Question

Make a second dilution by adding \(1.0 \mathrm{~mL}\) of the \(10^{-1}\) dilution to one of the \(9.0 \mathrm{~mL}\) dilution tubes. Mix well. This dilution contains \(1 / 100\) original sample and is \(10^{-2}\).

Short answer

Final dilution is \(10^{-2}\) or \(\frac{1}{100}\) of the original sample.

Step-by-step solution

Identify the Initial Dilution

Start with the initial dilution of the original sample, which is a dilution factor of \(10^{-1}\).

Measure the Volume of the First Dilution

Take \(1.0 \, \text{mL}\) of the \(10^{-1}\) dilution. Ensure the measurement is accurate for proper dilution.

Prepare the Dilution Tube

Get a tube with \(9.0 \, \text{mL}\) of diluent ready for the next step.

Combine the Dilutions

Add the \(1.0 \, \text{mL}\) of \(10^{-1}\) dilution into the tube containing \(9.0 \, \text{mL}\) of diluent. This mixture will reduce the concentration of the original sample further.

Mix Well

Ensure thorough mixing of the contents to achieve a uniform dilution. Shake or mix according to best lab practices.

Determine the Final Dilution Factor

The final dilution is calculated by multiplying the initial and the second dilution factors: \[\left(10^{-1} \right) \times \left(10^{-1} \right) = 10^{-2}\right)\]. This means the final dilution factor is \(10^{-2}\), or \(\frac{1}{100}\) of the original sample.

Key concepts

dilution factor

The dilution factor is a key concept when working with serial dilutions. It tells us how much a sample's concentration has been reduced. In each step of dilution, we divide the original concentration by a certain number.

For example, in this exercise, starting with a dilution factor of \(10^{-1}\) means the original concentration is reduced to one-tenth. When we take \(1.0 \, \text{mL}\) from this \(10^{-1}\) sample and add it to \(9.0 \, \text{mL}\), the concentration of the sample becomes \(10^{-2}\), or one-hundredth of the original. This is because \(10^{-1} \times 10^{-1} = 10^{-2}\).

Understanding dilution factors helps ensure accurate results in experiments. They allow for precise control over the concentration of a substance. Essentially, you can systematically decrease the concentration across a series of steps.

laboratory techniques

Good laboratory techniques are crucial in achieving reliable results. In this exercise, there are several key techniques to consider:

• Accurate Measurement: Using pipettes or syringes precisely measure \(1.0 \, \text{mL}\). This accuracy is critical for consistency.
• Proper Mixing: After combining the samples, mixing thoroughly is essential. This ensures even distribution of the diluted substance.
• Maintaining Cleanliness: Proper sterilization and cleanliness of equipment prevent contamination. Using sterilized tubes for diluents helps keep samples pure.
• Following Protocols: Adhering to specific mixing and handling protocols ensures replicable and valid results.

Mastering these techniques ensures that each dilution is accurate, and the results are reliable and reproducible. Lab techniques form the foundation for various scientific experiments.

sample preparation

Sample preparation is the initial, yet crucial step in any laboratory experiment. It involves readying the sample for dilution or analysis. Here’s what you need to keep in mind:

• Starting With a Clean Sample: Ensure the sample is pure and clean to avoid contamination.
• Labeling: Clearly label all tubes and containers to avoid mix-ups. This helps track samples through multiple dilutions.
• Accurate Measurements: Start with precise measurements. Using calibrated equipment to measure \(1.0 \, \text{mL}\) and \(9.0 \, \text{mL}\) is key.
• Gentle Handling: Handle all equipment and samples gently to maintain integrity.
• Initial Dilution: Prepare the initial sample by diluting it correctly before beginning serial dilutions.
  
  These steps in sample preparation ensure the experiment starts on a solid foundation. Accurately prepared samples lead to more reliable and credible results in the dilution process.