For a given solute in water, the energy changes are \(\Delta E_{\text {solute separation }}=835 \mathrm{~kJ}\), \(\Delta E_{\text {solvent separation }}=98 \mathrm{~kJ}\), and \(\Delta E_{\text {solvation }}=-805 \mathrm{~kJ} .\) Will this solute dissolve in water? Explain your answer, both numerically and in terms of the three-step model for a solute's dissolving in a solvent.

Short Answer

Expert verified
The solute will not dissolve in water, as the overall energy change for the process is positive (\(\Delta E_{\text{total}} = 128\, kJ\)), indicating an energetically unfavorable process. In this case, the solute-solvent interactions (-805 kJ) are not strong enough to overcome the solute-solute (835 kJ) and solvent-solvent (98 kJ) interactions.

Step by step solution

01

Breaking Solute-Solute Interactions

The energy change for breaking the solute-solute interactions is given as, \(\Delta E_{\text{solute separation}} = 835\, kJ\).
02

Breaking Solvent-Solvent Interactions

The energy change for breaking the solvent-solvent (water) interactions is given as, \(\Delta E_{\text{solvent separation}} = 98\, kJ\).
03

Forming Solute-Solvent Interactions

The energy change for forming new solute-solvent interactions (solvation) is given as, \(\Delta E_{\text{solvation}} = -805\, kJ\).
04

Calculating the Total Energy Change

Now, let's sum up all the energy changes to find the overall total energy change: \[\Delta E_{\text{total}} = \Delta E_{\text{solute separation}} + \Delta E_{\text{solvent separation}} + \Delta E_{\text{solvation}}\] Substituting values: \[\Delta E_{\text{total}} = 835\, kJ + 98\, kJ - 805\, kJ\] \(\Delta E_{\text{total}} = 128\, kJ\)
05

Final Conclusion

The overall energy change for the process is positive (\(128\, kJ\)), meaning it requires energy input to dissolve the solute in water. In this case, the solute-solvent interactions (-805 kJ) are not strong enough to overcome the solute-solute (835 kJ) and solvent-solvent (98 kJ) interactions. Since the energy change is positive, the solute will not dissolve in water, as it is an energetically unfavorable process.

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Key Concepts

These are the key concepts you need to understand to accurately answer the question.

Solvation Energy
Solvation energy is a key factor when considering whether a solute will dissolve in a solvent. It refers to the energy released when new interactions are formed between the solute and solvent molecules during the process known as solvation. This is often an exothermic process, meaning it releases energy, which can be observed as a negative value on the energy scale. In our discussed example, the solvation energy is \( \Delta E_{\text{solvation}} = -805\, kJ \).

This indicates that when the solute begins to interact with water (the solvent), it releases a significant amount of energy. However, for a solute to dissolve, this energy must be sufficient to overcome the energy required to break both solute-solute and solvent-solvent interactions. The ease of solvation and the resulting solubility of a substance can significantly impact various fields such as pharmaceuticals, where the solvation energy influences how effective a drug can be delivered into the body.
Solute-Solute Interactions
The concept of solute-solute interactions involves the forces that hold together the particles of the solute. These can include ionic bonds in salts or intermolecular forces in other compounds. In our textbook exercise, the energy needed to break these interactions is substantial, precisely \( \Delta E_{\text{solute separation}} = 835\, kJ \).

When a solute dissolves, these bonds or forces must be broken for the individual solute particles to be surrounded by solvent molecules. If the energy required to disrupt these interactions is too high, it might prevent the solute from dissolving, as the process would not be energetically favorable. These interactions are fundamental when considering solubility, as they directly influence the outcome of dissolving processes. By understanding the strength of these interactions, we can predict how a substance will behave when mixed with a particular solvent.
Solvent-Solvent Interactions
Parallel to solute-solute interactions are the solvent-solvent interactions. These are the forces between solvent molecules that need to be overcome to make room for the solute particles. In the context of our problem, the energy associated with breaking solvent-solvent interactions, specifically within water molecules, is \( \Delta E_{\text{solvent separation}} = 98\, kJ \).

While it might seem like a lower value compared to the energy needed to break solute-solute interactions, it is nonetheless a crucial part of the overall energy balance. Overcoming these interactions is necessary for creating a 'space' within the solvent for the solute molecules to be accommodated. Understanding these interactions helps explain the ‘like dissolves like’ principle, where polar solvents like water are better at dissolving polar or ionic solutes due to the ability to form energetically favorable interactions.
Energy Change in Dissolving
The energy change in dissolving a solute in a solvent is a comprehensive measure that incorporates the energy needed to break solute-solute and solvent-solvent interactions, alongside the energy released during solvation. It's the net result of these steps that determines whether a solute will dissolve. For the problem at hand, this total energy change is calculated as follows: \[ \Delta E_{\text{total}} = 835\, kJ + 98\, kJ - 805\, kJ \]\[ \Delta E_{\text{total}} = 128\, kJ \]Since the value is positive (\( 128\, kJ \)), it indicates that the overall process requires additional energy, making the dissolution of this particular solute in water energetically unfavorable. A negative total energy change would suggest the process is spontaneous and that the solute would readily dissolve.

From a practical standpoint, this calculation helps in determining solubility in various contexts, such as developing new chemical formulations or understanding natural phenomena like mineral dissolution in water bodies. However, it's important to remember that this is a simplified model and other factors such as temperature and pressure also play significant roles in the dissolving process.

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