Question

Substance A is a nonpolar liquid and has only dispersion forces among its constituent particles. Substance \(\mathrm{B}\) is also a nonpolar liquid and has about the same magnitude of dispersion forces among its constituent particles as substance A. When substance A and substance \(\mathrm{B}\) are combined, they spontaneously \(\mathrm{mix}\). 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 \(\Delta H_{\text {solute }}\) \(\Delta H_{\text {solvent }},\) and \(\Delta H_{\text {mix }}\)

Short answer

Substances A and B mix due to an increase in entropy and negligible changes in intermolecular forces. \right) \right.\(HH\Delta soln. is expected to be small and could be slightly positive, zero, or slightly negative. \right) \right.\)HH\Delta solute and \right) \right.\(HH\Delta solvent are both positive, while \right) \right.\)HH\Delta mix is small and could be slightly positive, zero, or slightly negative.

Step-by-step solution

Understand the mixing process

The mixing process of two nonpolar liquids, which have similar types and magnitudes of intermolecular forces, can be explained by considering entropy and intermolecular forces. The entropy, or the disorder of the system, increases when two substances mix, which is a spontaneous process that is favored thermodynamically. Furthermore, since the substances have similar intermolecular forces, there are no significant energy changes upon mixing.

Predict the sign and magnitude of \right) \right.\(HH\Delta soln.

Since substances A and B have about the same magnitude of dispersion forces, the energy required to separate the molecules of A and B (endothermic) should be about the same as the energy released when A and B mix (exothermic). Therefore, the overall change in enthalpy, \right) \right.\)HH\Delta soln., should be close to zero. Since the process is spontaneous and intermolecular forces do not change significantly, \right) \right.\(HH\Delta soln. is predicted to be small and either slightly positive, zero, or slightly negative.

Determine the signs and relative magnitudes of \right) \right.\)HH\Delta solute, \right) \right.\(HH\Delta solvent, and \right) \right.\)HH\Delta mix

The change in enthalpy for the solute (\right) \right.\(HH\Delta solute) and the solvent (\right) \right.\)HH\Delta solvent) when they separate from their respective pure states would be endothermic, resulting in a positive \right) \right.\(H value for both \right) \right.\)HH\Delta solute and \right) \right.\(HH\Delta solvent. However, when A and B mix to form a solution (\right) \right.\)HH\Delta mix), there might be a slight release or absorption of heat due to the interaction of A and B, but this value is expected to be small since their intermolecular forces are similar. The \right) \right.\(HH\Delta mix might be slightly positive, zero, or slightly negative. Overall, the magnitude of \right) \right.\)HH\Delta mix should be smaller than the magnitude of \right) \right.\(HH\Delta solute or \right) \right.\)HH\Delta solvent.

Key concepts

Dispersion Forces

Dispersion forces, also known as London dispersion forces, are a type of intermolecular force that arise due to the temporary polarization of electron clouds in atoms or molecules. Even though they are the weakest of all the van der Waals forces, they are significant in nonpolar molecules where other types of intermolecular attractions are absent.

When two nonpolar liquids, such as substance A and B in our exercise, are brought together, their dispersion forces play a crucial role in their ability to mix. Both substances have similar magnitudes of dispersion forces, which indicates that their electron clouds can induce similar temporary dipoles, leading to an attraction between the molecules of A and B. This mutual affinity helps to explain why these two nonpolar liquids mix spontaneously upon contact.

Nonpolar Liquids Mixing

The mixing of nonpolar liquids is primarily governed by intermolecular forces and entropy. In the case of substance A and B, the fact that they are nonpolar suggests that they have no permanent dipole moments and that the dominant forces between their molecules are dispersion forces.

Since both liquids have similar magnitudes of these forces, the energy required to separate and mix the molecules of A with those of B is largely unchanged. The lack of significant energy exchange during the mixing process leads to a nearly neutral enthalpy change, contributing to the spontaneous mixing of the substances.

Entropy in Chemistry

Entropy is a concept in chemistry associated with the degree of randomness or disorder within a system. It is a fundamental driving force for various chemical processes and is denoted by the symbol S. The second law of thermodynamics states that the total entropy of an isolated system can never decrease over time.

In the context of mixing two nonpolar liquids like substance A and B, the mixing results in an increase in entropy because the molecules of the two substances are distributed more randomly in the mixture than when they were separate. This increase in entropy favors the spontaneous mixing of the liquids. The overall process is guided not just by energetics, such as enthalpy changes, but also by this natural tendency towards higher disorder.

Enthalpy Change

Enthalpy change, denoted by \( \Delta H \), signifies the heat absorbed or released during a chemical or physical process at constant pressure. Enthalpy change is a part of the energy changes that take place in a reaction or process and can be categorized as either endothermic (absorbing heat) or exothermic (releasing heat).

When nonpolar substances with similar dispersion forces mix, the enthalpy change is expected to be minimal. This is due to the relatively equal amount of energy needed to separate the molecules (endothermic process) and the energy released when they intermingle (exothermic process). In this specific exercise, the enthalpy change (\Delta H_{\text{soln}}) would be nearly zero or slightly positive or negative, reflecting the subtle energetic balance of the mixing process.

Spontaneous Process

A spontaneous process is one that occurs naturally without the need for external intervention. The direction of spontaneous change is determined by a combination of enthalpy change and entropy change, as expressed by the Gibbs free energy equation, \( \Delta G = \Delta H - T\Delta S \), where \( \Delta G \) represents the change in free energy, \( \Delta H \) is the enthalpy change, T is the absolute temperature, and \( \Delta S \) is the entropy change.

A spontaneous process can be energetically favorable (\( \Delta G < 0 \) due to exothermic enthalpy changes or increased entropy or both. In our scenario of nonpolar liquids mixing, the spontaneous aspect of the process stems from the increased entropy. Since \( \Delta H \) is fairly neutral, the positive entropy change \( (\Delta S > 0) \) is the decisive factor making the mixture of substance A and B spontaneous.