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A Polymerase Chain Reaction (PCR) is a method of amplification which enables one to produce many copies of a certain DNA/RNA strand for many applications (as described in the link above).

I have never seen the actual process and the resulting PCR solution, but according to Wikipedia, the volume of the solution is of the micro- to milliliter magnitude.

I was wondering: if this process were allowed to continue on and on, while supplying all necessary nucleotides and other materials, to the magnitude of, say, liters - could we end up with a tangible mass of DNA/RNA?
In other words, will we be able to extract from the solution a solid mass of DNA/RNA that is visible to the naked eye? If yes, can we predict the physical characteristics of such mass?

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PCR amplifies only DNA not RNA.

A PCR reaction is typically within the micro liter volume, and can go down to the nano liter volume for qPCR. The maximum volume of a PCR tube is 200 microliters. The maximum volume a 96 well thermocycler can handle per well is usually 100 microliters. So the maximum amount of reagent volume one thermocycler can handle at a time us 9.6ml

I have never seen anybody scale a PCR to mili liter volume, as that would be rather expensive and excessive.

However if some some reason, somebody did do as you say, yes it is possible to obtain visible quantities of DNA. (Removal of impurities would be required first... ie unreacted dNTP, primers) And given that we can obtain visible quantities of DNA by extracting DNA from bacteria or salmon sperm.. I am sure a chemist somewhere would be able predict the physical properties of that DNA mass.

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    $\begingroup$ PCR on a milliliter scale can be useful e.g. for use as a template for large-scale in vitro RNA transcription. It's not the most common use for PCR, though. $\endgroup$
    – Mad Scientist
    Commented Apr 26, 2017 at 11:18
  • $\begingroup$ Presumably, if we were to go through N PCR cycles and start with a few dozen litres of solution, I don't see any reason why there's be a limit to the amount of DNA PCR can produce. The limitation is only in the size of the machines available in the market, not in the underlying chemistry. $\endgroup$
    – terdon
    Commented Apr 26, 2017 at 11:25
  • $\begingroup$ aside from machine limits, other limits are also present.. pyrophosphophate (PP) that produced went dNTP are polymerised is an inhibitor to polymerase enzyme.. Repeated heating will cause deamination of cytosine to form uracil. $\endgroup$
    – JayCkat
    Commented Apr 27, 2017 at 2:03

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