If `M_("normal")` is the normal molecular mass and `alpha` is the degree of ionization of `K_(3)[Fe(CN)_(6)]`, then the abnormal molecular mass of the complex in the solution will be :

Options

A. `M_("normol")(1+2a)^(-1)`
B. `M_("normol")(1+3a)^(-1)`
C. `M_("normol")(1+a)^(-1)`
D. equal to `M_("normol")`

Answer

To find the abnormal molecular mass of the complex \( K_3[Fe(CN)_6] \) in solution, we can follow these steps:

### Step 1: Identify the normal molecular mass and degree of ionization
Let \( M_n \) be the normal molecular mass of \( K_3[Fe(CN)_6] \) and \( \alpha \) be the degree of ionization.

### Step 2: Determine the dissociation of the complex
The complex \( K_3[Fe(CN)_6] \) dissociates in solution as follows:
\[ K_3[Fe(CN)_6] \rightarrow 3K^+ + [Fe(CN)_6]^{3-} \]
This means it produces a total of 4 ions (3 potassium ions and 1 ferrocyanide ion).

### Step 3: Calculate the number of ions produced
Let \( n \) be the number of ions produced upon dissociation. Here, \( n = 4 \).

### Step 4: Calculate the Van't Hoff factor \( i \)
The Van't Hoff factor \( i \) can be calculated using the formula:
\[ i = 1 + (n - 1) \cdot \alpha \]
Substituting \( n = 4 \):
\[ i = 1 + (4 - 1) \cdot \alpha = 1 + 3\alpha \]

### Step 5: Relate the normal and abnormal molecular mass
The relationship between the normal molecular mass \( M_n \) and the abnormal molecular mass \( M_a \) is given by:
\[ i = \frac{M_n}{M_a} \]
Rearranging this gives:
\[ M_a = \frac{M_n}{i} \]

### Step 6: Substitute the value of \( i \)
Substituting the expression for \( i \):
\[ M_a = \frac{M_n}{1 + 3\alpha} \]

### Step 7: Final expression for abnormal molecular mass
Thus, the abnormal molecular mass of the complex in solution is:
\[ M_a = \frac{M_n}{1 + 3\alpha} \]

### Summary
The abnormal molecular mass of the complex \( K_3[Fe(CN)_6] \) in solution is given by:
\[ M_a = \frac{M_n}{1 + 3\alpha} \]