Question

The molar heat of fusion of benzene is \(9.92 \mathrm{kJ} / \mathrm{mol}.\) Its molar heat of vaporization is \(30.7 \mathrm{kJ} / \mathrm{mol}\). Calculate the heat required to melt \(8.25 \mathrm{g}\) of benzene at its normal melting point. Calculate the heat required to vaporize \(8.25 \mathrm{g}\) of benzene at its normal boiling point. Why is the heat of vaporization more than three times the heat of fusion?

Short answer

The heat required to melt 8.25 g of benzene at its normal melting point is 1.037 kJ, and the heat required to vaporize 8.25 g of benzene at its normal boiling point is 3.248 kJ. The heat of vaporization is more than three times the heat of fusion because more energy is required to overcome the intermolecular forces between the molecules in the liquid phase as compared to the energy needed to overcome the forces between the molecules in the solid phase during fusion.

Step-by-step solution

Calculate the number of moles of benzene

We need to convert the mass of benzene (8.25 g) into moles. To do this, we need the molar mass of benzene, which is 78.11 g/mol. Number of moles = mass of benzene / molar mass of benzene Number of moles = \( \frac{8.25 g}{78.11 g/mol} \) #Step 2: Calculate the heat required to melt benzene#

Calculate the heat required to melt benzene

Multiply the number of moles of benzene by its molar heat of fusion (9.92 kJ/mol) to find the heat required to melt the benzene at its normal melting point. Heat of melting = number of moles × molar heat of fusion Heat of melting = \( \frac{8.25 g}{78.11 g/mol} \) × \( 9.92 kJ/mol \) #Step 3: Calculate the heat required to vaporize benzene#

Calculate the heat required to vaporize benzene

Multiply the number of moles of benzene by its molar heat of vaporization (30.7 kJ/mol) to find the heat required to vaporize the benzene at its normal boiling point. Heat of vaporization = number of moles × molar heat of vaporization Heat of vaporization = \( \frac{8.25 g}{78.11 g/mol} \) × \( 30.7 kJ/mol \) #Step 4: Explain why the heat of vaporization is more than three times the heat of fusion#

Explain the difference between heat of vaporization and heat of fusion

The heat of vaporization is the energy needed to change a substance from the liquid phase to the gaseous phase, while the heat of fusion is the energy needed to change a substance from the solid phase to the liquid phase. In the process of vaporization, more energy is required to overcome the intermolecular forces between the molecules in the liquid phase as compared to the energy needed to overcome the forces between the molecules in the solid phase during fusion. This is because, in the gaseous phase, the molecules are more dispersed, and the intermolecular forces are weaker. Hence, the heat of vaporization is more than three times the heat of fusion.

Key concepts

Heat of Fusion

The heat of fusion is an important concept in thermodynamics. It refers to the amount of energy required to change a substance from a solid to a liquid at its melting point. For benzene, this value is given as 9.92 kJ/mol.
When we melt 8.25 grams of benzene, we first need to determine how many moles are present using its molar mass, which is 78.11 g/mol.
By multiplying the moles of benzene by its molar heat of fusion, we can find the total heat required to melt the sample. This energy is needed to overcome the intermolecular forces holding the solid molecules together.
Though less than vaporization, this energy may still be significant depending on the substance and conditions.

Heat of Vaporization

The heat of vaporization refers to the energy required to convert a liquid into a gas at its boiling point. For benzene, the heat of vaporization is 30.7 kJ/mol, which is substantially higher than its heat of fusion.
This is because vaporization involves overcoming the intermolecular forces that are more pronounced in the liquid phase compared to the gaseous phase.
Calculating the heat needed to vaporize benzene involves a similar process to melting. We find the moles present in 8.25 grams and multiply by the molar heat of vaporization.

• This high value reflects the intense energy requirement to achieve a gaseous state, where benzene molecules move freely and are widely spaced apart.

Molar Mass Calculation

Calculating the molar mass of a substance is crucial for quantitative chemical analysis. The molar mass of benzene is given as 78.11 g/mol.
It helps us convert grams to moles, allowing us to calculate how much energy is involved in phase changes. Knowing this allows chemists to predict how a particular amount of energy affects a substance's state.
This conversion is foundational for any thermodynamic calculations. For 8.25 grams of benzene, divide the mass by its molar mass to determine the moles, aiding in calculating both melting and vaporizing heat requirements.

Intermolecular Forces

Intermolecular forces refer to the forces that exist between molecules, significantly influencing phase changes like melting and vaporizing.
In the context of benzene, we notice that more energy is required to overcome these forces when vaporizing than when melting.

• This is because liquid benzene molecules are closely packed, whereas gaseous molecules are spread out, requiring more energy to separate them.

Understanding these forces can explain why different substances have varying heats of fusion and vaporization. Benzene’s molecular interactions demand particularly high energy for vaporization, reflecting its strong intermolecular forces.

Phase Changes

Phase changes involve the transformation from one state of matter to another, influenced by energy input or removal. Common phase changes include melting, freezing, boiling, and condensing.
For benzene, melting involves transitioning from solid to liquid, requiring the heat of fusion, while vaporization means going from liquid to gas, needing the heat of vaporization.

• Each phase change has a characteristic energy value reflecting the intermolecular forces at play.

Understanding these helps in analyzing thermodynamic processes and designing experiments where temperature and energy manipulation is crucial.