Calculate the amount of heat (in kJ) required to convert 44.0 g of solid ethanol

Question

Calculate the amount of heat (in kJ) required to convert 44.0 g of solid ethanol (molar mass = 46.1 g/mol at -126.0 degree C to gaseous ethanol at 94 degree C. (specific heat capacities: solid: 2.42 J/g degree C, liquid: 2.44 J/g. degree C, gas: 1.70 J/g. degree C; heat of fusion: 4.9 kJ/mol; heat of vaporization: 38.6 kJ/mol; melting point: -114 degree C, boiling point: 78 degree C). Show all math steps (including temperature changes) and include units in the methods and answers. For each step, specify what you are solving for (heating liquid, melting solid etc.)

Explanation / Answer

Ti = -126.0

Tf = 94.0

here

Cs = 2.42 J/goC

Heat required to convert solid from -126.0 to -114.5

Q1 = m*Cs*(Tf-Ti)

= 44 g * 2.42 J/goC *(-114.5-(-126)) oC

= 1224.52 J

Lf = 4.9KJ/mol =

4900 J/mol

Lets convert mass to mol

Molar mass of C2H6O = 46.1 g/mol

number of mol

n= mass/molar mass

= 44.0/46.1

= 0.955 mol

Heat required to convert solid to liquid at -114.5 oC

Q2 = n*Lf

= 0.955 mol *4900 J/mol

= 4680.038 J

Cl = 2.44 J/goC

Heat required to convert liquid from -114.5 to 78.0

Q3 = m*Cl*(Tf-Ti)

= 44 g * 2.44 J/goC *(78--114.5) oC

= 20666.8 J

Lv = 38.6KJ/mol =

38600J/mol

Heat required to convert liquid to gas at 78.0 oC

Q4 = n*Lv

= 0.955 mol *38600 J/mol

= 36867.24 J

Cg = 1.7 J/goC

Heat required to convert vapour from 78.0 to 94.0

Q5 = m*Cg*(Tf-Ti)

= 44 g * 1.7 J/goC *(94-78) oC

= 1196.8 J

Total heat required = Q1 + Q2 + Q3 + Q4 + Q5

= 1224.52J + 4680.038J + 20666.8J + 36867.24J + 1196.8J

= 64635 J

= 64.64 KJ

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