Serial Dilution word Problems examples

The Basic Steps:

1. Identify the dilution factor (e.g., 1:2, 1:10, etc.).

2. Determine how many times you need to dilute (how many steps you’re taking).

3. Calculate the final concentration using the formula:
   Final Concentration = Initial Concentration × (Dilution Factor) ^ Number of Dilutions

Girlypop Mnemonic:

"Step By Step, Take It Slow"

• Step: Think about the starting concentration. This is where you begin.

• By: This is for the dilution factor. (e.g., 1:2 means you're diluting by half each time).

• Slow: This reminds you to do it step-by-step. Don't rush! Each dilution is a fraction of the previous step. For example, if you're doing a 1:10 dilution, you’re multiplying the concentration by 1/10 each time.

Example Problem:

You have a stock solution of 1000 µg/mL. You’re diluting it in a 1:10 series, and you need to find the concentration of the solution after 3 dilutions.

1. Start: The starting concentration is 1000 µg/mL.

2. Dilution Factor: 1:10, meaning each dilution is 1/10th the previous concentration.

3. Number of Dilutions: 3 (because you’re diluting it 3 times).

Use the formula: Final Concentration = Initial Concentration × (Dilution Factor) ^ Number of Dilutions

So, plug in the numbers: Final Concentration = 1000 µg/mL × (1/10) ^ 3

Now calculate: Final Concentration = 1000 × 1/1000 = 1 µg/mL

So, after 3 dilutions, the final concentration is 1 µg/mL.

Another Example:

You have a solution with a concentration of 500 µg/mL, and you’re doing a 1:2 serial dilution. How much of the solution is left after 4 dilutions?

1. Start: 500 µg/mL.

2. Dilution Factor: 1:2, so each dilution halves the concentration.

3. Number of Dilutions: 4.

Use the formula: Final Concentration = Initial Concentration × (Dilution Factor) ^ Number of Dilutions

Final Concentration = 500 µg/mL × (1/2) ^ 4

Final Concentration = 500 × 1/16 = 31.25 µg/mL

So, after 4 dilutions, the final concentration is 31.25 µg/mL.

Quick Tips:

• Remember, "Step By Step, Take It Slow" to make sure you’re identifying your starting point, dilution factor, and dilution steps before you calculate.

• Always make sure to multiply the dilution factor to the power of the number of dilutions to get the correct final concentration!

Now you’ve got this, girlypop! Just take it one step at a time! 🎉

No worries, girlypop! If you're not given a dilution ratio, you can still solve serial dilution problems by figuring it out from the information given. Here’s how to approach it:

1. Understand the Volume of Solution Used:

• Often, instead of directly giving you a dilution ratio, the problem will give you how much of the stock solution (the concentrated solution) you need to mix with a certain volume of solvent.

• For example, if the problem tells you:
  "Mix 1 mL of the stock solution with 9 mL of solvent," that means the dilution ratio is 1:10.

  • 1 part of stock solution to 10 parts total (1 + 9).

2. Create the Dilution Factor:

• The dilution factor can be found by looking at the ratio between the stock solution and the total volume. For example:

  • 1 mL of stock solution + 9 mL solvent = 1:10 dilution.

  • 0.5 mL stock solution + 4.5 mL solvent = 1:10 dilution.

  • 0.1 mL stock solution + 9.9 mL solvent = 1:100 dilution.

3. Repeat the Dilution:

• If the problem asks you to do multiple dilutions, you just repeat the dilution process, applying the same dilution factor each time.

Example Problem:

You have a stock solution of 500 µg/mL. To dilute it, you mix 2 mL of the stock solution with 8 mL of solvent. Then, you take 1 mL from this new solution and add it to 9 mL of solvent. What is the final concentration after the second dilution?

Step-by-Step:

1. Find the first dilution ratio:
   You mix 2 mL of stock with 8 mL of solvent, so the total volume is 2 + 8 = 10 mL.
   The dilution ratio is 2 mL / 10 mL = 1:5.

2. Find the second dilution ratio:
   You then take 1 mL from the first dilution and add it to 9 mL of solvent.
   The total volume is 1 + 9 = 10 mL, and the dilution ratio is 1 mL / 10 mL = 1:10.

3. Calculate the concentration after each dilution:
   After the first dilution:
   Final concentration after 1st dilution = 500 µg/mL × (1/5) = 100 µg/mL
   After the second dilution:
   Final concentration after 2nd dilution = 100 µg/mL × (1/10) = 10 µg/mL

Final Answer:

The concentration after the second dilution is 10 µg/mL.

Girlypop Tip:

If you're not given a dilution ratio, "Create the Mix" by figuring out how much of the concentrated solution is added to the solvent. From there, calculate the dilution ratio and follow through with each dilution step. Just keep track of the ratios and multiply the concentrations! ✨