# Can someone help me with this serial dilution?

Asked by Mr_Saturn512 (466) May 31st, 2013

The stock solution of DNA that I have is 500 ug/mL (micrograms per milliliter) I want that first in nanograms per microliter instead (ng/uL) I assume it’s 5,000ng/uL, right?

Now, from THAT stock solution, I want to eventually make a 100uL solution of 75ng/uL DNA. I need to make a dilution factor but I’m blanking out. It was easier when I had to make 5ng/uL. All I had to do was pipette 10uL from the stock and mix with 90uL of the buffer I’m using and then do the same thing to that again to get it down to 5ng/uL. (So two 1:10 dilutions) But since this is 75ng/uL now, I’m just having trouble applying what I know to this.

I’m aware there are several ways to do this. Such as just making a 5ng/uL solution and pipetting enough to make it 75ng/uL. But I would preferably need a shorter way to reduce pipetting error.

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## 5 Answers

Use conversion factors and let the units do the work for you.

500 ug/mL * 1000 ng/ug * .001 mL/uL

Note that ug and mL cancel and you’re left with ng/uL. The 1000 and .001 also cancel and you’re left with the original magnitude of 500.

For your dilution, you want:

500 ng/uL * x = 75 ng/uL
x = 500/75 = 6.67, which means you have to add 6.67 times the amount of liquid already present in order to dilute it down to the right molarity.

Does that help?

Mariah (23244)

Ahhhh, I see now. That was easier than I thought.

So all I need to do is add 6.67uL of the DNA stock solution to 93.33uL of buffer to make 100uL of a 75ng/uL DNA solution, right?

So if I also want to make a 25ng/uL solution I would just do 500/25 which is 20——wait, that doesn’t make sense. 20uL of 500ng/uL doesn’t sound right. It should be a lot less than the previous one.

Regarding your middle paragraph, no not quite. You need some of your solution plus an amount of buffer 6.67 times larger that, in total, add up to 100:

x + 6.67x = 100
7.67x = 100
x = 100/7.67 = about 13 uL of DNA solution, and 87 uL of buffer.

I’d wait for a second person to come and check my work, I did this all in a hurry.

Mariah (23244)

Oh jeez I’m sorry, I just noticed x should have been 75/500 not 500/75. If possible you should fix my error, otherwise I will come back when I have time and do it.

Mariah (23244)

OK I’m back and have some more time. Sorry about the convoluted way I went about this before, there is a more straight-forward way that I had forgotten. It’s been a few years since I took any chemistry.

The dilution equation is:

MiVi = MfVf

Where M is molarity, V is volume, the i subscript means initial, f subscript means final.

So you have Mi of 500, Mf of 75, Vf of 100, and you want to find Vi.

500Vi = 7500
Vi = 15, meaning you use 15 uL of your DNA solution and the remainder of the 100 uL (85 uL) should be buffer.

Mariah (23244)

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