I'm confused about why the boiling of liquids happen. The boiling point of a liquid is defined as the temperature in which it's vapor pressure is equal to the pressure of the gas above the liquid( for example the atmospheric pressure ), and vapor pressure is defined as the (temperature dependent) partial pressure of the gas state of the liquid in which the rate of condensation is equal to the rate of evaporation. So for example, let say we have a beaker of water at sea level( 1 atm of atmospheric pressure) and we heat it constantly( for example with a bunsen burner ) to 100ºC, since at that temperature the vapor pressure of water is equal to the atmospheric pressure of water, we have heated it to it's boiling point. What I don't understand is why after some time all beaker's water will became a gas and no liquid water will be left in the beaker, because the bubbles of water gas that form in the beaker will rise( due to lower density ), but once the reach the level of water they should constantly condense and evaporate at the same rate( due to the vapor pressure ) so the level of water should remain constant, because the amount of water that leaves as a gas is the same that condenses to the liquid, but we know that after some time all water will evaporate and diffuse into the atmosphere, so no liquid water will be left in the beaker.
I'm confused about this, why does the liquid completely evaporates when according to the vapor pressure, gas and liquid should be in equilibrium and some water should remain liquid in the beaker? What am I missing?. Thank you for your help, I haven't really found any explanation to this in the internet or in a textbook.