Calculation of Number of Colloidal Oil Particles

Given that the radius of the spherical oil drop is 2 microns.

We know that the volume of a sphere is given by the formula:

V = (4/3)πr^3

Where r is the radius of the sphere.

The volume of the oil drop is:

V1 = (4/3)π(2μm)^3 = 33.51 μm^3

The volume of each colloidal oil particle is:

V2 = (4/3)π(20A)^3 = 3.351×10^-17 μm^3

The number of colloidal oil particles that can be formed from the oil drop is:

N = V1/V2 = 9.99×10^23

Therefore, the number of colloidal oil particles that can be formed is approximately 9.99×10^23.

Calculation of Number of Molecules in One Particle

Given that the molar mass of the oil is 150 u.

We know that the number of molecules in one mole of a substance is given by Avogadro's number (6.022×10^23).

The number of molecules in one particle of radius 20A can be calculated as follows:

- Calculate the mass of one particle:

The density of the oil is required to calculate the mass of one particle. Let's assume the density to be 0.9 g/cm^3.

The mass of one particle is:

m = ρV2 = 2.99×10^-17 g

- Calculate the number of moles of the oil in one particle:

The number of moles of the oil in one particle is:

n = m/M = 1.99×10^-19 mol

- Calculate the number of molecules in one particle:

The number of molecules in one particle is:

N = n×NA = 1.20×10^4

Therefore, the number of molecules in one particle of radius 20A is approximately 1.20×10^4.

Explanation

The above calculations involve basic formulas of geometry, physics, and chemistry. The number of colloidal oil particles that can be formed from the oil drop depends on the volume of the oil drop and the volume of each colloidal oil particle. The number of molecules in one particle depends on the mass of the particle, the molar mass of the oil, and Avogadro's number. These calculations are important in understanding the behavior and properties of colloidal systems.