How much energy (in kilojoules) is released when 26.5g of ethanol vapor at 86.0C is cooled to -12.0C? Ethanol has mp = -114.5C , bp = 78.4C, delta H vap = 38.56 (KJ/mol) and delta H fus = 4.60 (KJ/mol) . The molar heat capacity is 113J/(K.mol) for the liquid and 65.7 J/(K.mol) for the vapor.
You must calculate the heat evolved in stages, then add all of the heats together to obtain the sum. Here is the way you go about it.
q1 = heat lost in moving the vapor from the starting point to the boiling point.
q1 = mass vapor x specific heat vapor x (Tfinal-Tinitial) where Tfinal will be the boiling point and Tinitial is where you start.
q2 = heat lost in condensing the vapor at the boiling point.
q2 = mass vapor at the boiling point x delta Hvaporization.
q3 heat lost in cooling the liquid vrom the boiling point to the melting (freezing) point.
q3 = mass liquid x specific heat liquid x (Tfinal-Tinitial) where Tfinal is the melting point and Tinitial is the boiling point.
q4 = heat lost is freezing the liquid.
q4 = mass liquid x heat fusion.
q5 = heat lost in moving the temperature from the freezing point to the final T.
q5 = mass solid x specific heat solid x (Tfinal - Tinitial) where Tfinal is the final T and Tinitial is the melting point.
qtotal = q1 + .....q5.
Watch the units. I note most of the specific heats are in J or kJ/mol but the mass is in grams.
To calculate the energy released when 26.5g of ethanol vapor is cooled, we need to consider the energy required for the phase change from vapor to liquid and the heat exchange during the cooling process.
1. Calculate the energy released during the phase change from vapor to liquid:
The molar heat of vaporization (delta H vap) is given as 38.56 KJ/mol. To find the energy released for 26.5g of ethanol, we need to convert the mass of ethanol to moles:
Molar mass of ethanol (C2H5OH) = 2(12.01 g/mol) + 6(1.008 g/mol) + 1(16.00 g/mol) = 46.07 g/mol
Number of moles = Mass (g) / Molar mass (g/mol) = 26.5 g / 46.07 g/mol
Now we can calculate the energy released during the phase change:
Energy released = Molar heat of vaporization (delta H vap) × Number of moles
2. Calculate the energy released during cooling:
First, we need to calculate the temperature change:
Temperature change = Final temperature - Initial temperature
= -12.0 °C - 86.0 °C
Next, we need to calculate the energy exchanged during the cooling process:
For cooling the liquid ethanol, we use the molar heat capacity of the liquid (113 J/(K.mol)). However, during the phase change from liquid to solid, we need to consider the molar heat of fusion (delta H fus), which is given as 4.60 KJ/mol.
Energy exchanged during cooling = Molar heat capacity (liquid) × Number of moles × Temperature change
+ delta H fus × Number of moles
3. Add the two energies together to get the total energy released:
Total energy released = Energy released during the phase change + Energy exchanged during cooling
Note: Make sure to convert the units appropriately to ensure consistent units for all calculations (e.g., converting grams to moles and Kelvin to Celsius).