Question

The volume of a colloidal particle, ${\text{V}}_{\text{c}}$ as compared to volume of solute particle,${\text{V}}_{\text{s}}$in a true solution could be
A. ${\displaystyle \frac{{\text{V}}_{\text{C}}}{{\text{V}}_{\text{S}}}}\text{ = }\text{1}{\text{0}}^{-\text{3}}$
B. ${\displaystyle \frac{{\text{V}}_{\text{C}}}{{\text{V}}_{\text{S}}}}\text{ = }\text{1}{\text{0}}^{\text{3}}$
C. ${\displaystyle \frac{{\text{V}}_{\text{C}}}{{\text{V}}_{\text{S}}}}\text{ = }\text{10}$
D. ${\displaystyle \frac{{\text{V}}_{\text{C}}}{{\text{V}}_{\text{S}}}}\text{ = }\text{1}{\text{0}}^{22}$

Answer 1

Hint: The shape of particles of the true and colloidal solution are considered as round or a sphere. We can compare the volume of the sphere to determine the ratio of the volume of both colloidal and true solution. For this we require the radius of the sphere. We know the radius is the size of the particles of colloid and true solution.

 Complete step by step answer:
A mixture in which a phase remains dispersed in the suspension is known as colloid. The size of colloidal particles range from $10$ to $1000{\text{A}}^{\circ }$.
A homogenous mixture is known as true solution. In the true solution, the size of the solute particles range from $1$ to $10{\text{A}}^{\circ }$.
We know the formula of volume of the sphere is, ${\displaystyle \frac{\text{4}}{\text{3}}}\pi {\text{r}}^{\text{3}}$
Where,
$\text{r}$is the radius of the sphere.
We can compare the volume of the colloidal and true solution as follows:
$${\displaystyle \frac{{\text{V}}_{\text{C}}}{{\text{V}}_{\text{S}}}}\text{ = }{\displaystyle \frac{{\displaystyle \frac{\text{4}}{\text{3}}}{\pi r}_{\text{C}}^3}{{\displaystyle \frac{\text{4}}{\text{3}}}{\pi r}_{\text{S}}^3}}$$
$${\displaystyle \frac{{\text{V}}_{\text{C}}}{{\text{V}}_{\text{S}}}}\text{ = }{\displaystyle \frac{{\text{r}}_{\text{C}}^3}{{\text{r}}_{\text{S}}^3}}$$

On substituting the lower values of the radius of the particles.
$${\displaystyle \frac{{\text{V}}_{\text{C}}}{{\text{V}}_{\text{S}}}}\text{ = }{\displaystyle \frac{{\left(10\right)}^3}{1^3}}$$
${\displaystyle \frac{{\text{V}}_{\text{C}}}{{\text{V}}_{\text{S}}}}\text{ = }\text{1}{\text{0}}^{\text{3}}$
So, the volume of a colloidal particle, ${\text{V}}_{\text{c}}$ as compared to volume of solute particle,${\text{V}}_{\text{s}}$in a true solution could be${\displaystyle \frac{{\text{V}}_{\text{C}}}{{\text{V}}_{\text{S}}}}\text{ = }\text{1}{\text{0}}^{\text{3}}$.

Additional information: Milk is an example of colloidal. In milk the fat globules remain suspended in a water-based solution. The fat particles are large and are not completely soluble in a water-based solution.
Due to the large size of colloid particles, suspended particles and suspension medium remain in the different phases. The colloidal state cannot easily pass through the various membranes of the body due to the large size of the colloidal particle thus it provides long time interaction of the drug with the body. So, the drugs are more effective works in colloidal form.

Therefore, option (B) ${\displaystyle \frac{{\text{V}}_{\text{C}}}{{\text{V}}_{\text{S}}}}\text{ = }\text{1}{\text{0}}^{\text{3}}$is correct.

Note:The size of the solute particle of a true solution is ten times less than the size of the colloidal particles. Due to the large size of suspended particles, colloidal states have large surface areas. The volume of the true solution is a thousand times less than the volume of the colloidal solution. Whereas in the case of true solutions, the size of particles is very small, the particles of true solutions have a very little surface area.