When dilute aqueous solution of \(\mathrm{AgNO}_{3}\) (excess) is added to KI solution, positively charged sol particles of \(\mathrm{AgI}\) are formed due to adsorption of ion (a) \(\mathrm{K}^{+}\) (b) \(\mathrm{Ag}^{+}\) (c) I (d) \(\mathrm{NO}_{3}\)

The term 'colloidal particles' refers to the tiny particles that exist in a colloidal system, which is the intermediate between a true solution and a suspension. These particles range in size from 1 to 1000 nanometers and are large enough to scatter light (an effect known as the Tyndall effect) yet too small to settle under the influence of gravity.

In the context of the textbook exercise, when a precipitation reaction occurs between \textsf{AgNO}\(_3\) and KI, colloidal particles of silver iodide (\textsf{AgI}) are formed. These particles arise because the product of the reaction is insoluble in water and forms a colloid. This colloidal system is unique as the particles acquire a charge during the formation process. The charging of colloidal particles can occur through adsorption, where ions from the surrounding solution attach to their surface. This process is crucial as it stabilizes the colloid by preventing the particles from clumping together, which would otherwise lead to the particles settling out as a precipitate.

A precipitation reaction is a chemical reaction that occurs in aqueous solutions when two ionic compounds are combined and produce a precipitate, an insoluble solid product that separates from the solution. Typically, these reactions follow the pattern of double displacement, where cations and anions swap partners.

In this reaction, \textsf{AgNO}\(_3\) and KI are mixed to form \textsf{AgI} as the insoluble solid precipitate and \textsf{KNO}\(_3\) as the soluble salt, as depicted by the equation: \textsf{AgNO}\(_3\) + KI → \textsf{AgI}\(_{(s)}\) + \textsf{KNO}\(_3\). The solid silver iodide that forms is then responsible for the establishment of a colloidal state, as it does not dissolve but remains dispersed throughout the solution. It is also during this reaction that adsorption occurs, leading to the charging of newly formed colloidal silver iodide particles.

Silver iodide \textsf{AgI} is a yellowish solid and is an important compound in the realm of colloidal chemistry. Due to its low solubility in water, it readily forms a colloid rather than a true solution. Silver iodide colloids have significant applications, most notably in photography and cloud seeding.

In the problem posed by the textbook, silver iodide colloids are produced as a result of the precipitation reaction between silver nitrate (\textsf{AgNO}\(_3\)) and potassium iodide (KI). When we talk about the 'positively charged sol particles of \textsf{AgI}', we mean that the surface of the silver iodide colloidal particles preferentially adsorbs positively charged ions from the surrounding solution. In this particular case, \textsf{Ag}\(_{+}\) ions are in excess and adhere to the surface of the silver iodide particles, thus bestowing the colloidal system with a positive charge. This charge is key in maintaining the stability of the colloid, as it prevents the particles from aggregating and falling out of solution.