The Van't Hoff factor of very dilute solution of `Ca(NO_(3))_(2)`

Options

A. 1
B. 2
C. 3
D. 4

Explanation

To determine the Van't Hoff factor (i) for a very dilute solution of calcium nitrate, \( Ca(NO_3)_2 \), we need to follow these steps:

### Step-by-Step Solution:

1. **Identify the Dissociation of Calcium Nitrate:**
Calcium nitrate, \( Ca(NO_3)_2 \), is a strong electrolyte. This means it completely dissociates into its ions when dissolved in water.

2. **Write the Dissociation Equation:**
The dissociation of \( Ca(NO_3)_2 \) can be represented as:
\[ Ca(NO_3)_2 \rightarrow Ca^{2+} + 2NO_3^{-} \]
Here, one formula unit of calcium nitrate produces one calcium ion (\( Ca^{2+} \)) and two nitrate ions (\( NO_3^{-} \)).

3. **Count the Total Number of Particles:**
From the dissociation equation, we can see that:
- 1 \( Ca^{2+} \) ion is produced.
- 2 \( NO_3^{-} \) ions are produced.
Therefore, the total number of particles produced upon dissociation is:
\[ 1 + 2 = 3 \]

4. **Determine the Van't Hoff Factor (i):**
The Van't Hoff factor (i) is defined as the number of particles into which a solute dissociates in solution. For \( Ca(NO_3)_2 \):
\[ i = 3 \]

5. **Conclusion:**
The Van't Hoff factor for a very dilute solution of \( Ca(NO_3)_2 \) is 3.

### Final Answer:
The Van't Hoff factor of a very dilute solution of \( Ca(NO_3)_2 \) is **3**.

---