Determining the final temperature at equilibrium

[Bridget Vause 1A]

An ice cube with a mass of 46.2 g at 0.0 is added to a glass containing 396 g of water at 45.0 . Determine the final temperature of the system at equilibrium. The specific heat capacity of water, Cs, is 4.184 J/g⋅, and the standard enthalpy of fusion, fus, of water is 6.01×103 J/mol. Assume that no energy is transferred to or from the surroundings.

I am plugging the numbers into the equation Hfus + q ice = -q water but I got 0.0256 which doesn't make sense. Please help.

Thanks!!

[Rachel 1J]

To start this problem, think about the transfer of heat occurring. You will conclude 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) Energy 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.

Try this and see if your answer is correct.