# Using a coffee-cup calorimeter, it is found that when an ice cube with a mass of 24.6 g melts,...

## Question:

Using a coffee-cup calorimeter, it is found that when an ice cube with a mass of 24.6 g melts, 8.19 kJ of heat are absorbed.

(a) Calculate the change in enthalpy per gram and per mole of water.

(b) Write the thermochemical equation for this physical change.

(c) What mass of ice must be melted to produce 10.0 kJ of heat?

## Heat of Fusion

Putting heat into a system raises it's temperature, and so the energy supplied to the system the higher the temperature. This is not true when the material reaches a temperature where a phase transition occurs. The energy supplied to a system is put into changing the phase of the material and not to raising the temperature. In the case of a solid to liquid phase transition this is called the Heat of Fusion.

(a) The reaction is performed under a constant pressure. This means

{eq}q = \Delta H {/eq}

The change in enthalpy per gram is therefore

{eq}\Delta H_{fus} = \frac {8.19}{24.6} = 0.333 {/eq} kJ/g

The number of moles in 24.6 g of ice is

{eq}n = \frac {24.6}{18.01528} = 1.37 {/eq} mol

The change in enthalpy per mole is therefore

{eq}\Delta H_{fus} = \frac {8.19}{1.37} = 6.00 {/eq} kJ/mol

(b) The balanced reaction for this physical change is

{eq}H_2O(s) \rightarrow H_2O(l) {/eq}

(c) The mass of ice that must be melted to produce 10.0 kJ of heat is

{eq}m = \frac {10.0}{0.333} = 30.0 {/eq} g 