[james_sch1]

I have the following initial concentration of 5mg/ml EtOH. Suppose I take 30uL out of that sample and mix it with 30uL of EtOH. Then I take 30uL out of that sample and put it in another tube containing 30uL of EtOH and so on...

Just to confirm: I'm I halving the concentration each time right? So it would be 5mg/mL, 2.5 mg/mL, 1.25 mg/mL etc

[opti384]

I just have some questions. I don't get what "uL" is and also aren't concentrations usually in molar, molal , or percent concentration? Just wondering.

[nigel433]

No. You are increasing the concentration. If you said you
were putting the sample into an equal volume of water
(which I assume is your solvent) you would be decreasing
the concentration.

Also, no you are not exactly halving; because to halve it
you would need to add the amount of solvent which is
IN your solution.

[Doc Oc]

uL = microliters.  Different fields (or even people) talk about concentrations in different ways, and mg/mL is not uncommon.

Also, no, taking a small amount out does not increase the concentration unless you're evaporating the solvent.  Otherwise the ratio of solute/solvent is exactly the same.  Evaporating the solvent increases the concentration, diluting it in solvent decreases the concentration.

With regard to the original question, the first dilution is the key, and you didn't specify how much you started with.  If you started with 60 uL of a 5 mg/mL solution and then took 30 uL to dilute with 30 uL of EtOH, THEN you're cutting the concentration in half.  However, if you have 1 mL of a 5 mg/mL solution and take 30 uL, you're getting 1.5 mg out rather than 2.5.  But your formula for the remaining dilutions is correct.

[sjb]

Also, no, taking a small amount out does not increase the concentration unless you're evaporating the solvent.  Otherwise the ratio of solute/solvent is exactly the same.  Evaporating the solvent increases the concentration, diluting it in solvent decreases the concentration.

With regard to the original question, the first dilution is the key, and you didn't specify how much you started with.  If you started with 60 uL of a 5 mg/mL solution and then took 30 uL to dilute with 30 uL of EtOH, THEN you're cutting the concentration in half.  However, if you have 1 mL of a 5 mg/mL solution and take 30 uL, you're getting 1.5 mg out rather than 2.5.  But your formula for the remaining dilutions is correct.

True, but is not the original solution a solution of ethanol in some unspecified other solvent?

That's the way I, and I think nigel433 are reading the question. In which case the concentration of the original solvent is decreasing, but the concentration of ethanol is actually increasing?

[Doc Oc]

First, I made a mistake in my calculation and was off by a full order of magnitude, taking 30 uL of a 5 mg/mL solution would yield 0.15 mg solute, not 1.5.

sjb, I see what you're saying.  I assumed the OP had dissolved something in EtOH to make the 5 mg/mL solution in EtOH.  However, if it's 5 mg/mL of EtOH in something else then yes, Nigel is correct.  I guess the OP needs to make some clarifications.