Ethanol (C2H5OH) melts at -114 C and boils at 78 C. The enthalpy of fusion of et

Question

Ethanol (C2H5OH) melts at -114 C and boils at 78 C. The enthalpy of fusion of ethanol is 5.02 kJ/mol, and its enthalpy of vaporization is 38.56 kJ/mol. The specific heat of solid and liquid ethanol are 0.97 J/gK are 2.3 J/gK respectively.

Part A How much heat is required to convert 48.5 g of ethanol at 40 C to the vapor phase at 78 C? Express your answer using two significant figures.

Part B How much heat is required to convert 48.5 g of ethanol at -151 C to the vapor phase at 78 C? Express your answer using two significant figures

Explanation / Answer

Part A : step 1 : ethanol (l) at 40 oC to 78 oC (l)

q1 = mCpdT = 48.5 x 2.3 x (78 - 40) = 4.239 kJ

step 2 : ethanol (l) at 78 oC to vapor at 78 oC

q2 = mdHv = 48.5 x 38.56/46.07 = 40.554 kJ

Total heat required to convert ethanol liquid to gas = q1 + q2 = 44.833 kJ

Part b : step 1 : ethanol (s) at -151 oC to solid 0 oC

q1 = mCpdT = 48.5 x 0.97 x 151 = 7.104 kJ

step 2 : ethanol (s) to ethanol (l) at 0 oC

q2 = mdHf = 48.5 x 5.02/46.07 = 5.285 kJ

step 3 : ethanol (l) at 0 oC to (l) at 78 oC

q3 = mCpdT = 48.5 x 2.3 x (78-0) = 8.701 kJ

step 4 : ethanol (l) at 78 oC to gas at 78 oC

q4 = mdHv = 48.5 x 38.56/46.07 = 40.554 kJ

Total heat required = q1 + q2 + q3 + q4 = 61.644 kJ

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