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Density/temp graph of water shows water at 0 °C to have the same density as water in between 5-6°C so why does ice not form between 5-6 °C

if you see the graph ( density/temp) for anomalous expansion of water then it is in the shape of a curved tick mark, so there are two temp at which water has the same density as ice.

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Ice does not form between 5-6 ?C because the temperatures are above the freezing point. This means that the vapor pressure is low thus the ice cannot be formed.

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0 degrees is the freezing/melting point, but you can have 0 degree water without it being ice. 0 degree water still has more energy than ice, so in order to freeze you have to remove more energy from the water. Also, remember that when water freezes, the molecules line up in such a way that ice is actually less dense than water of the same temperature.

So it kinda goes like this:
0 degree ice is X density. Add energy, it melts, and the 0 degree water is *more* dense than the ice. Then as you add energy aka heat it up, water becomes less and less dense.

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Check this:
http://www2.volstate.edu/CHEM/Density_of_Water.htm
Slightly different.