Question

How much heat energy is required to convert 55.4 g of solid iron at 21 °C to liquid iron at 1538 °C? The molar heat of fusion of iron is 13.8 kJ/mol. Iron has a normal melting point of 1538 °C. The specific heat capacity of solid iron is 0.449 J/g·°C.

Answer 1

Q = heat change for conversion of solid iron 21 ^oC to solid iron at 1538 ^oC + heat change for

conversion of soild iron at 1538^oC to liquid iron at 1538^oC

Amount of heat released , Q = mcdt + mL

                                          = m(cdt + L)

Where

m = mass of iron = 55.4 g

c = specific heat capacity of solid iron is 0.449 J/g·°C.

L= Heat of fusion of iron = molar heat of fusion of iron/molar mass

                                    = 13.8 (kJ/mol) / 55.8 (g/mol)

                                    = 13.8x1000 (J/mol) / 55.8 (g/mol)

                                     = 274.3 J/g

dt = change in temperature = 1538 - 21 = 1517 ^oC

Plug the values we get

Q = m(cdt + L)

   = 55.4x [ (0.449x1517)+274.3 ]

= 52.9x10³ J

= 52.9 kJ

Therefore the required heat is 52.9 kJ