Question

What amount of thermal energy (in kJ) is required to convert 42.0 g of ethanol at -171 °C completely to gaseous ethanol at 99 °C? The melting point of ethanol is -114 °C and its normal boiling point is 78 °C.

The heat of fusion of ethanol is 5.0 kJ mol^-1

The heat of vaporization of ethanol at its normal boiling point is 35.0 kJ mol^-1

The specific heat capacity of solid ethanol is 1.05 J g^-1 °C^-1

The specific heat capacity of liquid ethanol is 2.44 J g^-1 °C^-1

The specific heat capacity of gaseous ethanol is 1.01 J g^-1 °C^-1

Answer 1

Process 1 : All solid ethanol is heated from -171 ^oC to melting point -114 ^oC

Energy required, E1 = (mass of ethanol) * (specific heat of solid ethanol) * (final temp. - initial temp.)

E1 = (42.0 g) * (1.05 J/g.^oC) * (-114 ^oC - (-171 ^oC))

E1 = 2513.7 J

E1 = 2.5137 kJ

Process 2 : All solid ethanol is melted to liquid ethanol at melting point -114 ^oC

Energy required, E2 = (moles of ethanol) * (heat of fusion of ethanol)

E2 = (mass ethanol / molar mass ethanol) * (heat of fusion of ethanol)

E2 = (42.0 g / 46.07 g/mol) * (5.0 kJ/mol)

E2 = (0.912 mol) * (5.0 kJ/mol)

E2 = 4.56 kJ

Process 3 : All liquid ethanol is heated from -114 ^oC to boiling point 78 ^oC

Energy required, E3 = (mass of ethanol) * (specific heat of liquid ethanol) * (final temp. - initial temp.)

E3 = (42.0 g) * (2.44 J/g.^oC) * (78 ^oC - (-114 ^oC))

E3 = 19676.16 J

E3 = 19.68 kJ

Process 4 : All liquid ethanol is vaporized to gaseous ethanol at boiling point 78 ^oC

Energy required, E4 = (moles of ethanol) * (heat of vaporization of ethanol)

E4 = (mass ethanol / molar mass ethanol) * (heat of vaporization of ethanol)

E4 = (42.0 g / 46.07 g/mol) * (35.0 kJ/mol)

E4 = (0.912) * (35.0 kJ/mol)

E4 = 31.908 kJ

Process 5 : All gaseous ethanol is heated from 78 ^oC to 99 ^oC

Energy required, E5 = (mass of ethanol) * (specific heat of gaseous ethanol) * (final temp. - initial temp.)

E5 = (42.0 g) * (1.01 J/g.^oC) * (99 ^oC - 78 ^oC)

E5 = 890.82 J

E5 = 0.8908 kJ

Total energy required = E1 + E2 + E3 + E4 + E5

Total energy required = (2.5137 kJ) + (4.56 kJ) + (19.68 kJ) + (31.908 kJ) + (0.8908 kJ)

Total energy required = 59.6 kJ