The molar heat capacity of C6H6(ℓ) is 136J/mol · ◦C and of C6H6(g) is 81.6 J/mol · ◦C. The molar heat of fusion for benzene is 9.92 kJ/mol and its molar heat of vaporization is 30.8 kJ/mol. The melting point of benzene is 5.5◦C, its boiling point is 80.1◦C, and its molecular weight 78.0 g/mol. How much heat would be required to convert 702 g of solid benzene (C6H6(s)) at 5.5◦C into benzene vapor (C6H6(g)) at 100.0◦C?
In steps. First convert 702 g C6H6 to mols. mols = grams/molar mass.
q1 to melt benzene @ 5.5 C = mols C6H6 x molar heat fusion
q2 to raise C6H6 liquid to it's boiling point = mols C6H6 x heat capacity of liquid x (Tfinal-Tinitial) = ? Where Tfinal is boiling point Temperature and Tinitial is melting point temperature.
q3 to vaporize the C6H6 at the boiling point = mols C6H6 x heat vaporization = ?
q4 to raise T to 100 C = mols C6H6 x specific heat vapor x (Tfinal - Tinitial) = ? where Tfinal is 100 C and Tinitial is boiling point temperature.
qtotal = q1 + q2 + q3 + q4.
Note that some of the units are in J/mol and others in kJ/mol. Keep the units straight and remember that when adding, all of the units must be the same.
Post your work if you get stuck.
To calculate the heat required to convert solid benzene (C6H6) at 5.5°C into benzene vapor (C6H6) at 100.0°C, we need to consider the following steps:
1. Calculate the heat required to raise the temperature of the solid benzene from 5.5°C to its melting point (Tm):
Q1 = mass × specific heat capacity × ΔT
Q1 = 702 g × 136 J/mol·°C × (Tm - 5.5°C) / molar mass
2. Calculate the heat required to melt the solid benzene at its melting point:
Q2 = moles × heat of fusion
Q2 = 702 g / molar mass × 9.92 kJ/mol
3. Calculate the heat required to raise the temperature of the liquid benzene from its melting point to its boiling point (Tb):
Q3 = moles × specific heat capacity × ΔT
Q3 = 702 g / molar mass × 136 J/mol·°C × (Tb - Tm)
4. Calculate the heat required to vaporize the liquid benzene at its boiling point:
Q4 = moles × heat of vaporization
Q4 = 702 g / molar mass × 30.8 kJ/mol
5. Calculate the heat required to raise the temperature of the benzene vapor from its boiling point to 100.0°C:
Q5 = moles × specific heat capacity × ΔT
Q5 = 702 g / molar mass × 81.6 J/mol·°C × (100.0°C - Tb)
6. Add up all the calculated heats to get the total heat required:
Heat required = Q1 + Q2 + Q3 + Q4 + Q5
To apply these calculations, we need the molecular weight (molar mass) of benzene, which is given as 78.0 g/mol.
Note: The molar heat capacity values provided are given for the gas and liquid phases. For solid benzene, we will assume the same molar heat capacity as the liquid phase.
Now we can substitute the values into the equations and calculate the total heat required.