Calculate the total heat required (in joules) to convert 3.95 grams liquid ethanol (c2h5oh) at 25.0 °c to gas at 95.0 °c, given that the boiling point of ethanol is 78.5 °c, heat of vaporization is 40.5 kj/mol, the specific heat of liquid ethanol is 2.45 j/g-k, and the specific heat of gaseous ethanol is 1.43 j/g-k

The total heat required is 4088.6 J

Explanation:

We have three processes which involve heat absorption. We have to calculate the heat of each process and then to calculate the total heat.

1- liquid ethanol is heated from 25ºC (298 K) to the boiling point 78.5ºc (351.5 K). We use specifi heat of liquid ethanol to calculate the heat absorbed in this part:

H1= m x Sh x ΔT

H1= m x Sh x (Tfinal - Tinitial)

H1= 3.95 g x 2.45 J/g.K x (351.5 K -298 K)

H1= 517.7 J

2- State change: liquid ethanol is vaporized it turns gaseous ethanol The process occur at constant temperature (78.5ºC= 351.5 K). We need the molecular weight of ethanol (2 x 14 + 5 + 16 + 1= 46 g/mol) to cancel mol unit:

H2= m x ΔHvap x 1/Mw

H2= 3.95 g x 40.5 KJ/mol x 1 mol/46 g

H2= 3.477 KJ= 3477 J

3- Gaseous ethanol is heated from 78.5ºC to a final temperature of 95ºC (368 K). We use the specific heat of gaseous ethanol:

H3= m x Sh x ΔT

H3= 3.95 g x 1.43 J/g.K x (368 K - 351.5 K)

H3= 93.2 J

The total heat required is calculated as follows:

Htotal= H1 + H2 + H3

Htotal= 517.7 J + 3477.7 J + 93.2 J

Htotal= 4088.6 J

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