Question

Ethanol (C₂H₅OH) melts at -114°C. The enthalpy of fusion is 5.02 kJ/mol. The specific heats of solid and liquid ethanol are 0.97 J/gK and 2.3 J/gK, respectively. How much heat (kJ) is needed to convert 25.0 g of solid ethanol at -135°C to liquid ethanol at -50°C?

Answer 1

This is calculated in 3 stages.

1) To heat the solid ethanol from -135°C to melting point -114^oC (dT = 21°C)

Q = mcdT

         Q = heat ,

m = mass of ethanol = 25 g

        c = specific heat of solid etthanol = 0.97 J/g/K

        dT = temperature difference = 21°C = 21 K

Q = 25 g x 0.97 J/g/°K x 21 K = 509.25 J

Q = 509.25 J

2) To melt the solid ethanol at -114°C to liquid ethanol at -114°C.

Q = moles x Enthalpy of fusion

    = (25 g / 46 g /mol) x 5.02 x 10³ J/mol

    = 2728.3 J

Q = 2728.3 J

3) To heat the liquid ethanol from -114°C to -50°C

Q = mcdT where c = specific heat of liquid ethanol , dT = 64°C = 64 K

   = 25 g x 2.3 J/g/K x 64 K

= 3680 J

Q = 3680 J

Therefore,

Total heat required = 509.25 J + 2728.3 J + 3680 J = 6917.55 J