# Question 1037e

Nov 18, 2015

Here's what I got.

#### Explanation:

You would pick a sample of the stock solution and dilute it.

For example, let's say that you start with a $\text{100.0-mL}$ sample of the stock solution. This solution would contain

100.0color(red)(cancel(color(black)("mL"))) * (4.5 * 10^8"cells")/(1color(red)(cancel(color(black)("mL")))) = 4.5 * 10^(10)"cells"

Now, when you're diluting this solution, you're essentially keeping the number of cells constant and changing the volume of the solution.

The concentration of the cells will change not because the number of cells change, but because the volume of the solution changes.

So, what volume would you need to have in order for $4.5 \cdot {10}^{10}$ cells to represent a concentration of $4.5 \cdot {10}^{4}$ cells per mililiter?

4.5 * 10^10color(red)(cancel(color(black)("cells"))) * "1 mL"/(4.5 * 10^4color(red)(cancel(color(black)("cells")))) = 10^6"mL"

This means that you must add enough water to your initial $\text{100.0-mL}$ sample to make the total volume of the solution equal to ${10}^{6} \text{mL}$.

SIDE NOTE To make the calculations a little easier, pick an original sample of $\text{1.00-mL}$. You would have $4.5 \cdot {10}^{8}$ cells in this sample. The volume of the final sample would be

4.5 * 10^8color(red)(cancel(color(black)("cells"))) * "1 mL"/(4.5 * 10^4color(red)(cancel(color(black)("cells")))) = 10^4"mL"#

Therefore, you must add enough water to the original $\text{1.00-mL}$ sample to make the total volume equal to ${10}^{4} \text{mL" = "10 L}$.