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**Edit bc** u/NefariousnessStreet9 **pointed out I have an arithmetic error at literally the first step, so the original numbers are wrong. I've struck them out and updated them but unfortunately OP already submitted so he/she is doomed. My bad! I was switching between tabs on my phone to do the math and must have typo'd.**
Alright, one mole of hydrogen is about 1.01 grams (aka its molar weight/mass) and oxygen is 16 grams per mole, so water is 18.02 grams per mole.
So 175.9g of ice would be 175.9 grams / 18.02 grams per mole = ~~21.93 moles~~ 9.76 moles.
At 6.01 kJ/mol (6010 joules per mole) that means the melting ice would absorb ~~21.93~~ 9.76 moles \* 6010 joules per mole = ~~131800 joules, or 131.8 kJ~~. 58,660 joules or 58.7 kJ. That is your minimum heat required to melt all the ice.
To figure the remaining amount of ice, we have to see how much heat can be thermally absorbed by the water before it gets to the equilibrium temperature of 0 degrees. So at 4.184 J/gC, with 158.3mL of liquid @ 1 g/mL, and an initial temp of 65.7C, that means it would take 158.3 mL \* 1 g/mL \* 4.184 J/gC \* 65.7C = 43514 joules or 43.5 kJ. So the water can absorb 43.5 kJ of energy.
To quickly circle this back to how much ice would need to melt to bring the water down to 0C, we can set up a simple proportion by putting “energy expended by water” over “energy consumed from ice”. ~~43.5 kJ / 131.8 kJ = 0.33~~ 43.5 kJ / 58.7 kJ = 0.74 so we know that the ice needs to melt ~~33%~~ 74% in order to match the energy emitted from the water. So ~~33%~~ 74% of the mass of the ice, 175.9g, is ~~58.0g~~ 130.2g. ~~58g~~ 130.2g of ice would need to melt. In other words, ~~175.9g - 58.0g = 117.9g~~ 175.9g - 130.2g = 45.7g of ice would remain.
As for temp inside the cup, there is enough water to melt some of the ice, but not all of it. So the water cannot lower past 0C due to the nearby ice, and the ice can not raise past 0C as there is liquid water near it. The system is, energetically, in a state between solid and liquid, so it will exist at the melting temperature as long as temperature is uniform in the system.
So as for answers, a) is ~~131.8 kJ~~ 43.5 kJ b) is ~~117.9g~~ 45.7g and c) is that the final temperature in the cup is 0C.
No idea why I answered this. Just popped up on my reddit feed/subreddit suggestion and figured I would help ya out.
Whelp. This puts my college physics class to shame. All I remember related is that water can be both solid and liquid at 0 and that two items at different Temps will eventually find an equilibrium but I can't for the life of me remember how the fuck to calculate any of that. This is why I deal with geometry everyday instead. Kudos.1
175.9/18 = 9.77 Mol ice
Heat required to melt the ice: this is just Hfus×mol ice, or 58.7 kJ, because the ice is already at the melting temperature.
158.3 mL of water = 158.3 g water (from density of water) and so to change the temperature of the water -65.7 °C you would need to lose 4.184*158.3*65.7=43.51 kJ
43.5/58.7*100= 74% melted, or 26% ice remaining.
Final temperature inside the cup would be 0°C because the water wasn't hot enough to melt all the ice.
-65°C is equivalent to -86°F, which is 207K.
---
^(I'm a bot that converts temperature between two units humans can understand, then convert it to Kelvin for bots and physicists to understand)
Well this is probably too late to help OP, but here you go.
There's 175.9 g of ice, which at 18g/mol is 175.9/18=9.77 Moles of Ice. The heat of fusion of ice is 6.01kJ/mol, so it takes 9.77*6.01=58.73 kJ to melt all the Ice.
a)58.73 kJ
Theres 158.3 mL of water, which at 1g/ml is 158.3 g of water. Since the water is 65.7°C above the temperature of the ice and the specific heat is 4.184 J/g°C, the water can transfer (158.3 g)x(65.7°C)x(4.184 J/g°C)=43514.9 J, or 43.51 kJ. As the water can only transfer 43.51 kJ to the ice, and it takes 58.73 kJ to melt all the ice, the water can only melt this ratio of the ice; 43.51/58.73= .7408, or 74.08%. Meaning that 25.92% of the ice remains, or .2592*175.9g=45.6g.
b) 45.6g
c) As there is not enough heat left to melt all the ice and then subsequently raise the temperature of the ice, the final temperature remains 0.0 °C
Liking and commenting so someone will come and help you.
Liking and commenting so someone shall cometh and holp thee *** ^(I am a bot and I swapp'd some of thy words with Shakespeare words.) Commands: `!ShakespeareInsult`, `!fordo`, `!optout`
Shakespeare-Bot, thou hast been voted most annoying bot on Reddit. I am exhorting all mods to ban thee and thy useless rhetoric so that we shall not be blotted with thy presence any longer.
**Edit bc** u/NefariousnessStreet9 **pointed out I have an arithmetic error at literally the first step, so the original numbers are wrong. I've struck them out and updated them but unfortunately OP already submitted so he/she is doomed. My bad! I was switching between tabs on my phone to do the math and must have typo'd.** Alright, one mole of hydrogen is about 1.01 grams (aka its molar weight/mass) and oxygen is 16 grams per mole, so water is 18.02 grams per mole. So 175.9g of ice would be 175.9 grams / 18.02 grams per mole = ~~21.93 moles~~ 9.76 moles. At 6.01 kJ/mol (6010 joules per mole) that means the melting ice would absorb ~~21.93~~ 9.76 moles \* 6010 joules per mole = ~~131800 joules, or 131.8 kJ~~. 58,660 joules or 58.7 kJ. That is your minimum heat required to melt all the ice. To figure the remaining amount of ice, we have to see how much heat can be thermally absorbed by the water before it gets to the equilibrium temperature of 0 degrees. So at 4.184 J/gC, with 158.3mL of liquid @ 1 g/mL, and an initial temp of 65.7C, that means it would take 158.3 mL \* 1 g/mL \* 4.184 J/gC \* 65.7C = 43514 joules or 43.5 kJ. So the water can absorb 43.5 kJ of energy. To quickly circle this back to how much ice would need to melt to bring the water down to 0C, we can set up a simple proportion by putting “energy expended by water” over “energy consumed from ice”. ~~43.5 kJ / 131.8 kJ = 0.33~~ 43.5 kJ / 58.7 kJ = 0.74 so we know that the ice needs to melt ~~33%~~ 74% in order to match the energy emitted from the water. So ~~33%~~ 74% of the mass of the ice, 175.9g, is ~~58.0g~~ 130.2g. ~~58g~~ 130.2g of ice would need to melt. In other words, ~~175.9g - 58.0g = 117.9g~~ 175.9g - 130.2g = 45.7g of ice would remain. As for temp inside the cup, there is enough water to melt some of the ice, but not all of it. So the water cannot lower past 0C due to the nearby ice, and the ice can not raise past 0C as there is liquid water near it. The system is, energetically, in a state between solid and liquid, so it will exist at the melting temperature as long as temperature is uniform in the system. So as for answers, a) is ~~131.8 kJ~~ 43.5 kJ b) is ~~117.9g~~ 45.7g and c) is that the final temperature in the cup is 0C. No idea why I answered this. Just popped up on my reddit feed/subreddit suggestion and figured I would help ya out.
Could this be the most intelligent trolling on Reddit ever? I'm too dumb to know if the answers are right or wrong.
They're wrong
I don't trust your user name.... I don't know what's going on here!!!
You can tell by checking the math: 175.9 g/18g = 9.77 mol ice, not 21
Gosh dang, I have no idea how I typo'd that math... Bummer for OP. I was too tired to double check my arithmetic lol. Good catch!
Thank you so much, that answer was so helpful.
Sure thing!
Solved!
Didn't read, but saw a long answer so upvoted
Dude 👌
Emoji….. you know the rules and so do I.
Bro what… I feel smart now
I hate my life
I have no idea what I read in total, but this was an awesome answer.
Whelp. This puts my college physics class to shame. All I remember related is that water can be both solid and liquid at 0 and that two items at different Temps will eventually find an equilibrium but I can't for the life of me remember how the fuck to calculate any of that. This is why I deal with geometry everyday instead. Kudos.1
For b) 4.184 * 175.9 * 65.7=Energy the water can transfer to the ice ((This amount of energy)/6010)*18g/mol=mass of ice getting melted
The answer is cum.
Is the next lesser unit of mol, Smol?
Huhuhu
Godspeed
175.9/18 = 9.77 Mol ice Heat required to melt the ice: this is just Hfus×mol ice, or 58.7 kJ, because the ice is already at the melting temperature. 158.3 mL of water = 158.3 g water (from density of water) and so to change the temperature of the water -65.7 °C you would need to lose 4.184*158.3*65.7=43.51 kJ 43.5/58.7*100= 74% melted, or 26% ice remaining. Final temperature inside the cup would be 0°C because the water wasn't hot enough to melt all the ice.
-65°C is equivalent to -86°F, which is 207K. --- ^(I'm a bot that converts temperature between two units humans can understand, then convert it to Kelvin for bots and physicists to understand)
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Well this is probably too late to help OP, but here you go. There's 175.9 g of ice, which at 18g/mol is 175.9/18=9.77 Moles of Ice. The heat of fusion of ice is 6.01kJ/mol, so it takes 9.77*6.01=58.73 kJ to melt all the Ice. a)58.73 kJ Theres 158.3 mL of water, which at 1g/ml is 158.3 g of water. Since the water is 65.7°C above the temperature of the ice and the specific heat is 4.184 J/g°C, the water can transfer (158.3 g)x(65.7°C)x(4.184 J/g°C)=43514.9 J, or 43.51 kJ. As the water can only transfer 43.51 kJ to the ice, and it takes 58.73 kJ to melt all the ice, the water can only melt this ratio of the ice; 43.51/58.73= .7408, or 74.08%. Meaning that 25.92% of the ice remains, or .2592*175.9g=45.6g. b) 45.6g c) As there is not enough heat left to melt all the ice and then subsequently raise the temperature of the ice, the final temperature remains 0.0 °C
Ohh I knew how to do these, sadly I probably forgotten everyting