Water's heat of fusion is 80. cal/g , its specific heat is 1.0calg⋅∘c, and its heat of vaporization is 540 cal/g . a canister is filled with 330 g of ice and 100. g of liquid water, both at 0 ∘c . the canister is placed in an oven until all the h2o has boiled off and the canister is empty. how much energy in calories was absorbed?

Refer to the diagram shown below.

State 1:
The heat of fusion is required for the ice to become water.
The amount of heat required is
Q₁ = (330 g)*(80 cal/g) = 26,400 cal

State 2:
Sensible heat is required to raise water at 0 C to the boiling point of 100 C.
The heat required is
Q₂ = (430g)*(1 cal/(g-C))*(100 C) = 43,000 cal

State 3:
The heat of vaporization is required to boil off the water.
The heat required is
(430 g)*(540 cal/g) = 232,200 cal

Total heat absorbed is
Q₁+Q₂+Q₃ = 301,600

301,600 cal  or 301.6 kcal

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The answer to your question really depends on three things: how much water you have, how cold it is to start out, and how cold the things around it are. water actually freezes when it gets to 32 degrees fahrenheit (0 degrees celsius), but the time it takes to get there may be different.  let's start with the first. if you take two glasses, and fill one with a tiny bit of water, and the other about halfway, then put them both in the freezer, the one with less water will freeze first (you can try this at home, but i recommend using plastic cups and not glass ones).  now let's move on to the second part. let's say you have two glasses, and you fill one with really cold water that has been in the refrigerator, and the other with really hot water from the sink. if you put both of them in the freezer, the one that started out colder will freeze first.  for the third part, let's imagine that you have two glasses with the same amount of water in them, and the water is at the same temperature. imagine putting one outside on a really really cold day in georgia, and having a friend in alaska put one outside on the same day. since it would be so much colder in alaska, the glass of water there would freeze before yours.  so, if you took a tiny bit of really cold water in a glass, and put it outside on a cold day in alaska, it would freeze a lot faster than a big glass of hot water outside on a cold day in georgia.