5 ms·

I'm very interested in seeing that proof.

deleted 10y ago
[deleted]
paulmd 10y ago
> The concentrations of reactants and products in an equilibrium mixture are determined by the analytical concentrations of the reagents (A and B or C and D) and the equilibrium constant, K. The magnitude of the equilibrium constant depends on the Gibbs free energy change for the reaction.[2] So, when the free energy change is large (more than about 30 kJ mol−1), then the equilibrium constant is large (log K > 3) and the concentrations of the reactants at equilibrium are very small. Such a reaction is sometimes considered to be an irreversible reaction, although in reality small amounts of the reactants are still expected to be present in the reacting system. A truly irreversible chemical reaction is usually achieved when one of the products exits the reacting system, for example, as does carbon dioxide (volatile) in the reaction https://en.wikipedia.org/wiki/Reversible_reaction https://en.wikipedia.org/wiki/Reversible_reaction Assuming you do not outright lose some reactants from the system, the reverse reaction is still occurring. However, because the reaction constant is so small, the resulting product is highly probable to essentially immediately undergo the forward reaction. However, it will still be present in some equilibrium - just an incredibly low one, in the ratio of the reaction rate coefficients. You'll have 10^14 times as much of the forward reaction, or whatever.
- euyyn 10y ago
  Chemical reactions, ignoring those with nuclear interactions, are only bound by the law of conservation of energy and the decrease of entropy. A chemist looks at them in the macro scale, in which macroscopic properties like temperature and pressure are set, and thus each molecule's energy isn't a fixed value (instead being taken off a set, according to Maxwell's probability distribution). This, and the probabilistic nature of the law of entropy, leads to all allowed reactions happening somewhere at the micro scale, even if extremely rarely. If you look at the micro scale, though, and instead of having a soup of molecules you deal with single molecules, whether a reaction is possible or not isn't a probabilistic thing anymore. The energies your molecules have are actual numbers, and if they don't add up, you won't have a reaction.
  - paulmd 10y ago
    And what if there is a micro-scale reversal of entropy, as I previously mentioned? Let's say a collision of two electrons, or an electron with a surrounding gas molecule, that results in a sudden increase in orbital energy of an electron (plus another particle losing all its energy of course). Vanishingly unlikely of course, but with an uncountable number of collisions occurring every instant it will occur somewhere, sometime. You say that it's "observable" with single-particle experiments. Are you sure you've performed enough of those experiments to unconditionally guarantee that such situations will never under any circumstances occur? As an example of how you can be wrong on this: since the 1940s, Bi-209 was believed to be a stable element. However, recent research has actually determined that it is very slightly unstable - with a half life of approximately 4.6 x 10^19 years. That's more than one billion times the current estimated age of the universe. It's not stable at all, it just had unmeasurably low amounts of instability. If you sat around looking at a single-molecule sample of that reaction, you would see absolutely nothing - unless you had a few trillion years to sit around. That particular experiment doesn't exhibit the behavior you're trying to model. It's like saying that because Newton's Laws Of Motion adequately explain everything on Earth, they could never be superceded by General Relativity. I don't accept that other physical reactions categorically cannot occur at similarly improbable rates. The decay of smaller "stable" atoms, for example, may occur with a half-life of 10^100 or 10^1000 years that is simply beyond our current ability to measure. With a sufficient number of simulations you can come up all-heads any arbitrary number of times that you want to name. You can even roll a perfect 20 on a D20 any number of times. Even something like spontaneous fission is theoretically possible - it's just vanishingly unlikely.
    - euyyn 10y ago
      > And what if there is a micro-scale reversal of entropy, as I previously mentioned? Let's say a collision of two electrons, or an electron with a surrounding gas molecule, that results in a sudden increase in orbital energy of an electron (plus another particle losing all its energy of course). Vanishingly unlikely of course, but with an uncountable number of collisions occurring every instant it will occur somewhere, sometime. Sorry, I'm not sure what you mean by this. > You say that it's "observable" with single-particle experiments. Are you sure you've performed enough of those experiments to unconditionally guarantee that such situations will never under any circumstances occur? I said (in the other reply) it's observable "to the best of our measuring ability" (repetitions, and energy), precisely because we'll never reach 100% certainty. But your wrong claim wasn't "things that we don't know yet might be happening", rather "all particle interactions imaginable are happening all the time, just with a small probability". The former is tautologically true. The latter is just pseudoscience, as it is: 1. Unfalsifiable: the more we keep measuring that only some interactions happen in Nature, the further you'd just push that small probability. 2. Without predictive power. It's not like superseding Newton's laws of motion with GR. It's like saying "beyond the speeds and masses we've observed, objects are free from any laws of motion whatsoever". And furthermore adding that it can be proved. And that's only for laws like conservation of quark and lepton numbers. For conservation of energy and momentum, the prohibition is much stronger: Noether proved mathematically that they're another way of saying the laws of Nature are the same today than yesterday, and the same here than a meter away. Claiming they're being broken all the time is the same as saying the laws of physics are different all over the place, and from one moment to the next. The slightest evidence or proof of something of the sort, and we pretty much start all physics from scratch :)

deleted 10y ago

[deleted]

> The concentrations of reactants and products in an equilibrium mixture are determined by the analytical concentrations of the reagents (A and B or C and D) and the equilibrium constant, K. The magnitude of the equilibrium constant depends on the Gibbs free energy change for the reaction.[2] So, when the free energy change is large (more than about 30 kJ mol−1), then the equilibrium constant is large (log K > 3) and the concentrations of the reactants at equilibrium are very small. Such a reaction is sometimes considered to be an irreversible reaction, although in reality small amounts of the reactants are still expected to be present in the reacting system. A truly irreversible chemical reaction is usually achieved when one of the products exits the reacting system, for example, as does carbon dioxide (volatile) in the reaction https://en.wikipedia.org/wiki/Reversible_reaction https://en.wikipedia.org/wiki/Reversible_reaction Assuming you do not outright lose some reactants from the system, the reverse reaction is still occurring. However, because the reaction constant is so small, the resulting product is highly probable to essentially immediately undergo the forward reaction. However, it will still be present in some equilibrium - just an incredibly low one, in the ratio of the reaction rate coefficients. You'll have 10^14 times as much of the forward reaction, or whatever.

euyyn 10y ago
Chemical reactions, ignoring those with nuclear interactions, are only bound by the law of conservation of energy and the decrease of entropy. A chemist looks at them in the macro scale, in which macroscopic properties like temperature and pressure are set, and thus each molecule's energy isn't a fixed value (instead being taken off a set, according to Maxwell's probability distribution). This, and the probabilistic nature of the law of entropy, leads to all allowed reactions happening somewhere at the micro scale, even if extremely rarely. If you look at the micro scale, though, and instead of having a soup of molecules you deal with single molecules, whether a reaction is possible or not isn't a probabilistic thing anymore. The energies your molecules have are actual numbers, and if they don't add up, you won't have a reaction.
- paulmd 10y ago
  And what if there is a micro-scale reversal of entropy, as I previously mentioned? Let's say a collision of two electrons, or an electron with a surrounding gas molecule, that results in a sudden increase in orbital energy of an electron (plus another particle losing all its energy of course). Vanishingly unlikely of course, but with an uncountable number of collisions occurring every instant it will occur somewhere, sometime. You say that it's "observable" with single-particle experiments. Are you sure you've performed enough of those experiments to unconditionally guarantee that such situations will never under any circumstances occur? As an example of how you can be wrong on this: since the 1940s, Bi-209 was believed to be a stable element. However, recent research has actually determined that it is very slightly unstable - with a half life of approximately 4.6 x 10^19 years. That's more than one billion times the current estimated age of the universe. It's not stable at all, it just had unmeasurably low amounts of instability. If you sat around looking at a single-molecule sample of that reaction, you would see absolutely nothing - unless you had a few trillion years to sit around. That particular experiment doesn't exhibit the behavior you're trying to model. It's like saying that because Newton's Laws Of Motion adequately explain everything on Earth, they could never be superceded by General Relativity. I don't accept that other physical reactions categorically cannot occur at similarly improbable rates. The decay of smaller "stable" atoms, for example, may occur with a half-life of 10^100 or 10^1000 years that is simply beyond our current ability to measure. With a sufficient number of simulations you can come up all-heads any arbitrary number of times that you want to name. You can even roll a perfect 20 on a D20 any number of times. Even something like spontaneous fission is theoretically possible - it's just vanishingly unlikely.
  - euyyn 10y ago
    > And what if there is a micro-scale reversal of entropy, as I previously mentioned? Let's say a collision of two electrons, or an electron with a surrounding gas molecule, that results in a sudden increase in orbital energy of an electron (plus another particle losing all its energy of course). Vanishingly unlikely of course, but with an uncountable number of collisions occurring every instant it will occur somewhere, sometime. Sorry, I'm not sure what you mean by this. > You say that it's "observable" with single-particle experiments. Are you sure you've performed enough of those experiments to unconditionally guarantee that such situations will never under any circumstances occur? I said (in the other reply) it's observable "to the best of our measuring ability" (repetitions, and energy), precisely because we'll never reach 100% certainty. But your wrong claim wasn't "things that we don't know yet might be happening", rather "all particle interactions imaginable are happening all the time, just with a small probability". The former is tautologically true. The latter is just pseudoscience, as it is: 1. Unfalsifiable: the more we keep measuring that only some interactions happen in Nature, the further you'd just push that small probability. 2. Without predictive power. It's not like superseding Newton's laws of motion with GR. It's like saying "beyond the speeds and masses we've observed, objects are free from any laws of motion whatsoever". And furthermore adding that it can be proved. And that's only for laws like conservation of quark and lepton numbers. For conservation of energy and momentum, the prohibition is much stronger: Noether proved mathematically that they're another way of saying the laws of Nature are the same today than yesterday, and the same here than a meter away. Claiming they're being broken all the time is the same as saying the laws of physics are different all over the place, and from one moment to the next. The slightest evidence or proof of something of the sort, and we pretty much start all physics from scratch :)