[Paige120]

I am having a difficult time solving this problem:
How much energy does it take to convert 0.5 kg ice at -20 degrees celsius to steam at 250 degrees celsius? specific heat capacities: ice, 2.1 J/g degree C; liquid, 4.2 J/g degree C; steam, 2.0 J/g degree C; delta Hvap = 40.7 kJ/mol; delta Hfus = 6.02 kJ/mol.

So far I tried finding the energy in each state by using mass x specific heat x change in temperature and I got
ice = (.5)(2.1)(20) = 21 kJ
liquid= (.5)(4.2)(100)= 210 kJ
steam= (.5)(2)(150) = 150 kJ

I don't even know if this is correct, but then I used the heat of vaporization and times it by the moles of water (40.7)(2.78 mol) and subtracted that from the total because that is the heat lost.
I then multipled the moles by the heat of fusion and added that to the total since that is the heat absorbed, but I am still not getting the correct answer so I don't know what it is I am doing incorectly.

[DrCMS]

0.5kg of ice, water or steam is how many moles?

To melt 0.5kg of ice do you need to add energy or remove it?

To turn 0.5kg of water to steam do you need to add energy or remove it?

[Paige120]

.5 kg of water, ice, and steam is 2.78 moles.
And wouldn't you need to add energy for both melting ice and boiling the water?
Which is why I was just adding the energies at each state together.
I realize the water when turned to steam gives off energy as well in vaporization, which is why I tried subtracting that one

[DrCMS]

.5 kg of water, ice, and steam is 2.78 moles.

No it is not try your maths again.

And wouldn't you need to add energy for both melting ice and boiling the water?

Yes you do.

Which is why I was just adding the energies at each state together.

No the changes of temperature at each state are different to the energy added or released when changing states.

I realize the water when turned to steam gives off energy as well in vaporization, which is why I tried subtracting that one

NO it does not you've already said correctly that you add energy to water to boil it now you are saying wrongly that it releases energy.  To go from a gas to liquid releases energy but liquid to gas absorbs it.

[kayamusty]

I am having a difficult time solving this problem:
How much energy does it take to convert 0.5 kg ice at -20 degrees celsius to steam at 250 degrees celsius? specific heat capacities: ice, 2.1 J/g degree C; liquid, 4.2 J/g degree C; steam, 2.0 J/g degree C; delta Hvap = 40.7 kJ/mol; delta Hfus = 6.02 kJ/mol.

So far I tried finding the energy in each state by using mass x specific heat x change in temperature and I got
ice = (.5)(2.1)(20) = 21 kJ
liquid= (.5)(4.2)(100)= 210 kJ
steam= (.5)(2)(150) = 150 kJ

I don't even know if this is correct, but then I used the heat of vaporization and times it by the moles of water (40.7)(2.78 mol) and subtracted that from the total because that is the heat lost.
I then multipled the moles by the heat of fusion and added that to the total since that is the heat absorbed, but I am still not getting the correct answer so I don't know what it is I am doing incorectly.

you have done right. but you should add melting and evaporation. Q=m.Lm and Q=m.Le

[Paige120]

Well I found my problem with moles. So there are 27.8 moles in .5 kg water.

you have done right. but you should add melting and evaporation. Q=m.Lm and Q=m.Le

Does that just mean multiply moles by the heat of fusion and heat of vaporization? I tried that but I am still a little short of what the answer is supposed to be.

No the changes of temperature at each state are different to the energy added or released when changing states.

Is the energy added/released when changing states the energy related to heat of fusion and heat of vaporization? If it isn't I have no idea what to do.  So is what I was doing with finding the energy during each state correct or no?

[DrCMS]

Well I found my problem with moles. So there are 27.8 moles in .5 kg water.

you have done right. but you should add melting and evaporation. Q=m.Lm and Q=m.Le

Does that just mean multiply moles by the heat of fusion and heat of vaporization? I tried that but I am still a little short of what the answer is supposed to be.

Yes using 27.8moles I get 1679.8kJ in total.

No the changes of temperature at each state are different to the energy added or released when changing states.

Is the energy added/released when changing states the energy related to heat of fusion and heat of vaporization? If it isn't I have no idea what to do.  So is what I was doing with finding the energy during each state correct or no?

Yes they are the latent heat of fusion and vapourisation which both require energy in your question.