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Postby AlyssaYeh_1B » Fri Jan 31, 2020 11:06 pm

An ice cube of mass 50.0g at 0.0ºC is added to a glass containing 400.0g of water at 45.0ºC. What is the final temperature of the system? Assume that no heat is lost to the surroundings.

How would this problem be solved? I understand that we need to use the enthalpy of fusion and the specific heat of water, but I'm unsure of how to start.

Katherine Wu 1H
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Re: 4C.13

Postby Katherine Wu 1H » Fri Jan 31, 2020 11:28 pm

The heat gained by the water in the ice cube will be equal to the heat lost by the initial sample of hot water. The enthalpy change for the water in the ice cube will be composed of two terms: the heat to melt the ice at 0 celsius to the final temperature.
heat (ice cube) = (50g/18.02 g.mol^-1)(6.01 x 10^3 J.mol^-1) + (50.0g)(4.184 J.celsius^-1.g^-1)(Tfinal - 0 celsius)
heat (water) = (400g)(4.184 J.celsius^-1.g^-1)(Tfinal - 45 celsius)
Set these two equal to each other, then solve for Tfinal.

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Re: 4C.13

Postby MaggieHan1L » Sun Feb 02, 2020 1:30 pm

Whenever there is phase change you add the heat of fusion/vaporization to the amount of energy it takes to raise the substance a certain amount of degrees. If you look at the phase change curve you can see it's flat then it starts increasing in temperature. The flat area is the phase change.

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