You have 20mL of a solution of concentration 0.015mg/mL of x in test tube #1.
Prepare serial dilutions of your stock solution, and calculated the concentration of x as follows:
Add 10mL of distilled water and 10mL of stock solution from test tube 1 to test tube 2.
Add 10mL of distilled water and 10mL of stock solution from test tube 2 to test tube 3.
.....and it keeps going.
So, obviously I will use the formula c1v1=c2v2.
So the concentration of test tube #1 is just 0.015mg/mL.
So, for test tube #2, c1=0.015mg/mL, and v1=20mL, and c2 is what we are trying to solve for. But what is v2? Can someone please tell me what v2 is and explain what it is. I think it's 40mL, giving c2=0.00750 mg/mL. But can someone please explain how I know what volumes to add! And maybe even explain what v2 for the next test tube would be? Is it 80mL?
never mind, i got it :)
To determine the value of v2, let's break down the serial dilution process step by step.
In the first step, you start with a stock solution of concentration 0.015 mg/mL in test tube #1, which has a volume of 20 mL. This is your initial solution.
Now, according to the serial dilution protocol, you add 10 mL of distilled water and 10 mL of the stock solution from test tube #1 to test tube #2. As a result, the total volume of the solution in test tube #2 becomes 20 mL (10 mL of water + 10 mL of stock solution).
This means that v2 for test tube #2 is indeed 20 mL. So, using the formula c1v1 = c2v2, you have:
(0.015 mg/mL)(20 mL) = c2(20 mL)
Solving for c2:
c2 = (0.015 mg/mL)(20 mL) / (20 mL)
= 0.015 mg/mL
So, the concentration of x in test tube #2 is also 0.015 mg/mL, as it is the same as the concentration of the stock solution.
For the next test tube, test tube #3, you perform the same process. Add 10 mL of distilled water and 10 mL of the solution from test tube #2, which has a volume of 20 mL. Therefore, the total volume in test tube #3 becomes 40 mL (10 mL of water + 10 mL of solution from test tube #2 + 20 mL of solution from test tube #2).
Therefore, v2 for test tube #3 is 40 mL. Using the formula c1v1 = c2v2:
(0.015 mg/mL)(20 mL) = c2(40 mL)
Solving for c2:
c2 = (0.015 mg/mL)(20 mL) / (40 mL)
= 0.0075 mg/mL
As a result, the concentration of x in test tube #3 is 0.0075 mg/mL.
Following this pattern, for each subsequent test tube, you continue adding 10 mL of water and 10 mL of the previous solution. The volume doubles each time, as the 10 mL addition combines with the previous total volume.
Therefore, for the next test tube, test tube #4, v2 would indeed be 80 mL.
I hope this explanation helps you understand the dilution process and how to determine the volumes for each test tube in the serial dilution.