how much heat required to convert ethanol in solid state to liquid state

Ethanol (C_{2}H_{5}OH) melts at 114 °C and boils at 78 °C. Its density is 0.789 g/mL. The enthalpy of fusion of ethanol is 5.02 kJ/mol, and its enthalpy of vaporization is 38.56 kJ/mol. The specific heats of solid and liquid ethanol are 0.97 J/g°C and 2.3 J/g°C, respectively. How much heat (in kJ) is required to convert 25.0 g of ethanol at 25 °C to the vapor phase at 78 °C? Enter your answer with the correct number of significant figures, and DO NOT include units.
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Ethanol (C_{2}H_{5}OH) melts at 114 °C and boils at 78 °C. Its density is 0.789 g/mL. The enthalpy of fusion of ethanol is 5.02 kJ/mol, and its enthalpy of vaporization is 38.56 kJ/mol. The specific heats of solid and liquid ethanol are 0.97 J/g°C and 2.3 J/g°C, respectively. How much heat (in kJ) is required to convert 25.0 g of ethanol at 25 °C to the vapor phase at 78 °C? Enter your answer with the correct number of significant figures, and DO NOT include units.
Q = m*c *ΔT
where,
Q is the heat
m is the mass
c is the specific heat
and ΔT is the temperature difference ( t final  t initial)
You also need the molecular weight of ethanol: 46.1 g/mol
Calculate the heat needed from the lowest temperature to the melting point , i e. from the ethanol in solid form to its lowest temperature 114 degreec celcius mentioned in problem:
Q(s) = 63.0 g * 0.97 J/g*K * [114 deg C  (139 deg C)] = 1528 J/g
Calculate the heat need to melt the solid ethanol :
Heat of fusion = 5.2 kJ/mol = 5200 J/mol / 46.1 g/mol = 109 J/g
Q(melt) = 63 g * 109 J/g = 6860 J/g
Calculate the heat needed to bring the ethanol in liquid form to its boiling point 78 deg celc:
Q(l) = 63.0 g * 2.3 J/g*K * [78 deg C  (114 deg C)] = 27821 J/g
Calculate the heat need to vaorize the boiling ethanol i.e from from liquid to vapour change:
Heat of vaporization = 38.56 kJ/mol = 38560 J/mol / 46.1 g/mol = 836 J/g
Q(vap) = 63 g * 836 J/g = 52696 J/g
To get the total heat add up all the steps:
Q(tot) = Q(s) + Q(melt) + Q(l) + Q(vap) = 88905 J/g = 88.9 kJ/g
chemistry123
Thu, 20130214 17:07