Question

How much heat does it take to change 100g of solid octane (C8H18) at -65 degrees C to octane vapor at 135 degrees C? (Delta H vap= 41.53 kJ/mol, Cgas= 238.95 J/K-mol, delta H fus= 20.74 kJ/mol, Cliq=255.68 J/K-mol, Tb= 126 degrees C, Tf=-57 degrees C, Csolid= 111.5 J/K-mol)

Answer 1

Answer – We are given, ∆H vap= 41.53 kJ/mol, C gas= 238.95 J/K-mol,          ∆H fus= 20.74 kJ/mol, C liq=255.68 J/K-mol, Tb= 126^oC, Tf=-57 ^oC, C solid= 111.5 J/K-mol

Mass of octane = 100 g

First we need to calculate the moles of octane-

Moles of octane = 100 g / 114.23 g.mol^-1

                           = 0.875 moles

Now first we need to calculate the heat from the -65^oC to -57^oC

We know

Heat, q1 = m*C solid * ∆t

              = 0.875 moles * 111.5 J/K.mol * (-57^oC –(-65^oC)

              = 780.8 J

Now heat from -57^oC to -57^oC

q2 = m*∆H fus

     = 0.875 moles * 20740 J/mol

     =18156.4 J

Heat from the -57^oC to 126^oC

q3 = m*C liq* ∆t

    = 0.875 moles * 255.68 J/K.mol * (126^oC –(-57^oC)

    = 40960.7 J

heat from 126^oC to 126^oC

q4 = m*∆H vap

     = 0.875 moles * 41530 J/mol

     =36356.4 J

Heat from the   126^oC to 135^oC

q5 = m*C gas* ∆t

    = 0.875 moles * 238.95 J/K.mol * (135^oC –126^oC)

    = 1882.6 J

Now total heat q = q1+ q2+q3+q4+q5

                           = 780.8 J + 18156.4 J + 40960.7 J + 36356.4 J + 1882.6 J

                          = 98137 J

                          = 98.137 kJ

So, 98.137 kJ heat does it take to change 100g of solid octane (C8H18) at -65 degrees C to octane vapor at 135 degrees C