Question #a673e

1 Answer
Aug 14, 2017

Answer:

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"#.