Question

1. you wish to count the number of bacteria in 1 ml of a solution but there are too many to count! so you mix the 1 ml with 9 ml of water to dilute it, and then draw 1 ml of the new mixture. still too many, so you now mix with 9 ml of water and draw 1 ml of this new solution and now count 75 nasty little bacteria swimming around. how many bacteria are in the original solution? ( c_1cdot v_1 = c_2cdot v_2 )

Explanation:

Step1: Calculate the dilution factor for the first dilution

The first dilution: \(V_1 = 1\space ml\), \(V_2=1 + 9=10\space ml\). Using the formula \(C_1V_1 = C_2V_2\), the dilution factor \(D_1=\frac{V_2}{V_1}=\frac{10}{1} = 10\)

Step2: Calculate the dilution factor for the second dilution

The second dilution: \(V_1'=1\space ml\) (from the first - diluted solution), \(V_2'=1 + 9 = 10\space ml\). The dilution factor \(D_2=\frac{V_2'}{V_1'}=\frac{10}{1}=10\)

Step3: Calculate the total dilution factor

The total dilution factor \(D = D_1\times D_2=10\times10 = 100\)

Step4: Calculate the number of bacteria in the original solution

If the number of bacteria in the final \(1 - ml\) sample is \(n = 75\), and the total dilution factor is \(D = 100\), then the number of bacteria in the original \(1 - ml\) solution \(N=n\times D\)

\(N=75\times100\)

Answer:

7500