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

A) 8.48 kJ

B) 18.5 kJ

C) 32.2 kJ

D) 29.4 kJ

E) 9.97 kJ

I am studying for a test and am unable to answer this question. I was however able to answer questions like it, but there seems to be one step I am missing

Answer 1

This is calculated in 3 stages.

1) To heat the acetone from -154°C to melting point -95oC (dT = 59°C)

Q = mcdT

         Q = heat ,

m = mass of acetone = 87.1 g

        c = specific heat of acetone (solid) = 1.65 J/g°C

        dT = temperature difference = 59°C

Q = 87.1 g x 1.65 J/g°C x 59°C = 8479.2 J

Q = 8479.2 J

2) To melt the acetone at -95°C to liquid acetone at -95°C.

Q = m x Enthalpy of fusion

    = 87.1 g / 58.8 g/mol x 7.27 kJ/mol

    = 10779.3 J

Q = 10779.3 J

3)

3) To heat the liquid acetone from -95°C to -42oC

Q = mcdT where c = specific heat of water , dT = 53°C

   = 87.1 g x 2.16 J/g°C x 52°C

= 9783 J

Q = 9783 J

Therefore,

Total energy is required = 8479.2 J + 10779.3 J + 9783 J = 29041 J = 29.04 kJ

Therefore,

Ans= D