Question

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

Answer 1

Mass of acetone, m = 87.1 g

Step 1. Calculate the energy required to heat it from -154ºC to -95ºC

$\Delta$T = - 95 - (- 154)

= 59 ^oC
q = m*c* $\Delta$T
q = (87.1g)*(1.65 J/g°C)*(59)
q = 8.479 kJ

Step 2. Calculate the heat of fusion

q = (ΔHfus)*(m)/(M)
q = (7.27)*(87.1/58.08)
q = 10.902 kJ

Step 3. Calculate the heat required to bring it from -95^oC to -42^oC.

$\Delta$T = - 42 - (- 95)

= 53^oC

q = m*c*$\Delta$T  
q = (87.1)*(2.16)*(53)
q = 9.971 kJ

Step 4. Calculate total energy required.

Total energy = 8.479 kJ + 10.902 kJ + 9.971 kJ

= 29.352 kJ

So, energy required to heat 87.1 g acetone from a solid at -154.0°C to a liquid at -42.0°C = 29.352 kJ