Why does the air pressure not increase when I shake a coke bottle? I tried this experiment lately and this happened, I shook a coke bottle and its air pressure remained the same but the coke came squirting out when I opened the lid. How is this possible?
 A: Shaking the container distributes small bubbles through the liquid. These act as nucleation points at which the dissolved CO2 can boil out of the solution, much like how water in a steel pan will start to boil at places where the pan is scratched. If the pressure in the container is lower than the vapor pressure of the CO2 still in solution, pressure will increase up to the vapor pressure rapidly as CO2 boils out quickly at the distributed nucleation points, rather than continuing its slow process of evaporating out through the surface. If, however, the pressure in the container is already higher than the vapor pressure, pressure will not increase much. In either case, the pressure inside the container only affects the degree to which the soda will froth up insofar as it increases the maximum amount of CO2 that can be dissolved in the solution. The concentration of CO2 in solution and the availability of nucleation points are the primary factors in "fizziness".
A: The soda is bottled with supersaturated CO$_2$.  The vapor pressure of this liquid is well above atmospheric pressure.  With the small head space and the bottled sealed, the pressure in the bottle will rise to this value.  At that point the CO$_2$ is in equilibrium between gas and dissolved.  You can measure the pressure at this point and usually find it between 2.5 and 3.5 atm.  Because it is at equilibrium, shaking it up (unless you do so long enough to raise the temperature) isn't going to affect the pressure.
That probably leads to the question of why you can open a can of soda without problem, but opening a shaken can causes such trouble.
When you open a normal bottle of soda, this elevated pressure is removed, but the gas can't leave the soda quickly.
One way to think of it is that the gas dissolved in the liquid is like water behind a dam.  The pressure of the water wants to force it out.  But if there's only a single small pipe, the water will drain slowly and calmly.  A normal bottle of soda might take a few hours to remove most of the gas.
When you shake the soda, you form nucleation sites for the gas to more easily leave the soda.  It's as if you've opened many, many more pipes.  Now the pressure is sufficient to push a huge amount of water.
In both situations the pressure is the same.  The difference is in the increase in the area where the pressure can do work.
