When an excess of a very dilute aqueous solution of \(KI\) is added to a very dilute aqueous solution of \(AgNO_3\), the colloidal particles of \(AgI\) are associated with which of following Helmholtz double layer?

\(AgI/I^- ⋮ K^+\)

The correct answer is option 4. \(AgI/I^- ⋮ K^+\). 

Let us go through the explanation of what happens when a very dilute aqueous solution of potassium iodide (\(KI\)) is added to a very dilute aqueous solution of silver nitrate (\(AgNO_3\)), leading to the formation of a colloidal solution of silver iodide (\(AgI\)).

Precipitation of Silver Iodide (AgI)

Chemical Reaction: When \(KI\) is added to \(AgNO_3\), a precipitation reaction occurs:

\(KI (aq) + AgNO_3 (aq) \rightarrow AgI (s) + KNO_3 (aq)\)

Silver iodide (\(AgI\)) forms as an insoluble solid, which precipitates out of the solution.

Formation of a Colloidal Solution

If the concentration of \(AgNO_3\) and \(KI\) is kept very low, the precipitate of \(AgI\) does not settle out but remains dispersed in the solution as tiny particles, forming a colloidal solution. A colloid consists of particles (colloidal particles) dispersed in a medium. These particles are larger than typical molecules but small enough to remain suspended.

Charge on Colloidal Particles and the Helmholtz Double Layer

Colloidal particles tend to acquire a charge due to the adsorption of ions from the surrounding solution. This charge plays a crucial role in stabilizing the colloid by preventing the particles from aggregating and settling out.

Adsorption of Ions: In this scenario, you have two possible ions from the added electrolytes: \(Ag^+\) from \(AgNO_3\) and \(I^-\) from \(KI\).

Excess of KI: Since \(KI\) is in excess, the surface of \(AgI\) particles will preferentially adsorb \(I^-\) ions from the \(KI\) solution.

The preference for adsorption of \(I^-\) ions occurs because they are more abundant in the solution.

Primary Adsorption Layer: The \(AgI\) colloidal particles will adsorb \(I^-\) ions onto their surface. This adsorption creates a primary adsorption layer on the \(AgI\) particles, giving them a negative charge.

Diffuse Layer: The negative charge on the \(AgI\) particles attracts positively charged ions from the solution, typically \(K^+\) ions from the dissociation of \(KI\).  These \(K^+\) ions form a diffuse layer around the negatively charged \(AgI\) particles. This layer is called the counterion layer and serves to balance the charge of the primary adsorption layer.

Helmholtz Double Layer Structure

The combination of the primary adsorption layer and the diffuse layer forms what is known as the Helmholtz double layer.

Primary Layer: Negatively charged \(I^-\) ions are directly adsorbed on the surface of \(AgI\).

Diffuse Layer: Positively charged \(K^+\) ions surround the negatively charged \(AgI\) particles.

Stabilization of the Colloid

The Helmholtz double layer stabilizes the colloidal solution by creating a repulsive force between the similarly charged colloidal particles, preventing them from coming together and coagulating (forming larger particles that would precipitate out of the solution). In this case, the \(AgI\) particles remain dispersed in the solution because the repulsion between the negatively charged particles (due to the \(I^-\) ions adsorbed on their surfaces) is strong enough to keep them apart.

Given the above explanation, the correct Helmholtz double layer structure around the colloidal \(AgI\) particles is:

Primary Layer: \(I^-\) ions adsorbed on \(AgI\).

Diffuse Layer: \(K^+\) ions from the solution.

Thus, the correct representation of the Helmholtz double layer for the \(AgI\) colloidal particles is option 4: \(AgI/I^- ⋮ K^+\).