An ice cube, weighing 100g, is dropped in 1kg of water at 20 degrees C. Does the ice melt? If not, how much remains? What is the final temperature?
The latent heat of fusion of ice at 0C is 6.025 kJ/mol, and the molar heat capacity of water is 75.3 J/K mol
The Attempt at a Solution
moles of H20= 55.51mol mol of Ice= 5.55mol
heat contained in 1000g of water, using heat capacity, C=q/dT
q= 75.3 J/K mol * 293.15K * 55.51mol= 1.225x10^6 J
The heat required to melt 5.55mol of ice is:
5.55mol x 6.025 kJ/mol= 3.34x10^4 J
Here is where I get stuck. At first I tried to say that the heat of the water dropped by how much energy it took to melt the ice, and then use that as q and calculate T=q/C. This gives a reasonable answer, but then if you add enough ice, you would get an answer that is below 0C for final temp, which makes no sense.
So what do I do now?
EDIT: I think my above method is wrong because it neglects the energy of water from the melted ice. So if I calculate q for 1000g of water at 293K, then add that to q for water at 273K, and then divide that by C of water, should I get the right temperature?
EDIT 2: Nope, I still get a temperature lower than freezing if I just add up all the heat of the system and divide by the heat capacity if I do the same calculation for 10x as much ice.