fraction (1.333...), which rounds to 1.33 in the provided options; be mindful of rounding when selecting the closest match.
- The 1.5 and 2 values are consistent with the concentration halving or reducing by one-and-a-half-fold across the specified transitions, which aligns with the provided concentrations.

Summary of the intended matches (based on DF = C1 / C2):
- C → 1.5
- A → 1.5
- B → 1.33
- D → 2

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