Question

Substance A is a nonpolar liquid and has only dispersion forces among its constituent particles. Substance \(B\) is also a nonpolar liquid and has about the same magnitude of dispersion forces among its constitucnt particles as substance A. When substance A and B are combincd, they spontancously mix. a. Why do the two substances mix? b. Predict the sign and magnitude of \(\Delta H_{\text { soln }}\) . c. Determine the signs and relative magnitudes of \(\Delta H_{\text { solure }}, \Delta H_{\text { solveat }},\) and \(\Delta H_{\operatorname{mix}}\)

Short answer

Substances A and B mix due to similar dispersion forces. \(\Delta H_{\text {soln}}\) is slightly positive and small. \(\Delta H_{\text {solute}}\) and \(\Delta H_{\text {solvent}}\) are positive; \(\Delta H_{\text {mix}}\) is negative, and all have small magnitudes.

Step-by-step solution

Understand the mixing of two nonpolar liquids

Two nonpolar substances generally mix because they are subject to similar intermolecular forces, which allows their molecules to interact and disperse into each other without substantial energy changes.

Predict the sign and magnitude of \(\Delta H_{\text {soln }}\)

The enthalpy change of mixing, \(\Delta H_{\text {soln}}\), for nonpolar liquids with similar magnitudes of dispersion forces is expected to be small and likely close to zero. The sign should be slightly positive, due to the endothermic breaking of intermolecular forces, offset by the exothermic formation of new interactions between the two substances.

Determine the signs and relative magnitudes of \(\Delta H_{\text {solute}}\), \(\Delta H_{\text {solvent}}\), and \(\Delta H_{\text {mix}}\)

The sign of \(\Delta H_{\text {solute}}\) and \(\Delta H_{\text {solvent}}\) should be positive as energy is required to separate the particles (endothermic process). The sign of \(\Delta H_{\text {mix}}\) should be negative, as energy is released when the particles mix (exothermic process). The magnitude of \(\Delta H_{\text {mix}}\) may be small, and the overall \(\Delta H_{\text {soln}}\) is expected to be close to zero if the two substances are very similar.

Key concepts

Intermolecular Forces

Intermolecular forces are the forces of attraction and repulsion between molecules that determine many of the physical properties of substances. In the case of nonpolar substances like substance A and B, these forces are primarily dispersion forces. Dispersion forces, also known as London dispersion forces, arise due to the temporary dipoles created when electrons within a molecule move about and create an uneven distribution of charge. Even though these forces are relatively weak compared to other types of intermolecular forces, they play a significant role in nonpolar liquids mixing.

From the exercise, the spontaneous mixing of substance A and B occurs because the dispersion forces within and between the molecules are similar, allowing them to intermingle without significant resistance or the need for energy input. Thus, nonpolar liquids with comparable dispersion forces tend to mix readily.

Enthalpy Change

Enthalpy change, denoted by \( \Delta H \), is a measure of the total heat content of a system and reflects the energy absorbed or released during a chemical process. When nonpolar liquids mix, \( \Delta H \) is indicative of the amount of energy needed to break the intermolecular forces between the solute and solvent particles (\( \Delta H_{\text{solute}} \) and \( \Delta H_{\text{solvent}} \)) versus the energy released when new interactions form (\( \Delta H_{\text{mix}} \)).

In our scenario, because substance A and B are similar, the enthalpy change upon mixing (\( \Delta H_{\text{soln}} \)) is expected to be minimal. The energy used to disrupt the interactions within each substance is nearly balanced by the energy released as the two substances come together. Therefore, the overall \( \Delta H_{\text{soln}} \) would be close to zero, which means the mixing process requires little energy change and is neither strongly endothermic nor exothermic.

Dispersion Forces

As mentioned earlier, dispersion forces are the weakest among the intermolecular forces, yet they are ubiquitous because all molecules exhibit them. They result from the momentary fluctuations of electron distribution, which leads to temporary dipole moments that can induce further temporary dipoles in adjacent molecules. These induced dipoles attract each other, resulting in a force that, though weak individually, can become significant over many interactions.

For nonpolar liquids such as substance A and substance B, dispersion forces are the sole type of intermolecular interaction. Because both substances experience similar dispersion forces, they can mix freely without causing a large disturbance of their molecular interactions, leading to a neutral or near-neutral enthalpy change upon mixing.

Thermodynamics in Chemistry

Thermodynamics in chemistry involves the study of energy changes accompanying chemical reactions and physical processes. The first law of thermodynamics, also known as the conservation of energy, indicates that energy cannot be created or destroyed – only converted from one form to another. This principle helps us understand the mixing of nonpolar substances from an energy perspective.

In the mixing of nonpolar liquids like substance A and B, the thermodynamic considerations involve assessing the balance between energy needed to overcome existing intermolecular forces and the energy released upon formation of new interactions. This balance leads to the prediction of enthalpy change associated with the solution process. Since the energy changes for breaking and forming interactions are nearly identical for similar nonpolar molecules, the mixing occurs with little energy involvement and aligns with thermodynamic principles predicting spontaneity.

Nonpolar Substances Mixing

When nonpolar substances mix, the process is usually characterized by an ease of mixing and a lack of significant energy exchange. This is due to the similarity in the nature of the molecules themselves. They lack distinct poles, and hence, no strong directional intermolecular forces exist to impede their mixing. As two nonpolar liquids come into contact, like our substances A and B, each molecule disperses into the other without needing to break strong attractions or form highly favorable new ones.

The blending of nonpolar substances can be seen as a process of maximizing entropy, another concept in thermodynamics, often symbolized as \( \Delta S \). Entropy is a measure of the disorder or randomness in a system. As nonpolar liquids mix, the increase in entropy (disorder) reflects a more favorable and spontaneous state, typically occurring without significant temperature changes or heat flow, hence the near-zero enthalpy change. This aspect of nonpolar substance mixing can be particularly important when considering solutions and mixtures in chemistry.