Ethanol (c2h5oh) melts at -114â°c. the enthalpy of fusion is 5.02 kj/mol. the specific heats of solid and liquid ethanol are 0.97 j/g-k and 2.3 j/g-k, respectively. how much heat (kj) is needed to convert 25.0 g of solid ethanol at -135â°c to liquid ethanol at -50â°c?

You'll want to add three amounts of heat. 

(1) Specific heat of lowering the temperature from -135°C to the melting point -114°C
(2) Latent heat of fusion/melting
(3) Specific heat of elevating the temperature from -114°C to -50°C

(1) E = mCΔT = (25 g)(0.97 J/g·°C)(1 kJ/1000 J)(-114 - -135) = 0.509 kJ
(2) E = mΔH = (25 g)(5.02 kJ/mol)(1 mol/46.07 g ethanol) = 2.724 kJ
(3) E = mCΔT = (25 g)(2.3 J/g·°C)(1 kJ/1000 J)(-50 - -114) = 3.68 kJ

Summing up all energies, the answer is 6.913 kJ.