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

Submitted by moeriahh on Thu, 02/14/2013 - 16:08

1.  Ethanol (C2H5OH) 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.

Ethanol (C2H5OH) 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