6th Edition, 8.91

[Hai-Lin Yeh 1J]

In 1750 Joseph Black performed an experiment that eventually led to the discovery of enthalpies of fusion. He placed two 150.-g samples of water at 0.00 C (one ice and one liquid) in a room kept at a constant temperature of 5.00 C. He then observed how long it took for each sample to warm to its final temperature. The liquid sample reached 5.00 C after 30.0 min. However, the ice took 10.5 h to reach 5.00 C. He concluded that the difference in time that the two samples required to reach the same final temperature represented the difference in heat required to raise the temperatures of the samples. Use Black’s data to calculate the enthalpy of fusion of ice in kilojoules per mole. Use the known heat capacity of liquid water.

I understood everything, except why do we estimate that it took 10 hrs to melt instead of 10.5 since it took 10.5 to reach 5.00C?

[Manya Bali 4E]

It takes .5 hours for the water at 0 degrees celsius to go to 5 degrees celsius.
It takes 10.5 hours for the ice to go from being ice to being water at 5 degrees celsius. The ice therefore must take some amount of time to become water at 0 degrees celsius and some other amount of time to go from being water at 0 degrees to 5 degrees (.5 hours, which we know from the first statement.) Therefore, the amount of time it takes for the ice to go from solid to liquid (at 0 degrees) is 10.5-.5 = 10 hours.