A 2 kg amount of Mercury is heated from -100C to 456C. The specific heat capacit

Question

A 2 kg amount of Mercury is heated from -100C to 456C. The specific heat capacity for solid Mercury is 0.07 kJ/kgK and for gaseous Mercury is 0.1 kJ/kgK at constant atmospheric pressure. Determine how much energy (i.e. heat) is needed to raise the temperature of solid Mercury to its melting point. Determine how much energy (i.e. heat) is needed to change the state of solid Mercury to liquid Mercury. Determine how much energy (i.e. heat) is needed to raise the temperature of liquid Mercury to its boiling point. Determine how much energy (i.e. heat) is needed to change the state of liquid Mercury to gaseous Mercury. Determine how much energy (i.e. heat) is needed to raise the temperature of gaseous Mercury from its boiling point to 456C. On graph paper draw a temperature versus heat added graph showing how much heat is added to heat the Mercury from -100C to 456C. Please hand this in separately from webassign, with your name on it. What is the average kinetic (motion) energy per molecule of the Mercury molecules at the beginning and end of the process. The constant that relates temperature and average kinetic energy per molecule for mercury is given by 3/2, k_B Joules per molecule Joules per molecule

Explanation / Answer

a) Melting point of mercury T2 = -38.8 oC = -38.8 + 273 K = 234.2 K

                                        T1 = -100 oC = -100 + 273 K = 173 K

Heat energy required to raise the temp of solid mercury to its melting point is

Q = mC (T2-T1)   C = specific heat capacity of solid mercury

      = 2 kg x 0.07 kJ/kgK x [ 234.2 - 173] K

     = 8.568 kJ

   = 8568 J

b) moles of mercury = mass / molar mass

                              = 2kg/ 200.6 g/mol

                              = 2000 g/ 200.6 g/mol

                              = 9.97 mol

Heat energy needed to change the state of solid mercury to liquid mercury

    Q = moles of mercury x Enthalpy of fusion of mercury

   = 9.97 mol x 2.29 kJ/mol

    = 22.8313 kJ

= 22831.3 J

e)

Boiling point of mercury T1 = 356.7 oC = 356.7 + 273 K = 629.7 K

                                     T1 = 456 oC = 456 + 273 K = 729 K

Heat energy required to raise the temp of gaseous mercury from its boiling point to 456 oC is

Q = mC (T2-T1)   C = specific heat capacity of gaseous mercury

      = 2 kg x 0.1 kJ/kgK x [ 729 - 629.7] K

     = 19.86 kJ

     = 19860 J

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