Serial dilution worksheet example demonstrating how to achieve a countable plate by diluting a cell culture through multiple steps.

Problem Analysis and Solution

The worksheet describes a serial dilution process starting with a stock culture of cells. The goal is to calculate various dilution factors, cell concentrations, and expected colony counts at different stages of the dilution series. Let's solve each question step by step.

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#### Given Information:
- Starting cell concentration: \( 3.0 \times 10^6 \) cells/mL
- Dilution steps:
1. Take 1 mL of solution and dilute it in 99 mL of broth (Flask A).
2. Take 1 mL from Flask A and dilute it in 99 mL of broth (Flask B).
3. Take 1 mL from Flask B and dilute it in 9 mL of broth (Tube C).

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Step-by-Step Solution:

#### 1. What is the dilution factor at Flask A?
- Dilution factor is calculated as:
\[
\text{Dilution factor} = \frac{\text{Total volume after dilution}}{\text{Volume of sample added}}
\]
- For Flask A:
- Volume of sample added = 1 mL
- Total volume after dilution = 1 mL (sample) + 99 mL (broth) = 100 mL
- Dilution factor = \( \frac{100}{1} = 10^2 \)

Answer: \( 10^2 \)

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#### 2. What is the cell concentration of Flask A?
- The cell concentration after dilution is calculated as:
\[
\text{New concentration} = \text{Initial concentration} \times \text{Dilution factor}
\]
- Initial concentration = \( 3.0 \times 10^6 \) cells/mL
- Dilution factor for Flask A = \( 10^{-2} \) (since the concentration decreases by a factor of \( 10^2 \))
\[
\text{Cell concentration in Flask A} = 3.0 \times 10^6 \times 10^{-2} = 3.0 \times 10^4 \text{ cells/mL}
\]

Answer: \( 3.0 \times 10^4 \) cells/mL

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#### 3. What is the dilution from Flask A to Flask B?
- For Flask B:
- Volume of sample added = 1 mL (from Flask A)
- Total volume after dilution = 1 mL (sample) + 99 mL (broth) = 100 mL
- Dilution factor = \( \frac{100}{1} = 10^2 \)

Answer: \( 10^2 \)

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#### 4. What is the Final Dilution factor at Flask B?
- The final dilution factor at Flask B is the product of all dilution factors up to Flask B:
\[
\text{Final dilution factor at Flask B} = \text{Dilution factor at Flask A} \times \text{Dilution factor from Flask A to Flask B}
\]
- Dilution factor at Flask A = \( 10^2 \)
- Dilution factor from Flask A to Flask B = \( 10^2 \)
\[
\text{Final dilution factor at Flask B} = 10^2 \times 10^2 = 10^4
\]

Answer: \( 10^4 \)

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#### 5. If we plated 1 mL of culture from Flask B, how many colonies would we expect?
- Cell concentration in Flask B:
- Initial concentration in Flask A = \( 3.0 \times 10^4 \) cells/mL
- Dilution factor from Flask A to Flask B = \( 10^{-2} \)
\[
\text{Cell concentration in Flask B} = 3.0 \times 10^4 \times 10^{-2} = 3.0 \times 10^2 \text{ cells/mL}
\]
- Expected colonies from 1 mL:
\[
\text{Colonies} = \text{Concentration in Flask B} \times \text{Volume plated}
\]
- Concentration in Flask B = \( 3.0 \times 10^2 \) cells/mL
- Volume plated = 1 mL
\[
\text{Colonies} = 3.0 \times 10^2 \times 1 = 300
\]

Answer: 300

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#### 6. What is the dilution from Flask B to Tube C?
- For Tube C:
- Volume of sample added = 1 mL (from Flask B)
- Total volume after dilution = 1 mL (sample) + 9 mL (broth) = 10 mL
- Dilution factor = \( \frac{10}{1} = 10^1 \)

Answer: \( 10^1 \)

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#### 7. What is the Final Dilution factor of this series of dilutions (at Tube C)?
- The final dilution factor at Tube C is the product of all dilution factors:
\[
\text{Final dilution factor at Tube C} = \text{Final dilution factor at Flask B} \times \text{Dilution factor from Flask B to Tube C}
\]
- Final dilution factor at Flask B = \( 10^4 \)
- Dilution factor from Flask B to Tube C = \( 10^1 \)
\[
\text{Final dilution factor at Tube C} = 10^4 \times 10^1 = 10^5
\]

Answer: \( 10^5 \)

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#### 8. If we plated 1 mL of Tube C, how many colonies would we get?
- Cell concentration in Tube C:
- Initial concentration in Flask B = \( 3.0 \times 10^2 \) cells/mL
- Dilution factor from Flask B to Tube C = \( 10^{-1} \)
\[
\text{Cell concentration in Tube C} = 3.0 \times 10^2 \times 10^{-1} = 3.0 \times 10^1 \text{ cells/mL}
\]
- Expected colonies from 1 mL:
\[
\text{Colonies} = \text{Concentration in Tube C} \times \text{Volume plated}
\]
- Concentration in Tube C = \( 3.0 \times 10^1 \) cells/mL
- Volume plated = 1 mL
\[
\text{Colonies} = 3.0 \times 10^1 \times 1 = 30
\]

Answer: 30

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#### 9. Is that a countable plate?
- A countable plate must have between 30 and 300 colonies.
- From Tube C, we expect 30 colonies.
- Since 30 is within the range of 30–300, the plate is countable.

Answer: Yes

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Final Answers:

1. \( \boxed{10^2} \)
2. \( \boxed{3.0 \times 10^4} \)
3. \( \boxed{10^2} \)
4. \( \boxed{10^4} \)
5. \( \boxed{300} \)
6. \( \boxed{10^1} \)
7. \( \boxed{10^5} \)
8. \( \boxed{30} \)
9. \( \boxed{\text{Yes}} \)