# Question a673e

Aug 14, 2017

Here's what I got.

#### Explanation:

For starters, I think that there's a typo in your question. Instead of $\text{5 nM}$ stock solution, I think that you should have $\text{5 mM}$ stock solution.

I say this because a $\text{5-nM}$ stock solution would not produce any of the possible answers provided to you.

Let's assume that you are indeed working with a $\text{5-nM}$ stock solution. A $1 : 20$ dilution implies that you take $1$ part of stock solution and add $19$ parts of water to get a total volume of diluted solution equal to $20$ times that of the stock solution.

$\textcolor{b l u e}{\underline{\textcolor{b l a c k}{\text{1:20 dilution " implies V_"diluted" = 20 * V_"stock}}}}$

In your case, a $\text{5-nM}$ stock solution will contain $\text{5 nmoles}$ of solute for every $\text{1 L}$ of solution.

To make the calculations easier, pick a $\text{1-L}$ sample of stock solution. After you perform the $1 : 20$ dilution, the total volume of the stock solution will be

${V}_{\text{diluted" = 20 * "1 L" = "20 L}}$

So if $\text{20 L}$ of diluted solution contain $\text{5 nmoles}$ of solute, you can say that $\text{1 L}$ of diluted solution will contain

1 color(red)(cancel(color(black)("L diluted solution"))) * "5 nmoles solute"/(20color(red)(cancel(color(black)("L diluted solution")))) = "0.25 nmoles solute"

So this solution contains $\text{0.25 nmoles}$ of solute for every $\text{1 L}$ of solution, which is equivalent to saying that the solution has a concentration of $\text{0.25 nM}$.

You can play around with this value a bit to convince yourself that none of the possible answers match.

Now, look what happens with a $\text{5-mM}$ stock solution. This time, you have

1 color(red)(cancel(color(black)("L diluted solution"))) * "5 mmoles solute"/(20color(red)(cancel(color(black)("L diluted solution")))) = "0.25 mmoles solute"

The diluted solution would thus have a concentration of $\text{0.25 mM}$, which is equivalent to

(0.25 color(red)(cancel(color(black)("mmoles"))))/(1color(red)(cancel(color(black)("L")))) * (1color(red)(cancel(color(black)("L"))))/(10^3color(white)(.)"mL") * (1color(red)(cancel(color(black)("mole"))))/(10^3color(red)(cancel(color(black)("mmoles")))) * (10^9color(white)(.)"nmoles")/(1color(red)(cancel(color(black)("mole")))) = "250 nmoles/mL"#

In this case, the answer would be (b) $\text{250 nmol/mL}$.