The boiling point of ethanol is at 78.37°C. So, the energy must include sensible heat to raise 19°C to the boiling point and latent heat to change liquid to gas. The equation would be
Energy = Sensible heat + Latent heat
Energy = mCpΔT + mΔH
For ethanol,
Cp = 46.068 + 102,460T - 139.63T² - 0.030341T³ + 0.0020386T⁴ J/kmol·K
ΔH = 38,560 J/mol
Integrate the Cp expression to determine CpΔT:
CpΔT = ∫₂₉₂³⁵²(46.068 + 102,460T - 139.63T² - 0.030341T³ + 0.0020386T⁴ )dT
The upper limit is (78.37+273) = 352 K, while the lower limit is (19 + 273) = 292.
CpΔT = 2384857192 J/kmol·K
2,000 J = m(2384857192 J/kmol)(1 kmol/1000 mol) + m(38,560 J/mol)
m = 8.253×10⁻⁴ moles of ethanol
Since the molar mass of ethanol is 46.07 g/mol,
Mass = (8.253×10⁻⁴ mol)(46.07 g/mol)
Mass = 0.038 g ethanol
