Geometric Series Question

[zmike]

1. Homework Statement

you are geometrically diluting/mixing 0.1 g of powder A with 100g of powder B, how many times do you have to mix the 2 together to finish the process?
*each time you can only mix an equal portion of powder B to what you currently have mixed.

Eg.
1:1
2:2
4:4

3. The Attempt at a Solution

So the first time you mix them it will be
0.1 g + 0.1 g --> 2^0
then
0.2 g + 0.2 g --> 2^1

Would the correct formula be 101.1 = 0.1*2^n ?

help?? thanks

 

[mighty2000]

Hello,

Thank you for your question. The formula you have written, 101.1 = 0.1*2^n, is not correct for this scenario. The correct formula for geometric dilution is A1V1 = A2V2, where A1 is the initial concentration, V1 is the initial volume, A2 is the final concentration, and V2 is the final volume.

In this case, the initial concentration of powder A is 0.1 g in 100 g of powder B, so A1 = 0.1 g/100 g = 0.001 g/g. The final concentration is 0.1 g in 200 g of powder B, so A2 = 0.1 g/200 g = 0.0005 g/g. The initial volume is 100 g of powder B, so V1 = 100 g. The final volume is 200 g of powder B, so V2 = 200 g.

Plugging these values into the formula, we get:

0.001 g/g * 100 g = 0.0005 g/g * 200 g

Simplifying, we get:

0.1 g = 0.1 g

This shows that the concentration of powder A remains the same after each mixing step, so you can mix the two powders together as many times as you like and the final result will still be 0.1 g of powder A in 200 g of powder B.

I hope this helps clarify the formula for geometric dilution and how it applies to your scenario. Let me know if you have any further questions.