States of matter; liquids and solids

[babysnatcher]

Water at 0°C was placed in a dish inside a vessel maintained at low pressure by a vacuum pump. After a quantiti of water had evaporated, the remainder froze. If 9.31 g of ice at 0°C was obtained, how much liquid water must have evaporated? The heat of fusion of water is 6.01 kJ/mol and its heat of vaoprization is 44.9 kJ/mol at 0°C.

Ok so I have conversion factors in specific places that coincedently generated the correct answer and I know this because my answer matches the books answer. But I don't understand the reasoning. Why does this work? I need to know what is really going on. And how to be able to know the answer is correct without peeking.

 

[PeterO]

Water at 0°C was placed in a dish inside a vessel maintained at low pressure by a vacuum pump. After a quantiti of water had evaporated, the remainder froze. If 9.31 g of ice at 0°C was obtained, how much liquid water must have evaporated? The heat of fusion of water is 6.01 kJ/mol and its heat of vaoprization is 44.9 kJ/mol at 0°C.

Ok so I have conversion factors in specific places that coincedently generated the correct answer and I know this because my answer matches the books answer. But I don't understand the reasoning. Why does this work? I need to know what is really going on. And how to be able to know the answer is correct without peeking.

It seems you need just over 7 times the energy to vapourise the water than to freeze it, so around 1/7th will have evaporated when the rest has frozen.