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
To calculate the total heat needed to convert gaseous ethanol to liquid ethanol, you need to consider the following steps:
1. Calculate the heat needed to change the temperature of gaseous ethanol from 300°C to its boiling point at 1 atm (78.5°C).
First, find the number of moles of gaseous ethanol:
0.539 mol ethanol
Next, calculate the heat needed to change the temperature using the heat capacity for gaseous ethanol (c_ethanol_gas):
Heat = number of moles (n) x molar heat capacity (c_ethanol_gas) x change in temperature (ΔT)
Heat = 0.539 mol x 1.43 J/g·°C x (78.5 - 300) °C
Heat = -7,852 J (note the negative sign indicates heat is being lost)
2. Calculate the heat needed for the vaporization of gaseous ethanol at its boiling point.
Using the molar enthalpy of vaporization (ΔH_vap), calculate the heat needed for the vaporization of the given number of moles (n) of ethanol:
Heat = number of moles (n) x molar enthalpy of vaporization (ΔH_vap)
Heat = 0.539 mol x (-40.5 kJ/mol) x 1000 J/kJ
Heat = -21,829 J (note the negative sign indicates heat is being lost)
3. Calculate the heat needed to change the temperature of the liquid ethanol (vapor) from its boiling point (78.5°C) to its final temperature (25.0°C).
Convert the number of moles of ethanol (n) to grams (g):
Mass = number of moles (n) x molar mass (MW_ethanol)
Mass = 0.539 mol x 46 g/mol
Mass = 24.794 g
Calculate the heat needed to change the temperature using the heat capacity for liquid ethanol (c_ethanol_liquid):
Heat = mass (m) x specific heat capacity (c_ethanol_liquid) x change in temperature (ΔT)
Heat = 24.794 g x 2.45 J/g·°C x (78.5 - 25.0) °C
Heat = 32,930 J
Finally, calculate the total heat by summing up all the heats:
Total Heat = Heat needed to change temperature of gaseous ethanol + Heat needed for vaporization + Heat needed to change temperature of liquid ethanol (vapor)
Total Heat = (-7,852 J) + (-21,829 J) + (32,930 J)
Total Heat = 3,249 J
Therefore, the total heat needed to convert 0.539 mol of gaseous ethanol to liquid ethanol is 3,249 J.