Question

Question #a673e

Answer 1

Here's what I got.

Explanation:

For starters, I think that there's a typo in your question. Instead of `"5 nM"` stock solution, I think that you should have `"5 mM"` stock solution.

I say this because a `"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 `"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.

`color(blue)(ul(color(black)("1:20 dilution " implies V_"diluted" = 20 * V_"stock")))`

In your case, a `"5-nM"` stock solution will contain `"5 nmoles"` of solute for every `"1 L"` of solution.

To make the calculations easier, pick a `"1-L"` sample of stock solution. After you perform the `1:20` dilution, the total volume of the stock solution will be

`V_"diluted" = 20 * "1 L" = "20 L"`

So if `"20 L"` of diluted solution contain `"5 nmoles"` of solute, you can say that `"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 `"0.25 nmoles"` of solute for every `"1 L"` of solution, which is equivalent to saying that the solution has a concentration of `"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 `"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 `"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) `"250 nmol/mL"`.