Question

The heat of fusion of aluminum is \(3.95 \mathrm{kJ} / \mathrm{g}\). What is the molar heat of fusion of aluminum? What quantity of energy is needed to melt \(10.0 \mathrm{g}\) of aluminum? What quantity of energy is required to melt \(10.0 \mathrm{mol}\) of aluminum?

Short answer

The molar heat of fusion of aluminum is 106.65 kJ/mol. To melt 10.0 g of aluminum, 39.5 kJ of energy is required. To melt 10.0 mol of aluminum, 1066.5 kJ of energy is needed.

Step-by-step solution

Find the molar mass of aluminum

To find the molar heat of fusion, we need to know the molar mass of aluminum. Aluminum's atomic number is 13, which means it has a molar mass of 27.0 g/mol.

Calculate the molar heat of fusion of aluminum

We are given the heat of fusion of aluminum as 3.95 kJ/g. To find the molar heat of fusion, we multiply the heat of fusion by the molar mass: Molar heat of fusion = (Heat of fusion in kJ/g) × (Molar mass in g/mol) \(Molar\: heat\: of\: fusion = 3.95\: \frac{kJ}{g} \times\: 27.0\: g/mol\) \(Molar\: heat\: of\: fusion = 106.65\: kJ/mol\) So, the molar heat of fusion of aluminum is 106.65 kJ/mol.

Calculate the energy required to melt 10.0 g of aluminum

Now, we can calculate the energy required to melt 10.0 g of aluminum using the heat of fusion: Energy = (Heat of fusion in kJ/g) × (Mass in g) \(Energy = 3.95\: \frac{kJ}{g} \times\: 10.0\: g\) \(Energy = 39.5\: kJ\) So, 39.5 kJ of energy is required to melt 10.0 g of aluminum.

Calculate the energy required to melt 10.0 mol of aluminum

Lastly, we will calculate the energy required to melt 10.0 mol of aluminum using the molar heat of fusion: Energy = (Molar heat of fusion in kJ/mol) × (Moles of aluminum) \(Energy = 106.65\: \frac{kJ}{mol} \times\: 10.0\: mol\) \(Energy = 1066.5\: kJ\) So, 1066.5 kJ of energy is required to melt 10.0 mol of aluminum.

Key concepts

Heat of Fusion

The concept of heat of fusion is pivotal in understanding phase changes in substances. It refers to the amount of energy needed to change one gram of a solid into a liquid without changing its temperature. This process occurs at the melting point of the substance and involves breaking the bonds between the particles in the solid state.

In the context of the exercise, aluminum's heat of fusion is given as 3.95 kJ/g, which signifies the energy required to melt a single gram of solid aluminum into liquid. When determining the energy to melt a specific mass, such as 10.0 g of aluminum, this heat of fusion is multiplied by the mass to calculate the total amount of energy needed for the phase change. It is a crucial property used in many scientific and industrial applications, such as determining the energy for refrigeration or the production of metals.

Molar Mass

Molar mass represents the mass of one mole of a substance and is expressed in grams per mole (g/mol). One mole corresponds to Avogadro's number of particles, which is approximately 6.022 × 10²³ particles. The molar mass allows chemists to convert between grams of a substance and moles, making it possible to relate physical masses to chemical formulas and equations.

For aluminum, the molar mass is 27.0 g/mol, as determined from its atomic number and average atomic mass. In the exercise, the knowledge of aluminum's molar mass is essential for calculating the molar heat of fusion, which is the energy required to melt one mole of solid to liquid at the substance's melting point. By multiplying the heat of fusion (per gram) by the molar mass, we obtain the energy involved in melting a mole of the solid substance.

Enthalpy of Phase Change

Enthalpy of phase change, often simply referred to as the heat of fusion in the context of melting, is the heat absorbed by a substance as it transforms from one phase to another at constant temperature and pressure. The term describes a form of latent heat, specifically the amount required for a phase change without a change in temperature.

In our example with aluminum, when calculating the energy for melting aluminum on a molar basis, we are discussing the enthalpy of phase change. This is the same concept as the molar heat of fusion and reflects how much energy is needed to overcome the intermolecular forces holding the solid aluminum together, thus turning it into a liquid phase. This enthalpy change is a characteristic property of every pure substance and is typically expressed in kJ/mol, as demonstrated in step 2 and step 4 of the problem's solution.