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/g⋅K are 2.3 J/g⋅Krespectively.

1. 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.

2. How much heat is required to convert 48.5 g of ethanol at -157 ∘C to the vapor phase at 78 ∘C? Express your answer using two significant figures.

Answer 1

Q1.

m = 48.5 g of ethanol T = 40°C (liquid) to T = 78°C in vapor

Qsensible = methanol * Cpliquid * (Tb-Ti)

Qsensible = 48.5 * 2.3 * (78-40) = 4238.9 J

Qvaporization = mol ethano * Latent Heat = 48.5/46 * 38.56 = 40.6556 kJ = 40650 J

Qtotal = 4238.9 +40650 = 44888.9 J 44.88 kJ

Qtotal = 45 kJ

Q2.

heat for

-157°C

Qsensible = methanol * Cpliquid * (Tb-Ti) = 48.5*0.97 * (-114 - - 157) = 2022.935 J

Qmelting = methanol * Latent heat of fussin = 48.5/46 * 5.02 *1000 = 5292.82 J

Qsensible(-114 to 40) = 48.5 * 2.3 * (78--114) = 4238.9 J

Qpreivous = 45 kJ

Qtotal = (2022.935 +5292.82 +4238.9 ) /1000 + 45 = 56.554 kJ = 57 kJ