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When we increase the temperature of water in an open container, the vapour pressure increases.But boiling (phase transition at constant temperature and pressure) occurs only when the vapour pressure equals atmospheric pressure.My understanding is, till that point the atmosphere can hold the water vapour like a cover or lid but when equilibrium partial pressure of water vapour(vapour pressure) tries to increase beyond atmospheric pressure, the atmosphere cant hold the vapour and boiling starts.Is this right?

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The molecules in the liquid phase are more confined than in the vapor phase.Temperature and molecular repulsion tend to separate the molecules while the pressure and molecular attraction tend to confine the molecules. When any substance in the liquid phase, at atmospheric pressure, it means that this pressure is sufficient to confine the molecules together to form liquid. The molecules should possess equal energy to overcome this pressure for the liquid to boil. When this energy is supplied as heat, the repulsion increases so that the molecules are able to overcome the atmospheric pressure which is holding the molecules together. Hence the molecular confinement can be broken only when the vapor pressure becomes equal to or greater than the atmospheric pressure which is referred to as boiling.

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Molecules favor the phase that requires the least amount of work to be in. When I say work, I mean the chemical potential. At equilibrium the chemical potential for a species is the same in both phases. As you add heat to the liquid you change the energy of the system, sure, but the real phenomena is that you change how much work is required to keep a molecule in the liquid phase. The vapor phase in this example is staying constant. If your heat addition/removal increases the amount of work required to insert a molecule into the liquid, meaning it becomes easier to insert a molecule into the vapor, then that is where the molecules will shift, to the easier phase to exist in. They will shift until the chemical potentials are the same in both phases. Boiling is simply a point where molecules rush from one phase to another rather than slowly migrating.

At all times, there are molecules going back and forth between both phases,at equilibrium they are the same rates, at boiling there is more going to the vapor because the work required for a molecule to exist is the vapor is lower (constant in this case) and the work required for a molecule to exist in the steadily heating (boiling) liquid is increasing (high).

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Boiling only occurs when vapour pressure becomes equal to atmospheric pressure. The reason behind it is that, atmospheric pressure resists the phase change i. e Liquid to gas. But when we equalize this pressure with atmospheric pressure the affect of atmospheric is neutrized and then energy which is absorbed by molecule is used to change the phase of liquid to solid. In this case temperature will not change because energy that is absorbed is used to break intermolecular forces and hence it is not contributing in increasing kienetic energy

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