How much energy is required to heat 87.1 g acetone (molar mass=58.08 g/mol) from a solid at - 154.0°C to a liquid at - 42.0°C? The following physical data may be useful. ΔHfus = 7.27 kJ/mol Cliq = 2.16 J/g°C Cgas = 1.29 J/g°C Csol = 1.65 J/g°C Tmelting = - 95.0°C.

The answer to the question above is

The energy required to heat 87.1 g acetone from a solid at - 154.0°C to a liquid at - 42.0°C = 29.36 kJ

Explanation:

The given variables are

ΔHfus = 7.27 kJ/mol

Cliq = 2.16 J/g°C

Cgas = 1.29 J/g°C

Csol = 1.65 J/g°C

Tmelting = - 95.0°C.

Initial temperature = - 154.0°C

Final temperature = - 42.0°C?

Mass of acetone = 87.1 g

Molar mass of acetone = 58.08 g/mol

Solution

Heat required to raise the temperature of solid acetone from - 154 °C to - 95 °C or 59 °C is given by

H = mCsolT = 87.1 g * 1.65 J/g°C * 59 °C = 8479.185 J

Heat required to melt the acetone at - 95 °C = ΔHfus*number of moles =

But number of moles = mass: (molar mass) = 87.1:58.08 = 1.5

Heat required to melt the acetone at - 95 °C = 1.5 moles*7.27 kJ/mol = 10.905 kJ

The heat required to raise the temperature to - 42 degrees is

H = m*Cliq*T = 87.1 g * 2.16 J/g°C * 53 °C = 9971.21 J

Total heat = 9971.21 J + 10.905 kJ + 8479.185 J = 29355.393 J = 29.36 kJ

The energy required to heat 87.1 g acetone from a solid at - 154.0°C to a liquid at - 42.0°C is 29.36 kJ