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Of course the CO2 comes out of the liquid, and it will even build up a lot of pressure if needed. The question is what happens at a molecular level to cause it to leave the liquid?

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The tangy taste of sodas comes from an acid in them. In most sodas, it's carbonic acid: ${\rm H}_2{\rm CO}_3$. Under pressure, like in a sealed can of soda at room temperature and usual pressure, the equilibrium reached keeps this molecule together. Once you open the can of soda, the lowered pressure inside the can "allows" this molecule to break apart into ${\rm H}_2{\rm O}$ and ${\rm CO}_2$. This is where the carbon dioxide bubbles come from. When you open a can, there is still the issue of how fast this reaction happens. If you've shaken it, you move some of the gas at the top of the can into little bubbles stuck to the sides. This primes the process for the carbonic acid to break down once the pressure is released. Essentially, it's already begun the formation of the bubbles, and that makes it easier for them to grow enough that they can detach and rise to the surface. This isn't always easy. If you've ever watched a simmer pot of water, you'll notice sometimes bubbles form at the bottom and then shrink and go away again. The opposite can happen too. Soda bubbles tend to get bigger as they rise as they pick up more ${\rm CO}_2$ from the carbonic acid in the surrounding liquid. So the rate depends on a number of things, but shaking helps the bubbles form.

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