Math Problem Statement

You conduct the following serial dilution: Step 1: You've diluted 100 µL of a bacterial stock with 700 µL distilled water. Step 2: You then take 100 µL of the dilution from step 1 and dilute it further with 900 µL of distilled water. A) What is the dilution factor after Step 1? B) What is the final/total dilution factor at the end of Step 2 from the starting stock?

Solution

Let's break down and solve the problem step by step.

Step 1:

  • You dilute 100 µL of bacterial stock with 700 µL of distilled water.
    • The total volume after dilution is 100μL+700μL=800μL100 \, \mu L + 700 \, \mu L = 800 \, \mu L.
    • The dilution factor for this step is the ratio of the total volume to the volume of the bacterial stock: Dilution Factor (Step 1)=Total VolumeVolume of Stock=800μL100μL=8\text{Dilution Factor (Step 1)} = \frac{\text{Total Volume}}{\text{Volume of Stock}} = \frac{800 \, \mu L}{100 \, \mu L} = 8

Step 2:

  • From the solution in Step 1, you take 100 µL and dilute it further with 900 µL of distilled water.
    • The total volume for this step is 100μL+900μL=1000μL100 \, \mu L + 900 \, \mu L = 1000 \, \mu L.
    • The dilution factor for this step is: Dilution Factor (Step 2)=Total VolumeVolume of Step 1 solution used=1000μL100μL=10\text{Dilution Factor (Step 2)} = \frac{\text{Total Volume}}{\text{Volume of Step 1 solution used}} = \frac{1000 \, \mu L}{100 \, \mu L} = 10

Final/Total Dilution Factor:

  • The total dilution factor is the product of the dilution factors from both steps: Total Dilution Factor=Dilution Factor (Step 1)×Dilution Factor (Step 2)=8×10=80\text{Total Dilution Factor} = \text{Dilution Factor (Step 1)} \times \text{Dilution Factor (Step 2)} = 8 \times 10 = 80

Final Answers:

A) The dilution factor after Step 1 is 8.

B) The final/total dilution factor at the end of Step 2 is 80.


Would you like more details or further explanation on any part of this?

Here are 5 related questions to expand on this:

  1. How would you calculate the dilution factor if you only added 500 µL of water in Step 1?
  2. If you wanted a final dilution factor of 100, how would you adjust the volumes in Step 2?
  3. Why is serial dilution preferred in microbiological applications?
  4. How can you verify the dilution factor experimentally?
  5. What impact does the accuracy of pipetting have on the dilution results?

Tip: Always make sure your pipette is calibrated properly to ensure the accuracy of the volumes used in dilutions.

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Math Problem Analysis

Mathematical Concepts

Dilution
Ratios

Formulas

Dilution Factor = Total Volume / Volume of Stock

Theorems

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Suitable Grade Level

Grades 9-12