Heat, q, is energy transferred between a system and its surroundings. For a proc

Question

Heat, q, is energy transferred between a system and its surroundings. For a process that involves a temperature change q = m middot C_a middot Delta T where C_a 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 middot Delta H where, n is the number of moles and Delta H is the enthalpy of fusion, vaporization, or sublimation. The following table provides the specific heat and enthalpy changes for water and ice. How many grams of ice at -16.4 degree C can be completely converted to liquid at 16.8 degree C if the available heat for this process is 5.42 times 10^3 kJ ? For ice, use a specific heat of 2.01 J/(g middot degree C) and Delta H_fus = 6.01kJ/mol. Express your answer to three significant figures and include the appropriate units. Value Units

Explanation / Answer

available heat = 5.42 x 10^3 KJ = 5.42 x 10^6 J

Let mass of ice = m ,

Heat required to heat ice from - 16.4 to 0C = specific heat of ice x temp change x mass of ice

                   = 2.01 J/gC x ( 16.4) C x m

         = 32.964 m ............(1)

moles of ice = mass / Molar mass = m/18.015 = 0.0555m

Heat required to convert to ice to water liquid , = specific heat of water x moles of ice

                = 6.01 KJ/mol x 0.0555m mol

              = 0.3336m KJ = 333.6 m    Joules ....................(2)

Heat required to rise water from 0 to 16.8 C = specific heat of water x temp rise x mass of water

                         = 4.18 J/gC x 16.8C x m

                       = 70.224 m ........(3)

total heat required = sum of three process mentioned above

5.42 x 10^6 J = 32.964m + 333.6 m + 70.224 m

m = 1.24 x 10^4 grams

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