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Lets say a liquid and gas above are in equilibrium.

(1) Now if I suddenly increase the pressure of the gas it will take some time for some molecules of the gas to enter the liquid and get dissolved. When its finally done and equilibrium is reached shouldn't the pressure of the gas be a little lesser?

(2) Conversely if I violently shake a carbonated water bottle shouldn't the pressure increase a tiny little bit?

  • In many sources I have read that the pressure doesn't change at all when shaking. It does increase a little bit because of the energy we are giving while shaking.

What I want to know is a detailed explanation of the above two main questions.

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    $\begingroup$ Are you asking about obvious facts you mention, or some sources you vaguely mention, that are either wrong, or you misunderstood their meaning - probably about equilibrium vapor pressure, which is constant? $\endgroup$
    – Mithoron
    May 21, 2020 at 22:48
  • $\begingroup$ Is the new equilibrium established instantly when i increase the pressure of the gas above the liquid which was already in equilibrium @Mithoron $\endgroup$
    – Shyam
    May 21, 2020 at 22:52
  • $\begingroup$ My question first. $\endgroup$
    – Mithoron
    May 21, 2020 at 22:55
  • $\begingroup$ Do you know that there are fluctuations if you see in micro scales? Your equilibrium is undergoing fluctuations. I am asking that if I suddenly change the pressure above the liquid from say 2units to 4 units in my measuring scale, it must take some time for some molecules to get into the liquid and dissolve. That will lower the concentration of gas above the liquid be it very small. And so shoudnt the final pressure be a bit lesser than 4 units @Mithoron $\endgroup$
    – Shyam
    May 21, 2020 at 23:03
  • $\begingroup$ Are you taking about liquid vapor pressure or pressure by air above the surface. Your vessel should be closed (constant volume) to make this any sense. $\endgroup$
    – Mathew Mahindaratne
    May 21, 2020 at 23:21

2 Answers 2

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1) If you induce a sudden chance in pressure you will indeed take the system out of equilibrium. Lets consider a closed recipient containing some liquid and some gas above. If you suddenly inject more gas into the recipient, the gas pressure is initially going to raise fast and then going to decrease slowly while part of the gas is dissolving, until the system reaches equilibrium again. However, this new equilibrium will have a higher gas pressure AND greater amount of gas dissolved in the liquid when compared to the initial equilibrium. Of the amount of gas you injected part will be dissolved and part will stay above the liquid, contributing to the higher gas pressure. It makes no sense to have pressure under the initial value, this would only be possible if the system hadn't been at equilibrium at the start.

2) Shaking doesn't increase the pressure, unless you shake the bottle long enough to cause a considerable increase in the temperature inside, but that would be quite an impressive amount of shaking. If you could take the system out of equilibrium by releasing some of the dissolved gas from the liquid phase, then that would increase the pressure, but shaking doesn't accomplish that, and I believe it wouldn't be possible to shift a system out of equilibrium like that without transference of matter or heat and without a change in volume or temperature.

There is a very interesting video by Veritasium on youtube about this bottle issue, I recommend you to watch it: https://www.youtube.com/watch?v=K-Fc08X56R0&t=3s

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Why should decrease when it does decrease ?

The gas with liquid vapour, previously in equilibrium with liquid, with suddenly increased pressure:

  • Vapour gets over-saturated and condenses until the saturated vapour pressure is reached again.
  • Gas starts dissolving and gas partial pressure decreases, until the new equilibrium between its partial pressure and it's molar fraction in liquid is achieved ( Henry's law ).
  • The kinetics of both processes is about exponential, asymptotically reaching new values of pressures.

Suddenly opened still and shaked carbonised drink bottles:

  • Shaking the bottle increases its temperature and equilibrium gas pressure by conversion of mechanical energy to thermal one via friction. But the increase is very light and can be neglected for very most cases. Definitely for the difference in visual effects after opening.
  • Shaking itself does not increase equilibrium nor current pressure. But it does one essential thing. It creates inner liquid-gas contact surface where $\ce{CO2}$ can evolve when pressure suddenly drops.
  • If pressure in a standing still bottle ( without bubbles ) suddenly drops, liquid gets suddenly over-saturated, but waits for a trigger to burst. Within the volume, gas had no seed where bubbles can grow. See the related Bubble chamber The only gas formation is at liquid surface, that does not lead to visible effects.
  • If previously shaken, there are already miriads of bubbles that rapidly start growing, leading to violent gas formation.
  • So it is all rather about the different kinetics.
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