Chemistry - Is it possible to achieve a level of "truly zero" concentration?
Solution 1:
It depends how you dilute it. If you take an aqueous solution of A and just add pure water (absolutely 100% water), the concentration of A will never quite be null. In this case however, you will reach a point where the concentration of A is so small that it can be considered null for your applications.
If, however, you dilute the solution, take a sample, then dilute that sample (and so on), you could reach a concentration of exactly 0M. Imagine you have diluted the solution enough so that it contains exactly 1 molecule of A. When you take your sample for the next dilution, if this molecule isn't in the sample, the concentration will be exactly null. If it does happen to be in the sample, it could be left behind when you draw the next sample, or the next, and so on.
In practice though, the water you use for the dilution will likely contain impurities. You will maybe not achieve exactly 0M, but the concentration could be so small that it is undetectable and have no measurable consequence.
Solution 2:
For an analytical chemist, the concept of zero concentration does not exist. The concentration cannot be exactly 0! Only a limit of detection can be developed in terms of statistics. This is why a senior respectable user here has written an entire monograph on this topic. Suppose you have a NaCl solution, and so called "pure water"*, matter how much you dilutions you perform, you cannot say with 100% confidence that there is no single ion sodium left in the solution now.
*Pure water cannot exist in any ordinary laboratory.
Solution 3:
Unequivocally yes! If your solute is something of which you can identify a single molecule in a macroscopic solvent sample (let´s say a fluorescent dye), then you can dilute down to zero, and be sure about it.
(For the nitpickers: This can be done in a finite number of steps, if you split the solution in two after each step, and keep diluting the part which shows a lower concentration. Divide et impera.)
If you´re unable to measure the concentration down to actual zero, then the statement "this has been diluted to zero" is not falsifiable, therefore unscientific (see Karl Popper), and as such not worth pondering. ;)
Solution 4:
Something like a zero concentration is achieved in the vapor phase in some materials. In this answer the triple-point vapor pressure of gallium is identified as so low that a measurement thereof defaults to zero with a high probability.
Solution 5:
Hypothetically, I think limitation for zero-dilution would be when you take a sample of diluted sample the possibility of having a solute molecule in there should be zero. To achieve this goal, the concentration of your solution should be less than $10^{-24}$ in power $\left(\frac{1}{6.022 \times 10^{23}}=1.66 \times 10^{-24}\right)$. To do so, if you have $\pu{1 M}$ of solution, you should add another $\pu{1.66 \times 10^{24} L}$ of water to get that dilution. Considering the whole water body of the Earth is about $\pu{1.3859 \times 10^{21} L}$ ($\pu{2.5511 \times 10^6 mile^3}$ according to USGS) you may run out of water before you get right concentration.:-)
That's why Raphaël has said its depends on how you want to do it. So, you may use the procedure called serieal dilution.