Question

Heat, q, is energy transferred between a system and its surroundings. For a process that involves a temperature change q=m?Cs??T where Cs is specific heat and m is mass. Heat can also be transferred at a constant temperature when there is a change in state. For a process that involves a phase change q=n??H where, n is the number of moles and ?H is the enthalpy of fusion, vaporization, or sublimation. The following table provides the specific heat and enthalpy changes for water and ice.

Substance       Specific heat [J/(g??C)]       ?H (kJ/mol)

water                        4.18                                  44.0

ice                            2.01    6.01

How many grams of ice at -13.5 ?C can be completely converted to liquid at 8.8 ?C if the available heat for this process is 4.86×10³ kJ ?

For ice, use a specific heat of 2.01 J/(g??C) and ?Hfus=6.01kJ/mol.

Express your answer to three significant figures and include the appropriate units.

Answer 1

Let m = mass of ice in grams

Heat gained by ice to raise the temperature from - 13.5C to 0C

Q1 = m x Cp x (T2-T1)

= m (g) x 2.01 J/gC x (13.5)C

= 27.135 m J

Phase change at 0C

Q2 = m x Hf = 6.01 kJ/mol x 1000J/kJ x 1mol/18g x m

= 333.88 m J

Heat gained by liquid to raise the temperature from 0C to 8.8C

Q3 = m x Cp x (T2-T1)

= m (g) x 4.18 J/gC x (8.8)C

= 36.784 m J

Total heat absorbed Q = Q1 + Q2 + Q3

4.86×10^3 kJ x 1000J/kJ = 27.135 m + 333.88 m + 36.784 m

397.799 m = 4.86*10^6

m = 12217.2252 g

m = 12.217 kg