Question

Explain why the molar conductivity at infinite dilution of a weak acid such as \(\mathrm{CH}_{3} \mathrm{CO}_{2} \mathrm{H}\) is high, but then decreases dramatically as the concentration is raised even slightly.

Short answer

At infinite dilution, weak acids like \\( \text{CH}_3\text{CO}_2\text{H} \\) fully dissociate, giving high molar conductivity. As concentration increases, ion interactions and reduced ionization decrease conductivity.

Step-by-step solution

Understand Molar Conductivity

Molar conductivity \( \Lambda_m \) measures the ability of ions to conduct electricity in a solution. It is defined as the conductivity of the solution divided by the molar concentration of the electrolyte.

Define Infinite Dilution

At infinite dilution, the concentration of the electrolyte approaches zero. Under these conditions, each ion is isolated and experiences no interaction with other ions, leading to maximum ion mobility and therefore high molar conductivity.

Analyze Weak Acid Behavior

For weak acids like \( \text{CH}_3\text{CO}_2\text{H} \), the degree of ionization is low at higher concentrations because the acid doesn’t fully dissociate. At infinite dilution, the weak acid ionizes completely, which results in a higher molar conductivity than at higher concentrations.

Consider Ion Interactions at Higher Concentrations

As the concentration of the solution increases, ions are closer together and experience interactions, such as ion pairing, which impede their mobility. Additionally, the weak acid ionizes less at higher concentrations due to the common ion effect, further reducing molar conductivity.

Conclude the Behavior

Thus, at infinite dilution, \( \text{CH}_3\text{CO}_2\text{H} \) exhibits high molar conductivity due to complete dissociation and minimal ion interactions. However, as concentration increases, interactions and reduced ionization dramatically decrease molar conductivity.

Key concepts

Infinite Dilution

Infinite dilution refers to a condition where the concentration of an electrolyte in a solution is extremely low, approaching zero. This is an important concept in understanding molar conductivity. At infinite dilution, ions are so far apart that they do not interact with each other. This lack of interaction means that the ions can move freely throughout the solution.
As a result of this freedom, the ions exhibit maximum mobility, allowing them to conduct electricity more efficiently. This scenario leads to the highest possible molar conductivity for the electrolyte. In other words, at infinite dilution, you get an ideal condition where ions are uninhibited by the presence of other ions, leading to optimal electrical conductivity.

Weak Acids

Weak acids, such as acetic acid (CH extsubscript{3}CO extsubscript{2}H), have an interesting behavior in solutions especially when considering different concentrations. Unlike strong acids, weak acids do not fully dissociate in solution. This means that at higher concentrations, the majority of acid molecules remain intact, with only a small fraction breaking apart into ions.
At infinite dilution, even weak acids can appear to be completely ionized due to the lack of interaction between ions. This results in a high molar conductivity because all possible ions are in solution, contributing to electrical conduction. However, as you increase the concentration, the degree of ionization drops since there is less space for the ions to separate from each other, reducing conductivity.

Ion Interactions

Ion interactions become significant as the concentration of a solution increases. At higher concentrations, ions are much closer together, and they start to exert forces on one another. These interactions can include attraction between oppositely charged ions, known as ion pairing, and repulsion between similarly charged ions.
This proximity and interaction impede the movement of ions, diminishing their mobility. It’s similar to trying to swim in a crowded pool: the more crowded it is, the harder it is to move through it. This effect is compounded in weak acid solutions, where the crowded environment reduces the already limited degree of dissociation of the acid, decreasing molar conductivity even further.

Ion Mobility

Ion mobility is a key factor in understanding molar conductivity but can be quite complex due to its dependency on various factors. It refers to the speed at which ions can move through a solution under the influence of an electric field. The greater the mobility, the higher the molar conductivity observed.
At infinite dilution, ion mobility is maximized because ions are not hindered by other ions or molecular interactions; they move freely. However, as concentration increases, mobility is severely reduced due to the reasons discussed with ion interactions. Additionally, even in infinite dilution, different ions can have different natural mobilities due to their size and charge, further influencing how effectively they conduct electricity in a given solution.