Textbook problem 4C.13

[Naibe Reynoso 2C]

Can someone help explain how to solve this problem, such as the logic used to find the final temperature of this system? I have been struggling to solve these types of problems as they can be solved very differently from one another. Could someone give advice as to how to approach these problems?

[Chem_Mod]

A good strategy which may help is to always ensure that you write down all the knowns and the one unknown before you begin problem solving.

Once you have all the variables, it should simplify the process of finding the appropriate equation and solving for the one unknown, such as final temperature.

[Rachel 1J]

I am going to pull my answer from a previous post I made regarding a similar problem. To start this problem, think about the transfer of heat occurring. The first thing you need to do is to recognize that if the ice starts at 0 degrees C, and the temperature of the ice will increase (from the higher temp water), then the ice will melt. Thus, you must also add in the enthalpy of the phase change from solid to liquid.

You'll find that the heat needed to melt ice + heat needed to bring melted ice to final temperature = heat released by water as it is cooled to the final temperature. There are 2 main formulas you need for this problem: 1) Enthalpy of a phase change, which is Q = n ΔH. In this case, because it is melting, ΔH will be ΔH(fusion). "n" is number of mols of the substance being phase changed. 2) Q = mc ΔT, the formula for finding heat released/absorbed from changes in temperature.

With these two formulas, your final setup looks like this:

nΔH + mcΔT (for ice) = - mcΔT (for water)

*where n is mols of ice. Convert the given grams to mols using the molar mass of water and given mass of the ice.

Make sure when you solve this problem that you pay attention to UNITS. There is a conversion between KJ and J present for using the given ΔH(fusion) and specific heat (c) values.