Explanation:

To understand why the correct answer is option C, let's first discuss what a micelle is and how it is formed.

A micelle is a colloidal particle that forms when certain molecules, called surfactants, are dissolved in a liquid. Surfactants have a hydrophilic (water-loving) head and a hydrophobic (water-repelling) tail. When the concentration of surfactant molecules in a solution exceeds a certain critical value, micelles start to form.

Formation of Micelles:
When surfactant molecules are added to a solvent, such as water, they arrange themselves in a specific way to minimize their exposure to the solvent. The hydrophilic heads of the surfactant molecules face outward towards the solvent, while the hydrophobic tails cluster together in the center, away from the solvent. This arrangement forms a spherical structure called a micelle.

The Role of Stearate Ions:
Stearate ions are an example of surfactant molecules that can form micelles. Stearate ions have a hydrophilic head (carboxylate group) and a long hydrophobic tail (a chain of carbon atoms).

When stearate ions are dissolved in water, they arrange themselves in a way that the hydrophilic heads face outward towards the water, while the hydrophobic tails cluster together in the center to form a micelle.

Determining the Number of Stearate Ions:
To determine the number of stearate ions required to form a micelle of colloidal size, we need to consider the structure of a micelle and the size of stearate ions.

The size of stearate ions is approximately 2-3 nanometers. A micelle of colloidal size is typically in the range of 10-100 nanometers.

If we assume that the micelle is at the lower end of the size range (10 nanometers), we can estimate the number of stearate ions required using the formula:

Number of stearate ions = Volume of micelle / Volume of a stearate ion

Assuming a micelle with a diameter of 10 nanometers (radius = 5 nanometers) and a stearate ion with a diameter of 2 nanometers (radius = 1 nanometer), we can calculate the volume of the micelle and the volume of a stearate ion.

Volume of micelle = (4/3)πr^3 = (4/3)π(5 nm)^3 = 523.6 cubic nanometers

Volume of stearate ion = (4/3)πr^3 = (4/3)π(1 nm)^3 = 4.189 cubic nanometers

Number of stearate ions = Volume of micelle / Volume of a stearate ion = 523.6 nm^3 / 4.189 nm^3 ≈ 125

Therefore, approximately 125 stearate ions are required to form a micelle of colloidal size.

Since none of the given options match the calculated value, we can conclude that the question may have been oversimplified or there may be additional information missing. Without further information, it is not possible to determine the exact number of stearate ions required.