The concentration of stain in the bottle was 5% and you added 100 microliters of it to 9.9ml of a buffer to make a working dilution of stain. You then combined 10 microliters of that diluted stain with 40 microliters of your diluted cells and put a few microliters of that mixture on the slide from which you took your photo. The effective (final) concentration of the stain is _____
5% x (100/109.9) x (10/50) = ?
To calculate the effective (final) concentration of the stain, we need to consider the dilutions made at each step of the process.
Step 1: Dilution of the original stain
The original stain concentration is 5%. We added 100 microliters (µl) of this stain to 9.9 milliliters (ml) of a buffer. To calculate the resulting concentration, we can use the formula:
C1 x V1 = C2 x V2,
where C1 is the original concentration, V1 is the volume added, C2 is the final concentration, and V2 is the final volume.
Plugging in the values:
C1 = 5% = 0.05
V1 = 100 µl
C2 = unknown (let's call it X)
V2 = 9.9 ml + 100 µl = 10 ml
0.05 x 100 µl = X x 10 ml
Simplifying the equation:
0.05 = 10X
Dividing by 10 on both sides:
X = 0.05 / 10 = 0.005
So, the concentration of the stain after dilution is 0.005 or 0.5%.
Step 2: Dilution of the diluted stain
From the previous step, we obtained a diluted stain solution with a concentration of 0.5%. We combined 10 µl of this diluted stain with 40 µl of a diluted cell solution.
To calculate the resulting concentration of the stain in this mixture, we can use the same formula as before:
C1 x V1 = C2 x V2
C1 = 0.005
V1 = 10 µl
C2 = unknown (let's call it Y)
V2 = 10 µl + 40 µl = 50 µl
0.005 x 10 µl = Y x 50 µl
Simplifying the equation:
0.005 = 50Y
Dividing by 50 on both sides:
Y = 0.005 / 50 = 0.0001
So, the effective (final) concentration of the stain in the mixture is 0.0001 or 0.01%.