How much energy (kJ) is released when 20g of ethanol vapor at 98.5∘C is cooled to -14.5∘C?
Ethanol has mp = -114.5 ∘C, bp = 78.4 ∘C, ΔHvap = 38.56 kJ/mol and ΔHfusion = 4.60 kJ/mol. The molar heat capacity is 113 J/(K⋅mol) for the liquid and 65.7 J/(K⋅mol) for the vapor.
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(20 g ethanol) / (46.06844 g ethanol/mol) = 0.4341 mol ethanol
(65.7 J/K⋅mol) x (98.5 - 78.4) x 0.4341 mol = 573.3 J by cooling vapor to the bp
(38.56 kJ/mol) x 0.4341 mol = 16739 J by condensing the vapor
(113 J/K⋅mol) x (78.4 - (-14.5)) x 0.4341 mol = 4557 J by cooling the liquid
573.3 J + 16739 J + 4557 J = 21869.3 J = 22 kJ total