How much heat in kJ is required to convert 42.36 g of ethanol, C 2 H 5 OH , at -

Question

How much heat in kJ is required to convert 42.36 g of ethanol, C2H5OH, at -129.4 °C to the vapor phase at 78°C? Ethanol
melts at -114°C and boils at 78°C. The enthalpy of fusion is found by a
first-year experimentalist to be 4.975 kJ/mol and its enthalpy of vaporization
to be 36.7 kJ/mol. The S.H. of solid ethanol was determined by this same
experimentalist to be 0.878 J/g-K, while the S.H. of liquid ethanol was found
to be 2.32 J/g-K?

the answer is 57.8

I want the method to solve this question

Please Explain with steps

Thank you

Explanation / Answer

Energy required to raise the temperature = m. c. t

where m is mass , c is specific heat and t is change in temperature

Q = 42.36 x 0.878 x 15.4 = 572.75 J or 0.573 KJ

Number of moles of ethanol = 42.36 / 46.07 = 0.92 moles

Heat of fusion = 0.91 x 4.975 = 4.574 KJ

Amount of energy to raise the temperature from -114 to 78oC will be

Q = 42.36 x 2.32 x [78 - (-114) ]

= 18.86KJ

Heat of vapourisation = 0.92 x 36.7

= 33.74 KJ

So the total energy = 0.573 + 4.574 + 18.86 + 33.74

= 57.8 KJ

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