Question

Two nonpolar organic liquids, hexane \(\left(\mathrm{C}_{6} \mathrm{H}_{14}\right)\) and heptane \(\left(\mathrm{C}_{7} \mathrm{H}_{16}\right),\) are mixed.(a) Do you expect \(\Delta H_{\text { soln to be a large }}\) positive number, a large negative number, or close to zero? Explain. ( b) Hexane and heptane are miscible with each other in all proportions. In making a solution of them, is the entropy of the system increased, decreased, or close to zero, compared to the separate pure liquids?

Short answer

(a) The change in enthalpy (∆H_solution) during the mixing process of hexane and heptane will be close to zero, as the interactions between the molecules are mainly due to weak dispersion forces, and the mixing process does not involve substantial gain or loss of energy. (b) When hexane and heptane are mixed, the entropy of the system (∆S) will increase compared to the separate pure liquids, as they become more disordered due to the intermingling of their molecules.

Step-by-step solution

In this problem, we are asked to determine whether the change in enthalpy during the mixing process, represented by ∆H_solution, is a large positive number, a large negative number, or close to zero. When mixing two nonpolar substances, the interactions between the molecules are mainly due to dispersion (or London) forces. These instantaneous dipoles are generally weak in nature, so when two nonpolar substances mix, the interactions between the molecules are not significantly different from the interactions in the pure substances. Therefore, there is no substantial gain or loss of energy during the mixing process, and the change in enthalpy (∆H_solution) will be close to zero. #b. Predicting the change in entropy during the mixing process#

Entropy is a measure of the randomness or disorder of a system. When two liquids are mixed, they generally become more disordered as the molecules of one liquid intermingle with molecules of the other liquid, creating greater distribution of molecular positions. Hexane and heptane are miscible in all proportions, meaning that they can mix completely with each other, leading to a significant increase in randomness for the system. Therefore, when hexane and heptane are mixed, the entropy of the system (∆S) will increase compared to the separate pure liquids.

Key concepts

Enthalpy Change in Mixing

Understanding the enthalpy change in mixing is foundational when studying solutions chemistry. Enthalpy, denoted as 'H', is a measure of the total energy of a thermodynamic system. It includes internal energy, which is the sum of kinetic and potential energies within the system, plus the product of pressure and volume. During the mixing of two substances, such as nonpolar organic liquids like hexane \( \left(\mathrm{C}_{6}\mathrm{H}_{14}\right) \) and heptane \( \left(\mathrm{C}_{7} \mathrm{H}_{16}\right) \), the change in enthalpy, \( \Delta H_{\text{soln}} \), is an indication of the energy adaptation due to interactions between the molecules.

The key to this concept is that the intermolecular forces in nonpolar liquids are relatively weak, and so when mixed, the energy change associated with breaking and forming new interactions is minimal. Therefore, the enthalpy change for such a process is generally close to zero, as there are no strong bonds being broken or formed. This is crucial in understanding the miscibility and behavior of nonpolar organic compounds when mixed.

London Dispersion Forces

London dispersion forces are a type of van der Waals force, which are the weakest intermolecular interactions and arise from the instantaneous dipoles that occur in all atoms and molecules. This temporary dipole induces a dipole in the neighboring molecules causing an attraction. These forces are present in nonpolar molecules like hexane and heptane and are a significant determining factor for their physical properties.

Contrary to ionic or covalent bonds, these induced dipoles are fleeting and do not require a significant amount of energy to either create or disrupt. In mixtures of nonpolar organic compounds, London dispersion forces serve as the primary interaction, and the similarities in the nature of the forces between the molecules of the pure compounds and the mixed solution explain the negligible enthalpy change during mixing.

Entropy in Chemical Systems

Entropy, symbolized by 'S', represents the degree of randomness or disorder in a system. In chemistry, it reflects the number of possible positions and energy states for molecules. When evaluating chemical systems, an increase in entropy usually indicates a more disordered system and is often associated with spontaneous processes.

In the case of mixing hexane and heptane, an increase in entropy occurs because the molecules of each substance distribute throughout the mixture, creating a more disordered system than when each liquid is separate. The mixing of miscible liquids, particularly organic compounds, is a perfect demonstration of entropy increase as it showcases how molecules spread out and enhance the disorder in the system. For students, it's important to recognize how entropy drives chemical processes, influencing the direction of reactions and the solubility of substances.

Miscibility of Organic Compounds

Miscibility is the ability of two or more substances to mix in all proportions, forming a homogeneous solution. In the context of organic chemistry, the miscibility of organic compounds depends greatly on the similarities between their molecular structures and polarities. Because hexane and heptane are nonpolar and have similar molecular sizes, they mix freely without the limitation of phase separation that is observed in systems where polar and nonpolar liquids are combined.

The understanding of miscibility is crucial for many industrial applications, such as creating pharmaceutical formulations, paints, and fuels, where the homogeneous mixing of compounds is essential. When approaching problems related to miscibility, consider the nature of intermolecular forces at play and how entropy favors the mixing of similar compounds to increase disorder.