A confusing question - melting ice

In summary, the problem deals with the change of phase from steam to liquid water and solid ice to liquid water. The heat of vaporization of water at 100°C is 2260 J/g, while the heat of fusion of ice is 335 J/g. Using the formula for energy released in a reaction, we can solve for the amount of ice melted by equating the energies released during the phase changes. The final answer is 675 g of ice melted. The concept of heat of vaporization is the difference between the heat of formation of vapor and the heat of formation of liquid.
  • #1
zhen
48
0
Question:

The heat of vaporization of water is 2260 J/g at 100°C. A 100.0 g sample of water condenses and all of the heat liberated is then transferred to a block of ice. How many grams of ice will melt? Assume the condensed water remains at 100°C and the melted ice remains at 0°C. The heat of fusion of ice is 335 J/g.

I am totally confused by this question, and I don't even know how to start. Can someone explain this question to me, or just give some hints?
 
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  • #2
zhen said:
A 100.0 g sample of water condenses
This means that 100.0 g of steam (at 100°C) condensed to become 100.0 g of liquid water (at 100°C). How much energy was released when the water changed phase? (How much energy is required to vaporize the water into steam?)
 
  • #3
I tried to solve it based on this forumla:
energy released by the reaction = specific heat capacity X mass of solution X increase in temperature...

2260 J/g X 100°C X 100g = 335 J/g X 100°C X (M)

M= 675 g...is this correct?

I am still very confused...
 
  • #4
Doc Al said:
This means that 100.0 g of steam (at 100°C) condensed to become 100.0 g of liquid water (at 100°C). How much energy was released when the water changed phase? (How much energy is required to vaporize the water into steam?)

what about the ice? " The heat of fusion of ice is 335 J/g."
 
  • #5
The heat of vaporization of water is 2260 J/g at 100°C. A 100.0 g sample of water condenses and all of the heat liberated is then transferred to a block of ice. How many grams of ice will melt? Assume the condensed water remains at 100°C and the melted ice remains at 0°C. The heat of fusion of ice is 335 J/g.
I can appreciate the confusion because this situation is phyiscally impossible, but the problem is trying to emphasize the change of phase - from vapor (steam) to liquid (water) and solid (ice) to water.

Now when a substance changes phase, it does so more or less at constant temperature.

In the problem the ice changes phase at 0°C to liquid water absorbing 335 J/g, and the steam changes phase at 100°C to liquid water giving 2260 J/g.
 
  • #6
zhen said:
I tried to solve it based on this forumla:
energy released by the reaction = specific heat capacity X mass of solution X increase in temperature...
2260 J/g X 100°C X 100g = 335 J/g X 100°C X (M)
M= 675 g...is this correct?


Yes. The latent heat of fusion at 0 C is 6.75 x the latent heat of fusion at 100 C. I've reddened your errors: you have NOT been asked to use heat capacities; there is, therefore, NO temperature change for the two separate systems for which you are calculating "latent heat changes."
I am still very confused...

"I can appreciate the confusion because this situation is phyiscally impossible..."​

Not really --- throw the ice in the upper pot of a double boiler, shove a steam line into the bottom pot rather than filling it and throwing it on the stove, and do the measurement with whatever degree of precision is desired (reducing heat capacities of apparatus (the double boiler) to less than uncertainties in measurement of water masses).
 
  • #7
thank you very much, and there is another question i want to confirm.
is it "heat of vaporization" = "heat of the formation of vapor" - "heat of formation of liquid"
 
  • #8
Yup. You got it.
 

1. What causes ice to melt?

Ice melts when its temperature increases past its melting point, causing the solid molecules to vibrate and break apart into liquid molecules.

2. Why does melted ice turn into water?

Melted ice turns into water because the heat energy causes the solid molecules to break apart, changing its state of matter from solid to liquid.

3. Can ice melt without heat?

No, ice needs heat energy to melt. However, ice can also melt through a process called sublimation, where it changes directly from a solid to a gas without becoming a liquid first.

4. Does the temperature affect how fast ice melts?

Yes, the temperature plays a significant role in how fast ice melts. The higher the temperature, the faster the ice will melt as more heat energy is being transferred to the ice molecules.

5. What happens to the molecules of ice as it melts?

The molecules of ice become more disordered and spread out as it melts. This is because the heat energy is causing them to vibrate and move apart, changing the solid structure of ice into a liquid state.

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