# Question 3481a

Mar 25, 2016

See below.

#### Explanation:

Structure of Micelles

The AgI micelle is formed by the reaction

${\text{AgNO"_3 + "KI" → "AgI" + "KNO}}_{3}$

The micelle core consists of many solid particles.

We can write this as:

$\underbrace{m \text{AgI")_color(red)("core}}$

With a surplus of ${\text{AgNO}}_{3}$, there will be next to the core a layer of preferentially adsorbed ${\text{Ag}}^{+}$ ions.

We can write this as:

underbrace( m "AgI")_color(red)("core")color(white)(l) n "Ag"^+, where $n$ is the number of ions.

The particle is now positively charged and attracts $\text{NO"_3^"-}$ ions from solution.

We now have an adsorption layer of oppositely charged counterions surrounding the core:

[underbrace(underbrace( m "AgI")_color(red)("core")color(white)(l)overbrace(n "Ag"^+ (n-x) "NO"_3^"-")^(color(brown)("adsorption layer")))_color(red)("granule")]^(x+)

The core, along with the adsorption layer, is called a granule.

The granule has a positive charge and is surrounded by a diffusion layer of $\text{NO"_3^"-}$ counterions.

underbrace([underbrace(underbrace( m "AgI")_color(red)("core")color(white)(l)overbrace(n "Ag"^+ (n-x) "NO"_3^"-")^(color(brown)("adsorption layer")))_color(red)("granule")]^(x+) overbrace(x color(white)(l)"NO"_3^"-")^(color(brown)("diffusion layer")))_color(blue)("micelle")#

The complete assembly is called a micelle.

Factors affecting stability of $\text{AgI}$ micelles

(a) Double layer overlap

Colloids with a double layer at their surfaces are stable due to repulsions caused by interpenetration of the diffuse parts of the double layers. (adapted from depts.washington.edu)

The like-charged ions in the diffuse layers repel each other, and this prevents the particles from getting close enough to attach to each other.

Ionic strength

An increase in electrolyte concentration compresses the double layers, so particles colliding with enough kinetic energy will be able to overcome the energy barrier to coagulation.