Need help please You are given a test tube containing 10 mL

You are given a test tube containing 10 mL of a solution with 6.7 times 10^9 cells/mL. You are to produce a solution that contains less than 100 cells/mL - but not exactly 100. What dilutions must you perform in order to arrive at the desired result? You should not dilute by more than a factor of 100 in any step.

Solution

We can here first use the formula of V1C1 = V2C2 to estimate the amount of volume we need to add to dilute our given mixture of 10 ml .

here V1 = 10 ml, C1 = 6.7 x 10^9 cells.

also V2 = unknown and C2 should be 100 or less.

therefore on equating we get:

V2 = 10 x 6.7 x 10^9 / 100

V2 = 6.7 x 10^8 ml

therefore it means that we need to add 6.7 x 10^8 ml of water in order to dilute it this much,

if we dilute our solution 10^8 times, then we would get 67 cells. that is if we rewrite the formula with the aim of getting 67 cells. then

V2 = 10 X 6.7 X 10^9 / 67

V2 = 1 x 10^8 ml

therefore now we need to do serial dilutions.

we take 1 ml from our 10 ml test tube and add it in 9 ml of water. the first step will give us 1/10th concentration of original tube. this is known as 1/10 or 10^1 dilution. when we again take 1 ml from this test tube and add it to 9 ml of water, it would give us 1/100 or 10^2 dilution. we need to do the same thing total 8 times in order to get 1/100000000 or 10^8 dilution .