Ethanol (C2H5OH) melts at -114 degrees Celsius and boils at 78decrees C. Its den

Question

Ethanol (C2H5OH) melts at -114 degrees Celsius and boils at 78decrees C. Its density is .789 g/ml. The enthalpy of fusion ofethanol is 5.02 kj/mol, and its enthalpy of vaporization is 38.56Kj/mol. The specific heat of solid and liquid ethanol are .97 J/g-kand 2.3 J/g-k, respectively. A) How much heat is required toconvert 25.0 g of ethanol at 25 degrees Celsius to the vapor phaseat 78 degrees Celsius? B) How much heat is required to convert 5.00L of ethanol at -140 degrees Celsius to the vapor phase at 78degrees Celsius? Thanks for any help that becomes available. Thanks for any help that becomes available.

Explanation / Answer

      Part A           mass =25.0 g , T1 = 25oC = 298 K                                    T2 = 78oC = 351 K ans s = 2.3 J /g-k               Step 1     heating ethanol (l) from 25oC to 78oC                      q1 = ms T                  = 25 x 2.3 x ( 78-25)                   =3047.5 J = 3.047 kJ Step2       evaporating 25 g ofethanol at 78oC                given Hvap = 38.56 Kj /mol          number of moles of ethanol = (25 / 46) = 0.543                q2 = 0.543 x 38.56 = 20.95 kJ      total heat required   Q =q1 +q2 = 24.003 kJ         part B:       volume of ethanol = 5.0 L= 5000 mL        density = 0.789 j/mL    mass = 0.789 x 5000 = 3945 g step 1 heating 3945 g of ethanol from-140oC to -114oC                       specific heatof solid ethanol = 0.97 J / g-K          q1 =msT                =3945 x 0.97 x ( -114- (-140oC)) = 99492.9 J =99.492 kJ step 2 melting of 3945 g of aolid ethanol at-114oC          given Hfus = 5.02 kJ /mol               numberof moles of ethanol = (3945 / 46) = 85.76           q2 = 85.76 x 5.02 = 430.51 kJ step 3 heating liquid ethanol at-114oC to 78oC           q3 = msT                = 3945 x 2.3 x (78- (-114))                  =1742.11 kJ step 4 evaporating 3945 g of ethanol at78oC              Hvap = 38.56 kJ /mol             number of moles = 85.76           q4 =85.76 x 38.56 = 3306.9 kJ       the total heat Q =q1 +q2 +q3 +q 4 =5579.01 kJ        4       

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