Question

For which of the following pair, the heat of mixing, \(\Delta H_{\text {mix }}\), is approximately zero? (a) \(\mathrm{CH}_{3} \mathrm{COOCH}_{3}+\mathrm{CHCl}_{3}\) (b) \(\mathrm{CH}_{3} \mathrm{COOH}+\mathrm{H}_{2} \mathrm{O}\) (c) \(\mathrm{C}_{2} \mathrm{H}_{5} \mathrm{OH}+\mathrm{CH}_{3} \mathrm{O} \mathrm{H}\) (d) \(\mathrm{CH}_{3} \mathrm{COCH}_{3}+\mathrm{C}_{6} \mathrm{H}_{6}\)

Short answer

The pair \(\mathrm{CH}_{3} \mathrm{COOCH}_{3} + \mathrm{CHCl}_{3}\) (a), will have a heat of mixing, \(\Delta H_{\text {mix}}\), that is approximately zero due to their similar intermolecular forces and interactions.

Step-by-step solution

Understand the Concept of Heat of Mixing

The heat of mixing, \(\Delta H_{\text {mix}}\), is the thermal energy change when two substances are combined to form a solution. An ideal solution would have an heat of mixing of zero when the interactions between the molecules of different substances are similar to the interactions among molecules within the pure substances. In other words, if the intermolecular forces (like dipole-dipole, hydrogen bonding, dispersion forces) between the different molecules are similar to those in the pure substances, the heat of mixing would be close to zero.

Analyze Each Pair for Intermolecular Forces

To determine when \(\Delta H_{\text {mix}}\) is approximately zero, we must consider the intermolecular forces predominant in each substance. (a) \(\mathrm{CH}_{3} \mathrm{COOCH}_{3}\) (acetone) has dipole-dipole interactions and \(\mathrm{CHCl}_{3}\) (chloroform) also has dipole-dipole interactions and possible hydrogen bonding, making them miscible with likely low heat of mixing. (b) Acetic acid (\(\mathrm{CH}_{3} \mathrm{COOH}\)) can form hydrogen bonds, and water (\(\mathrm{H}_{2} \mathrm{O}\)) also forms strong hydrogen bonds; this combination is likely to have an exothermic mixing due to hydrogen bond formation. (c) Ethanol (\(\mathrm{C}_{2} \mathrm{H}_{5} \mathrm{OH}\)) and methanol (\(\mathrm{CH}_{3} \mathrm{OH}\)) both can form hydrogen bonds. They are completely miscible with a possible slight exothermic effect but might still have a heat of mixing close to zero. (d) Acetone (\(\mathrm{CH}_{3} \mathrm{COCH}_{3}\)) and benzene (\(\mathrm{C}_{6} \mathrm{H}_{6}\)) interact primarily through dispersion forces, and their very different polarities suggest the mixture is non-ideal with a heat of mixing not close to zero.

Identify the Pair with Similar Intermolecular Forces

Since we are looking for a heat of mixing that is approximately zero, we must identify the pair where the intermolecular forces are most similar when mixed. Pair (a), containing acetone and chloroform, has the most similar intermolecular forces (both have significant dipolar interactions and can form hydrogen bonds) compared to the other pairs, suggesting they would have a heat of mixing closest to zero.

Key concepts

Intermolecular Forces

To understand the mysteries of mixing substances, we need to start with the basics – intermolecular forces. These are the attractions that occur between molecules and influence many properties, like boiling points, melting points, and solubilities. Imagine them as the relationships between neighboring molecules; the stronger the attraction, the more they prefer to stick together.

Common types of intermolecular forces include dipole-dipole interactions, where polar molecules mingle because of their partial charges. Then we have London dispersion forces, a bit like social networks connecting all kinds of molecules with temporary attractions. Not to forget hydrogen bonds, the promise rings of molecules like water, showing a strong commitment to stay together due to a hydrogen atom bonding with an electronegative atom like oxygen or nitrogen.

When two substances mix, if their molecules 'get along' due to similar intermolecular forces, they can mingle seamlessly without much energy change – leading to a negligible heat of mixing. But when there's a clash, like with oil and water, they'll keep their distance, and you can expect a notable heat of mixing due to their unsociable nature.

Ideal Solution

An ideal solution is the 'perfect roommate' scenario in the molecular world – it's when mixing two substances results in a homogenous mixture without any drama or energy change. In such a utopia, the molecules of each substance are so comfortable with each the other's company that they don't require any extra energy to mix and mingle. The intermolecular forces before and after they come together are like a mirror image – perfectly balanced.

This perfect balance means that the enthalpy change of mixing, or the heat evolved or absorbed when creating the solution, is zero. But this scenario is often an oversimplification and mainly serves as a standard to compare real-life mixtures against. Real-world solutions often have slight deviations due to differences in molecular interactions, but when these deviations are small, we can treat them as nearly ideal.

Enthalpy Change in Solutions

When the school bell rings for recess and students mix in the playground, they either peacefully play together or bicker and fight, expending energy. Similarly, when substances mix to form a solution, the overall energy of the system can change – this is the enthalpy change of the solution, symbolized by \( \Delta H_{\text{mix}} \).

For a solution with a zero enthalpy change, you could say it's a 'neutral' mix – no energy is lost or gained. It's like two friends with similar interests meeting – they just get along effortlessly. On the other hand, if the enthalpy change is positive, the mix is endothermic, and the solution feels cold as it absorbs energy. Conversely, an exothermic solution with a negative enthalpy change feels warm as it releases energy.

Understanding \( \Delta H_{\text{solution}} \) helps us predict how two substances will interact and is crucial in industries where precise mixtures are essential – like pharmacology or food science. In our textbook problem, knowing intermolecular forces helps us foresee which substance pairs would have that coveted zero enthalpy change upon mixing, like a harmonious friendship.