Question

A substance has a heat of vaporization of \(\Delta H_{\text { ap }}\) and heat of fusion of \(\Delta H_{\text { fus. }} .\) Express the heat of sublimation in terms of \(\Delta H_{\text { vap }}\) and \(\Delta H_{\text { fus }}\)

Short answer

\(\Delta H_{\text{sub}} = \Delta H_{\text{fus}} + \Delta H_{\text{vap}}\)

Step-by-step solution

Understanding the Process of Sublimation

Sublimation is the process where a substance goes from a solid to a gas phase without passing through the liquid phase. This process requires the sum of the energy needed for fusion (solid to liquid) and vaporization (liquid to gas).

Expressing the Heat of Sublimation

The heat of sublimation, \(\Delta H_{\text{sub}}\), is the total amount of heat required to convert a substance from solid to gas. Therefore, \(\Delta H_{\text{sub}}\) is the sum of the heat of fusion, \(\Delta H_{\text{fus}}\), and the heat of vaporization, \(\Delta H_{\text{vap}}\): \[\Delta H_{\text{sub}} = \Delta H_{\text{fus}} + \Delta H_{\text{vap}}\]

Key concepts

Phase Transition

In the world of physics and chemistry, a phase transition is a transformation within a material from one state of matter to another. This change happens when energy, in the form of heat, is either absorbed or released, causing the material to switch between solid, liquid, and gas phases.

A typical example can be seen when ice (solid water) melts into liquid water. As heat is introduced, the ice absorbs energy, which breaks the molecular bonds holding it tightly together, and it undergoes a phase transition into a liquid. This process of melting is called fusion. Conversely, when a liquid is cooled, it releases energy and transitions into a solid, which is known as solidification or freezing.

Another prime example is boiling, where a liquid absorbs heat and transitions into a gas (vaporization). If the gas is cooled, it releases heat and transitions back into liquid, a process known as condensation.

Heat of Fusion

The heat of fusion, denoted ewline as ewline ewline ewline ewline ewline ewline ewline is the quantity of heat required to change a substance from solid to liquid at its melting point, without changing its temperature. It is a specific type of latent heat since during the melting process, the temperature of the substance remains constant while it absorbs heat energy.

For instance, while ice melts into water, it does so at 0 degrees Celsius under standard atmospheric conditions, and the heat of fusion for water is around 334 joules per gram. This means each gram of ice requires 334 joules of energy to turn into water without any increase in temperature. This concept is crucial in understanding the energy exchange during the melting process of any substance.

Heat of Vaporization

The heat of vaporization, symbolized by ewline is the amount of energy that must be added to a liquid substance to transform it into a gas at its boiling point. Similar to the heat of fusion, this is another form of latent heat where the temperature of the substance does not change during the process of vaporization.

Water, for example, requires approximately 2260 joules of energy per gram to convert from liquid to gas at 100 degrees Celsius. This energy breaks the intermolecular forces in the liquid, allowing the molecules to disperse and form a gas. The heat of vaporization plays a vital role in many natural and industrial processes, such as the water cycle and cooling mechanisms.