The volume of a colloidal particle `V_C` as compared to the volume of a solute particle in a true solution `V_S` could be

Options

A. `(V_(c))/(V_(s))=10^(-3)`
B. `(V_(c))/(V_(s))=10^(3)`
C. `(V_(c))/(V_(s))~~10`
D. `(V_(c))/(V_(s))~~10^(22)`

Answer

To solve the problem of comparing the volume of a colloidal particle \( V_C \) with the volume of a solute particle in a true solution \( V_S \), we can follow these steps:

### Step 1: Understand the Size Ranges
- For a true solution, the particle size (diameter) ranges from 1 angstrom (Å) to 10 angstroms (Å).
- For a colloidal solution, the particle size (diameter) ranges from 10 angstroms (Å) to 1000 angstroms (Å).

### Step 2: Determine the Volume Formula
- The volume \( V \) of a spherical particle is given by the formula:
\[ V = \frac{4}{3} \pi r^3 \]
where \( r \) is the radius of the particle.

### Step 3: Express the Volumes
- Let \( r_C \) be the radius of a colloidal particle and \( r_S \) be the radius of a solute particle in a true solution.
- The volume of the colloidal particle \( V_C \) can be expressed as:
\[ V_C = \frac{4}{3} \pi r_C^3 \]
- The volume of the solute particle \( V_S \) can be expressed as:
\[ V_S = \frac{4}{3} \pi r_S^3 \]

### Step 4: Calculate the Volume Ratio
- The ratio of the volumes \( \frac{V_C}{V_S} \) can be simplified as follows:
\[ \frac{V_C}{V_S} = \frac{\frac{4}{3} \pi r_C^3}{\frac{4}{3} \pi r_S^3} = \frac{r_C^3}{r_S^3} \]

### Step 5: Relate the Radii to the Size Ranges
- From the size ranges, we can take representative values:
- For a colloidal particle, we can take \( r_C \approx 10 \) Å (which is 1 nm).
- For a solute particle in a true solution, we can take \( r_S \approx 1 \) Å (which is 0.1 nm).

### Step 6: Calculate the Ratio of Radii
- The ratio of the radii is:
\[ \frac{r_C}{r_S} = \frac{10 \text{ Å}}{1 \text{ Å}} = 10 \]

### Step 7: Calculate the Volume Ratio
- Now, substituting this into the volume ratio:
\[ \frac{V_C}{V_S} = \left(\frac{r_C}{r_S}\right)^3 = 10^3 = 1000 \]

### Conclusion
- Therefore, the volume of a colloidal particle \( V_C \) compared to the volume of a solute particle in a true solution \( V_S \) is:
\[ \frac{V_C}{V_S} = 10^3 \]

### Final Answer
- The correct answer is \( 10^3 \).

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