What is the Van't Hoff factor for sodium phosphate ?

Options

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

Answer

To find the Van't Hoff factor (i) for sodium phosphate (Na3PO4), we can follow these steps:

### Step 1: Identify the Dissociation of Sodium Phosphate
Sodium phosphate (Na3PO4) dissociates in solution into its constituent ions. The dissociation can be represented as:
\[ \text{Na}_3\text{PO}_4 \rightarrow 3 \text{Na}^+ + \text{PO}_4^{3-} \]

### Step 2: Count the Number of Ions Produced
From the dissociation equation, we can see that one formula unit of sodium phosphate produces:
- 3 sodium ions (Na⁺)
- 1 phosphate ion (PO₄³⁻)

Thus, the total number of ions (n) produced is:
\[ n = 3 + 1 = 4 \]

### Step 3: Use the Formula for Van't Hoff Factor
The Van't Hoff factor (i) is calculated using the formula:
\[ i = 1 + \alpha (n - 1) \]
where:
- \( \alpha \) is the degree of dissociation (which represents the fraction of the solute that dissociates).
- \( n \) is the number of ions produced.

### Step 4: Assume Complete Dissociation
In this case, since the degree of dissociation (α) is not provided, we assume complete dissociation, which means:
\[ \alpha = 1 \]

### Step 5: Substitute Values into the Formula
Now we can substitute the values into the formula:
- \( n = 4 \)
- \( \alpha = 1 \)

Substituting these values gives:
\[ i = 1 + 1 \times (4 - 1) \]
\[ i = 1 + 1 \times 3 \]
\[ i = 1 + 3 \]
\[ i = 4 \]

### Conclusion
The Van't Hoff factor for sodium phosphate (Na3PO4) is 4.

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