The molar conductivities of infinite dilution for sodium iodide, sodium acetate and aluminium acetate are 12.69, 9.10 and 24.52 S cm2 mol−1 respectively at 25 °C. What is the molar conductivity of AlI3 at infinite dilution?

To determine the molar conductivity of aluminum iodide (AlI3) at infinite dilution, we can utilize the concept of molar conductivities of its constituent ions. Molar conductivity at infinite dilution is a characteristic property that reflects the contribution of each ion to the overall conductivity of the solution. For AlI3, which dissociates into one aluminum ion (Al³⁺) and three iodide ions (I⁻), we can calculate its molar conductivity by summing the contributions from each ion based on their known conductivities.

Breaking Down the Components

The dissociation of aluminum iodide in solution can be represented as follows:

• AlI3 → Al³⁺ + 3 I⁻

From this equation, we see that for each mole of AlI3 that dissolves, we produce one mole of Al³⁺ ions and three moles of I⁻ ions. Therefore, to find the molar conductivity of AlI3 at infinite dilution, we need to use the known molar conductivities of the ions involved:

Ion Conductivities

We have the following molar conductivities at infinite dilution:

• Al³⁺: From your question, we can assume that the molar conductivity of Al³⁺ can be derived from aluminum acetate, since it often behaves similarly in solution. Thus, we can use its molar conductivity of 24.52 S cm² mol⁻¹.
• I⁻: The molar conductivity of iodide is inferred from sodium iodide, which is 12.69 S cm² mol⁻¹.

Calculating Molar Conductivity

The molar conductivity of AlI3 at infinite dilution can be calculated using the formula:

λ(AlI3) = λ(Al³⁺) + 3 * λ(I⁻)

Substituting the known values:

• λ(Al³⁺) = 24.52 S cm² mol⁻¹
• λ(I⁻) = 12.69 S cm² mol⁻¹

Now, plugging these into the formula:

λ(AlI3) = 24.52 + 3 * 12.69

λ(AlI3) = 24.52 + 38.07

λ(AlI3) = 62.59 S cm² mol⁻¹

Final Thoughts

The molar conductivity of aluminum iodide (AlI3) at infinite dilution is therefore 62.59 S cm² mol⁻¹. This value represents the ability of AlI3 to conduct electricity when fully dissociated in a solution. Understanding these relationships between ionic conductivities is essential for predicting the behavior of various compounds in solution, especially in electrochemistry and related fields.