Question

The molar heat of fusion of sodium metal is \(2.60 \mathrm{~kJ} / \mathrm{mol}\), whereas its heat of vaporization is \(97.0 \mathrm{~kJ} / \mathrm{mol} .\) a. Why is the heat of vaporization so much larger than the heat of fusion? b. What quantity of heat would be needed to melt \(1.00 \mathrm{~g}\) sodium at its normal melting point? c. What quantity of heat would be needed to vaporize \(1.00 \mathrm{~g}\) sodium at its normal boiling point? d. What quantity of heat would be evolved if \(1.00 \mathrm{~g}\) sodium vapor condensed at its normal boiling point?

Short answer

a. The heat of vaporization is much larger than the heat of fusion because it involves breaking more intermolecular forces and overcoming stronger metallic bonding forces between sodium ions in the liquid phase. b. To melt 1.00 gram of sodium: heat needed = \(\frac{1.00 \mathrm{~g}}{22.99 \mathrm{~g/mol}} × 2.60 \mathrm{~kJ/mol}\) c. To vaporize 1.00 gram of sodium: heat needed = \(\frac{1.00 \mathrm{~g}}{22.99 \mathrm{~g/mol}} × 97.0 \mathrm{~kJ/mol}\) d. The heat evolved when 1.00 gram of sodium vapor condenses: heat evolved = -\(\frac{1.00 \mathrm{~g}}{22.99 \mathrm{~g/mol}} × 97.0 \mathrm{~kJ/mol}\)

Step-by-step solution

a. Difference between heat of vaporization and heat of fusion

The heat of fusion is the energy required to change a substance from a solid to a liquid, while the heat of vaporization is the energy required to change a substance from a liquid to a gas. Generally, the heat of vaporization is much larger than the heat of fusion because it involves breaking more intermolecular forces to transform a liquid into a gas. In the case of sodium metal, the heat of vaporization is higher because additional energy is needed to overcome the stronger metallic bonding forces between sodium ions in the liquid phase.

b. Calculating heat to melt \(1.00 \mathrm{~g}\) of sodium

To find the heat needed to melt 1.00 gram of sodium, we will first need to determine how many moles of sodium are in 1.00 gram of sodium. The molar mass of sodium (Na) is 22.99 g/mol. First, calculate the moles of sodium: moles of Na = \(\frac{mass}{molar~mass}\) moles of Na = \(\frac{1.00 \mathrm{~g}}{22.99 \mathrm{~g/mol}}\) Next, we'll use the molar heat of fusion to determine the heat needed to melt the sodium: heat needed = moles of Na × molar heat of fusion heat needed = \(\frac{1.00 \mathrm{~g}}{22.99 \mathrm{~g/mol}} × 2.60 \mathrm{~kJ/mol}\)

c. Calculating heat to vaporize \(1.00 \mathrm{~g}\) of sodium

To find the heat needed to vaporize 1.00 gram of sodium, we will again use the moles of sodium calculated in part (b) and the molar heat of vaporization. heat needed = moles of Na × molar heat of vaporization heat needed = \(\frac{1.00 \mathrm{~g}}{22.99 \mathrm{~g/mol}} × 97.0 \mathrm{~kJ/mol}\)

d. Calculating heat evolved when \(1.00 \mathrm{~g}\) sodium vapor condenses

When a substance condenses, it releases heat. The heat evolved during condensation is equal in magnitude but opposite in sign to the heat of vaporization. heat evolved = - heat needed to vaporize \(1.00 \mathrm{~g}\) of sodium heat evolved = -\(\frac{1.00 \mathrm{~g}}{22.99 \mathrm{~g/mol}} × 97.0 \mathrm{~kJ/mol}\)

Key concepts

Heat of Fusion

The heat of fusion is a pivotal concept when understanding how matter transitions between its solid and liquid states. It represents the amount of energy needed to convert a solid into a liquid at its melting point without changing its temperature. This fascinating process requires breaking some, but not all, intermolecular forces holding the particles in place.

For sodium metal, the heat of fusion is relatively low, marked at only 2.60 kJ/mol, which means that changing sodium from solid to liquid requires less energy compared to many other substances. This is reflective of the bonds that are present in the solid form and their relative ease of separation to form a liquid. The heat of fusion is a crucial concept in various scientific and industrial applications such as metallurgy, where precise control of the melting process is essential.

Molar Mass

Molar mass is essentially the weight of one mole of a substance, usually expressed in grams per mole (g/mol). It's an indispensable tool for chemists, as it links the macroscopic world that we can measure, with the microscopic world of atoms and molecules that we can’t see.

When posed with a problem concerning melting or vaporizing a specific amount of a substance, like 1.00 g of sodium in our case, the molar mass allows us to convert grams into moles. With a known molar mass of sodium (22.99 g/mol), one can calculate the moles of sodium and subsequently use this to find out the required heat for a phase change. This in turn gives insight into the energy transitions involved in the phase change processes.

Intermolecular Forces

Intermolecular forces are the forces of attraction or repulsion which act between neighboring particles, such as atoms, molecules, or ions. They are decisive in dictating the physical properties of substances, including melting points, boiling points, and states of matter at given temperatures.

In the context of the heat of vaporization, they provide a compelling explanation for why it is vastly greater than the heat of fusion. When a substance changes from solid to liquid, some intermolecular forces are broken; however, a complete disruption of these forces occurs only when the substance transitions from liquid to gas, which demands significantly more energy. For sodium, with its metallic bonding, the energy required to surpass these forces in the liquid phase is considerably high and accounts for its steep heat of vaporization.

Phase Change

A phase change is a transition of matter from one state (solid, liquid, or gas) to another. These changes occur when energy is added or removed from a substance, changing its overall intermolecular forces. For instance, adding heat to a solid increases kinetic energy, leading to the solid melting and becoming a liquid.

During each phase change, the temperature of the substance remains constant while the energy is being used to change the state, a direct consequence of the heat of fusion or vaporization. Conversely, removing energy from a gas (as heat) will cause it to condense, converting it back to liquid, and this process would release an amount of energy equivalent to the heat of vaporization, which is demonstrated in the condensation of sodium vapor in the exercise.