The heat of vaporization of benzene, C6H6, is 30.7 kJ/mol at its boiling point of 80.1 °C. How much energy in the form of heat is required to vaporize 134 g benzene at its boiling point?
The amount of energy required to vaporize 134 g of benzene at its boiling point is 4,072 kJ. This can be calculated using the following equation:
Energy = (Mass of benzene (g) * Heat of vaporization (kJ/mol)) / Molecular weight of benzene (g/mol)
Energy = (134 g * 30.7 kJ/mol) / 78.11 g/mol
Energy = 4,072 kJ
To find the amount of energy required to vaporize a given mass of benzene, we need to use the heat of vaporization and the molar mass of benzene.
1. Calculate the number of moles of benzene:
- Molar mass of benzene (C6H6) = (12.01 g/mol * 6) + (1.01 g/mol * 6) = 78.11 g/mol
- Moles of benzene = Mass / Molar mass = 134 g / 78.11 g/mol = 1.716 mol
2. Calculate the energy required to vaporize the benzene:
- Energy required = Moles of benzene * Heat of vaporization
- Energy required = 1.716 mol * 30.7 kJ/mol = 52.8042 kJ
Therefore, 52.8 kJ of energy is required to vaporize 134 g of benzene at its boiling point.
To calculate the heat required to vaporize benzene, we can use the formula:
q = m * ΔHvap
Where:
q = heat required (in joules)
m = mass of benzene (in grams)
ΔHvap = heat of vaporization of benzene (in joules per gram)
First, we need to convert the mass of benzene from grams to moles. We can do this by dividing the mass by the molar mass of benzene.
The molar mass of benzene (C6H6) can be calculated by summing the atomic masses of all its elements:
C (carbon) = 12.01 g/mol (atomic mass)
H (hydrogen) = 1.01 g/mol (atomic mass)
Molar mass of benzene:
6 * C + 6 * H = 6 * 12.01 g/mol + 6 * 1.01 g/mol = 78.11 g/mol
Now that we know the molar mass of benzene is 78.11 g/mol, we can calculate the number of moles by dividing the given mass (134 g) by the molar mass:
moles of benzene = mass / molar mass = 134 g / 78.11 g/mol
Next, we calculate the heat required using the formula mentioned earlier:
q = moles of benzene * ΔHvap
To obtain the value of ΔHvap in joules per gram, we need to convert the given heat of vaporization from kJ/mol to J/g:
ΔHvap = (30.7 kJ/mol) * (1000 J/kJ) / (78.11 g/mol)
Finally, we can determine the heat required to vaporize the given mass of benzene:
q = (moles of benzene) * (ΔHvap)
Let's plug in the values and calculate the result.