Question

How much heat energy is required to convert 49.4 g of solid ethanol at − 114.5 ° C to gasesous ethanol at 140.7 ° C ? The molar heat of fusion of ethanol is 4.60 kJ/mol , and its molar heat of vaporization is 38.56 kJ/mol . Ethanol has a normal melting point of − 114.5 ° C and a normal boiling point of 78.4 ° C . The specific heat capacity of liquid ethanol is 2.45 J / g ⋅ ° C , and that of gaseous ethanol is 1.43 J / g ⋅ ° C .

Answer 1

Step-by-step explanation:

mass of ethanol (s)
`m=49.4\ gm`

molar specific heat of fusion
`\Delta H_f=4.6\ KJ/mol`

molar specific heat of vaporization
`\Delta H_v=38.56\ KJ/mol`

specific heat of liquid
`c_l=2.45\ J/g-^(\circ)C`

specific heat of gas
`c_v=1.43\ J/g-^(\circ)C`

no of moles of ethanol
`n=(49.4)/(46)=1.074\ mol`

`Q_1=n* \Delta H_f=1.074* 4.6=4.94\ KJ`

`Q_2=mc_l\Delta T=49.4* 2.45* (192.9)`

`Q_2=23.346\ KJ`

`Q_3=n* \Delta H_v=1.074* 38.56=41.41\ KJ`

`Q_4=mc_v\Delta T=49.4* 1.43* (192.9)=13.626\ KJ`

`Q_(net)=Q_1+Q_2+Q_3+Q_4`

`Q_(net)=83.322\ KJ`