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Can vapour pressure happen in an enclosed container with liquid at normal conditions?

I guess the answer is yes, but I don't understand why some liquid on the liquid surface may process sufficient kinetic energy to escape into gas phase.

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Yes, there is vapour pressure in a closed container.

The molecules in a liquid or gas don't all have the same energy: some have a little, other have a lot. There is a distribution formula in thermodynamics to describe that range of energies (in ideal gases its is called the Maxwell-Boltzmann distribution; liquids are a bit more complicated). The average energy of a molecule in a liquid isn't enough to get a molecule into the gas phase, but a proportion of the molecules have higher energies than that and they will have enough energy to escape the liquid phase.

The same is true for the molecules in the vapour, but in reverse. Some of them don't have enough energy to be in the vapour phase and they will end up back in the liquid. In equilibrium the number of molecules leaving the liquid equal those returning to it.

As temperature rises, a higher proportion of the molecules in the liquid have enough energy to escape and the vapour pressure rises.

The key to understanding this is realising that the average energy of the molecules is not representative of all the molecules. In reality energy is distributed unevenly with some molecules having more and other having less. When you realise this, there is no mystery why some have enough to escape the liquid.

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The kinetic theory of gases is based on the idea that particles are moving randomly. Even if all particles started motion with exactly the same speed, as they interact with each other and the walls of the container their velocities would become randomized. The kinetic energy of particles at a given temperature is an average; some particles are moving much faster, and can escape from a liquid. These faster-moving particles, removed from the liquid, leave the liquid a bit cooler. Thus, evaporation puts a liquid into a gas and chills the liquid.

For a more complete explanation, see this video.

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