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If you look at the concentration verses time graph of typical reactions, you can see that the concentration of reactants and products, when time goes towards infinity, becomes the equilibrium concentration. But! It never seems to reach that concentration (it converges towards that , but never reaches it). Which means that there is no 'real equilibrium??

I think this is true in terms of theory, where the number of molecules is considered to be infinite, while in reality, the number of molecule is finite. Then, in reality, it reaches equilibrium??

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  • $\begingroup$ Equilibrium is based on the speed of the forward and backward reactions. When the backwards and forwards are equal,there is basically no product being made (Net products that is). If you theoretically had infinite reactants, that means the forward reaction would always be at the highest is could possibly be, and it would never decreased, so it would never reach equilibrium. $\endgroup$ – Noel Aug 8 '16 at 9:12
  • $\begingroup$ The thing is, yes THEOCRATICALLY it can never reach equilibrium, but, in the graph of concentration verses time graph, when t is very very large, it is ALMOST close to the equilibrium state. But if that much difference in concentration is smaller than the concentration difference that can be achieved by a single molecule, then could we say that it reached equilibrium? $\endgroup$ – Danny Han Aug 8 '16 at 11:33
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Yes there is actual equilibrium. The Achilles and the turtle kind of argument fails for three reasons, one of which you mentioned yourself:

  1. Like you said, the number of molecules is finite, so the matter is not infinitely divisible; there must be a limit.
  2. More importantly, nobody really cares about one molecule. Anyway, it's not like the system is going to hit just the right number with one-molecule precision. No, there are going to be mighty fluctuations involving millions of molecules, and they never stop (that is, unless you freeze the system down to absolute zero, in which case reaching the equilibrium may indeed become problematic). Like anything with molecules, equilibrium is a statistical thing, and once we're within certain error margin from the theoretical figure, we might just as well consider the goal achieved.
  3. We may circumvent the argument altogether by playing with the conditions. Say, we want to get a saturated solution of some salt in water, and it just seems to take forever. But wait, what if we just heat the thing up a bit (which would make the solubility go up), dissolve the exact amount we need, and then cool it down again? Here is your saturated solution in a finite time. You may even make it supersaturated if you'd like.
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