From data below, calculate the total heat (J) needed to convert 0.539 mol gaseous ethanol at 300°C and 1 atm to liquid ethanol at 25.0°C and 1 atm.

Boiling point at 1 atm 78.5°C
c ethanol gas 1.43 J/g·°C
c ethanol liquid 2.45 J/g·°C
ÄH°vap 40.5 kJ/mol

help please Answer in J

my work:
.539 x 46= 24.79
24.79 x 1.43 x -221.50= -7852 J
.539 x -40.5= -21,829 J
24.79 x 2.45 x -53.5 = 32930 J

then -7852 + -21, 829 + -3249= -32930 J J

To calculate the total heat needed to convert gaseous ethanol to liquid ethanol, we need to consider two processes: warming the gaseous ethanol from 300°C to its boiling point at 78.5°C, and then cooling the ethanol from its boiling point to 25.0°C.

First, let's calculate the heat required to warm the gaseous ethanol from 300°C to its boiling point at 78.5°C.

Step 1: Calculate the energy required to increase the temperature of the ethanol gas:
mass of ethanol gas = 0.539 mol x molar mass of ethanol
mass of ethanol gas = 0.539 mol x 46 g/mol
mass of ethanol gas = 24.794 g

Heat required to warm the gaseous ethanol = mass x specific heat capacity x change in temperature (ΔT)
Heat required to warm the gaseous ethanol = 24.794 g x 1.43 J/g·°C x (78.5°C - 300°C)
Heat required to warm the gaseous ethanol = -7881.374 J (note the negative sign since the temperature is decreasing)

Next, let's calculate the heat required to vaporize the ethanol at its boiling point.

Step 2: Calculate the energy required to vaporize the ethanol:
Heat required to vaporize the ethanol = moles of ethanol x enthalpy of vaporization (ÄH°vap)
Heat required to vaporize the ethanol = 0.539 mol x 40.5 kJ/mol x 1000 J/kJ
Heat required to vaporize the ethanol = -21,829.5 J (note the negative sign again)

Finally, let's calculate the heat required to cool the vaporized ethanol from its boiling point to 25.0°C.

Step 3: Calculate the energy required to decrease the temperature of the liquid ethanol:
Heat required to cool the liquid ethanol = mass x specific heat capacity x change in temperature (ΔT)
Heat required to cool the liquid ethanol = 24.794 g x 2.45 J/g·°C x (78.5°C - 25.0°C)
Heat required to cool the liquid ethanol = -32,939.065 J (negative sign since the temperature is decreasing)

Now, add up the total heat required:
Total heat = Heat to warm + Heat to vaporize + Heat to cool
Total heat = -7881.374 J + (-21,829.5 J) + (-32,939.065 J)
Total heat = -62,649.939 J

Therefore, the total heat needed to convert 0.539 mol of gaseous ethanol at 300°C and 1 atm to liquid ethanol at 25.0°C and 1 atm is approximately -62,649.939 J. Note that the negative sign indicates that heat is being removed from the system.