Question

From the data below, calculate the total heat (in J) needed to convert 0.670 mol of gaseous ethanol at 300.0 C and 1 atm to liquid ethanol at 25.0 C and 1 atm:

b.p. at 1 atm: 78.5 C

H vap: 40.5 kJ/mol

c ethanol( g ): 1.43 J/g *C

c ethanol( l ): 2.45 J/g *C

Answer 1

mass of ethanol = 0.670 x 46.0 g/mol = 30.82 g

there is need of three steps :

1. gas from 300 C --> 78.5 C

heat change = m x C x deltaT

= 30.82 g x 1.43 J/g C x - 221.5 C

= - 9762.08 J

2. condense the gas to liquid at 78.5 C = m x H vap/mol
= 0.670 mol x - 40.5 kJ/mol

= - 27.135 kJ/mol

3. cool down the liquid from 78.5 C to 25 C = m x C x deltaT

= 30.82 g x 2.45J/g C x - 53.5 C

= - 4039.73 J

therefore

Total heat required =( - 9762.08 J ) + ( - 27.135 kJ/mol ) + ( - 4039.73 J )

= - 40936.81 J