What do we mean by the total energy change \(\Delta E_{\text {total }}\) for the dissolving process, and why is it important to know about this energy change?

The total energy change (\(\Delta E_{\text {total}}\)) for the dissolving process refers to the net difference in energy between the energy required to break the intermolecular forces (or bonds) holding the solute particles together, as well as the energy required to break the solvent-solvent interactions, and the energy released when new solute-solvent interactions are formed.

The dissolving process can be broken down into three sub-processes: 1. Breaking the intermolecular forces between the solute particles (requires energy, endothermic): \(\Delta E_{1}\) 2. Breaking the intermolecular forces between the solvent particles to create space for the solute particles (requires energy, endothermic): \(\Delta E_{2}\) 3. Forming new solute-solvent interactions (releases energy, exothermic): \(\Delta E_{3}\) The total energy change during the dissolving process can be calculated as: \(\Delta E_{\text {total}} = \Delta E_{1} + \Delta E_{2} - \Delta E_{3}\)

Understanding the total energy change during the dissolving process is important for several reasons: 1. Solubility determination: If \(\Delta E_{\text {total}}\) is negative (i.e., the process is exothermic), the substance is expected to be more soluble because the process releases energy and is favored at lower temperatures. Conversely, if \(\Delta E_{\text {total}}\) is positive (i.e., the process is endothermic), the substance is more soluble at higher temperatures because the higher temperature provides the energy needed for the dissolving process. 2. Predicting spontaneity: Knowing the energy change can help predict whether a reaction is spontaneous or not. A negative \(\Delta E_{\text {total}}\) often indicates that a reaction is spontaneous, while a positive \(\Delta E_{\text {total}}\) usually requires external energy input to proceed. 3. Heat and temperature effects: Understanding the energy change associated with dissolving a solute in a solvent is crucial for managing temperature-related problems, such as in chemical and industrial processes, where control of heat and temperature is essential. In summary, knowing the total energy change during the dissolving process helps us understand solubility trends, predict spontaneity, and manage heat and temperature in various applications.