Question

Two nonpolar organic liquids, benzene \(\left(\mathrm{C}_{6} \mathrm{H}_{6}\right)\) and toluene \(\left(\mathrm{C}_{7} \mathrm{H}_{8}\right),\) 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) Benzene and toluene 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 enthalpy of solution, \(\Delta H_{\text {soln }}\), is expected to be close to zero because the interactions between benzene and toluene molecules are similar to their interactions within their respective pure liquids, and the solution process does not require a large transfer of energy. (b) Mixing benzene and toluene increases the entropy of the system, compared to the separate pure liquids, due to the increase in molecular disorder when the two substances are mixed.

Step-by-step solution

Analyze \(\Delta H_{\text {soln }}\)

We need to analyze \(\Delta H_{\text {soln }}\) value when mixing two nonpolar organic liquids, benzene and toluene. In a solution process, two fundamental intermolecular interactions come into play: (1) separating solute and solvent molecules in the initial state (change in positive enthalpy), and (2) mixing solute and solvent molecules to form the solution (change in negative enthalpy). Since benzene and toluene are both nonpolar and have similar London dispersion forces, the energetic interactions between benzene and toluene molecules when mixed should be similar to the interactions between the benzene and benzene molecules in pure benzene or the toluene and toluene molecules in pure toluene.

Answer for (a)

Because the interactions between benzene and toluene molecules are similar to their interactions within their respective pure liquids, we can expect the enthalpy of solution, \(\Delta H_{\text {soln }}\), to be close to zero. There is no significant energy difference between the interactions of benzene-benzene and toluene -toluene. Therefore, the solution process does not require a large transfer of energy. So \(\Delta H_{\text {soln }}\approx 0\).

Analyze entropy change

When we mix benzene and toluene, we are increasing the number of possible ways the molecules can rearrange and distribute themselves in the solution. The resultant molecular mixture is more disordered than the separate pure liquids. Therefore, mixing benzene and toluene will increase the entropy of the system.

Answer for (b)

Benzene and toluene are miscible with each other in all proportions. As a result, making a solution of them will increase the entropy of the system, compared to the separate pure liquids. This increase in entropy of the system stems from the increase in molecular disorder when mixing the two substances.

Key concepts

Enthalpy of Solution

When discussing the mixing of two nonpolar organic liquids like benzene \((\text{C}_6 \text{H}_6)\) and toluene \((\text{C}_7 \text{H}_8)\), the concept of enthalpy of solution, \(\Delta H_{\text{soln}}\), becomes crucial. The enthalpy of solution is essentially a measure of the heat absorbed or released when substances are mixed. For benzene and toluene, both of which exhibit similar London dispersion forces, we can expect their interaction energies to be quite similar. This implies that when benzene and toluene are mixed, the energy required to break the bonds between their molecules is nearly balanced by the energy released upon formation of new intermolecular forces. Therefore, the enthalpy of solution \(\Delta H_{\text{soln}}\) is close to zero.

• When \(\Delta H_{\text{soln}}\) is close to zero, it suggests an ideal solution behavior.
• This means there is no significant heat exchange, neither endothermic nor exothermic.

This makes sense because both benzene and toluene, being nonpolar, have similar types of intermolecular forces and thus do not create a drastic change in energy dynamics upon mixing.

Entropy Change

Entropy is all about disorder and probability. When benzene and toluene are mixed, their entropy, or randomness, increases. This is because there are more ways for molecules to arrange themselves in a mixture than in a state where they are separate. Mixing them enhances the disorder, thereby increasing the entropy of the system.

• Increased entropy reflects more possible molecular arrangements.
• Systems naturally progress toward states with higher entropy.

Thus, mixing nonpolar organic liquids like benzene and toluene leads to an overall increase in entropy compared to them being separate. This increase in entropy is favorable and thermodynamically preferred.

Miscibility of Benzene and Toluene

Miscibility refers to the ability of two substances to mix in all proportions without separating into different phases. Benzene and toluene are miscible with one another because they are both nonpolar and exhibit similar intermolecular forces. Their London dispersion forces are compatible, allowing them to integrate well in any ratio.

• Their molecular structure and symmetry support this miscibility.
• Unlike polar substances, there is no lack of attraction or large energy barrier to mixing.

Due to these reasons, benzene and toluene can mix thoroughly, forming homogenous solutions across a range of concentrations.