# What mass of ice cream can be melted with the same quantity of heat as required to raise the temperature of 3.50 mol H20 (l) by 50.0 Celcius? (Delta H fussion = 6.01 kJ/mol H20 (s) )

caledon | High School Teacher | (Level 3) Senior Educator

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Well, this is a bit difficult to answer because we haven't been given any of the enthalpy values, or ingredients, for the ice cream. Nevertheless, I can offer some educated guesses.

First we should define some terms. In thermodynamics (the exchange of heat energy in a system) there are distinctly different energies that depend upon the type of matter (water, rock, ice cream) and the phase that it is in (solid, liquid, gas). Each type of matter reacts to heat energy differently depending upon whether it is changing its temperature or changing its phase. The energy required to change temperature is often very different from the energy required to change phase; changing phase is usually much higher per mole.

We've been given a certain amount of energy (the energy to raise the water by 50 degrees), and we're going to apply that energy to a phase change. Since the phase change energy is going to be pretty high, my guess is that the mass of melting ice cream is going to be pretty small.

(note that the Heat of "fusion" applies to both a liquid-to-solid phase change and a solid-to-liquid phase change)

How much energy is required to raise 3.5mol water by 50 degrees?

Water has a heat capacity of about 75.2 J/mol-K (joules per mol-Kelvin). Use the values in your textbook for a more specific answer. Kelvin and Celsius use the same unit scale so we won't bother to convert them, and we'll deal with the joules/kilojoules conversion after we have our answer.

75.2 Joules are required for every mole that we have, in order to raise it by 1 degree. We have 3.5 moles, so 3.5 * 75.2 = 263.2 joules per degree.

We need a total of 50 degrees of temperature change, so 263.2 * 50 = 13,160 joules.

This is the same as 13.16 kJ.

The provided value for delta-Hfusion is 6.01 kJ/mol, and we have 13.16 kJ to work with. So: 13.16 / 6.01 = 2.19 mol water. Multiply by molar mass (18) to get 39.42 grams.

Now, the problem with this answer is that the question didn't specify whether we're treating the ice cream as if it was just frozen water. I assume this is the case, because the delta-Hfusion value refers to water, which isn't relevant unless that's what's being melted. I would suggest asking for clarification on this point.

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tonys538 | Student, Undergraduate | (Level 1) Valedictorian

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In the problem you have provided values relevant only to water. The ice cream being referred to is more likely made of flavored water.

The heat of fusion of water 6.01 kJ/mol. To raise 3.5 mole of liquid water by 50 C requires 74.539*50*3.5 = 13053.25 J

To melt one mole of ice requires 6.01 kJ per mole. 13.05325 kJ of heat would melt approximately 2.17 moles of ice or solid water.