You need to make a 2 fold serial dilution starting at 1:100 and ending at 1:3200. You need 2 ml in each test tube when you are finished. You have 40 microliters of serum. do you have enough?
To determine if you have enough serum for the 2-fold serial dilution, we need to calculate the total volume of serum required.
In a 2-fold serial dilution, each dilution step is half the concentration of the previous step. In this case, we are starting with a 1:100 dilution and ending with a 1:3200 dilution.
Let's calculate the volumes for each step:
Step 1: 1:100 dilution
To get a 1:100 dilution, you need to mix 1 part of serum with 99 parts of diluent (usually a buffer or distilled water). Each step requires 2 ml in each test tube, so the volume of serum required for the first step is:
(2 ml / (100 + 1)) x 1 = 0.02 ml
Step 2: 1:200 dilution
To get a 1:200 dilution, you need to mix 1 part of the 1:100 dilution with 1 part of diluent. So, for each 1:100 dilution, we need to add 0.02 ml of the 1:100 dilution (which contains 0.02 ml of serum) with 0.02 ml of diluent. The total volume of serum required for the second step is:
(2 ml / (200 + 1)) x 1 = 0.01 ml
Step 3: 1:400 dilution
Using the same logic, the volume of serum required for the third step (1:400 dilution) is:
(2 ml / (400 + 1)) x 1 = 0.005 ml
And so on, until the last step:
Step 11: 1:3200 dilution
(2 ml / (3200 + 1)) x 1 = 0.000625 ml
Now let's calculate the total volume of serum required:
Total volume of serum = 0.02 ml + 0.01 ml + 0.005 ml + ... + 0.000625 ml
To check if you have enough serum (40 μl) for the dilution, we need to convert the volumes to the same units (μl):
Total volume of serum = 0.02 ml x 1000 μl/ml + 0.01 ml x 1000 μl/ml + 0.005 ml x 1000 μl/ml + ... + 0.000625 ml x 1000 μl/ml
Total volume of serum = 20 μl + 10 μl + 5 μl + ... + 0.625 μl
Total volume of serum = 20 + 10 + 5 + ... + 0.625 μl
Now, adding up the terms:
20 + 10 = 30
30 + 5 = 35
35 + 2.5 = 37.5
37.5 + 1.25 = 38.75
38.75 + 0.625 = 39.375
The total volume required is 39.375 μl, which is less than the 40 μl you have available. Therefore, you have enough serum to perform the 2-fold serial dilution.