A decimolar solution of potassium ferrocyanide is `50%` dissociated at `300K`. Calculate osmotic pressure of the solution. (Given `S = 8.341 JK^(-1) mol^(-1)`)

Explanation

To calculate the osmotic pressure of a decimolar solution of potassium ferrocyanide that is 50% dissociated at 300K, we can follow these steps:

### Step-by-Step Solution:

1. **Identify the Molarity of the Solution:**
The molarity of the potassium ferrocyanide solution is given as 0.1 M (decimolar).

2. **Determine the Degree of Dissociation:**
The solution is 50% dissociated, which means the degree of dissociation (α) is:
\[ \alpha = \frac{50}{100} = 0.5 \]

3. **Write the Dissociation Equation:**
Potassium ferrocyanide (K₄[Fe(CN)₆]) dissociates as follows:
\[ K_4[Fe(CN)_6] \rightarrow 4K^+ + [Fe(CN)_6]^{4-} \]
This results in the formation of 5 ions (4 potassium ions and 1 ferrocyanide ion).

4. **Calculate the Van’t Hoff Factor (I):**
The Van’t Hoff factor (I) can be calculated using the formula:
\[ I = 1 + (n - 1) \cdot \alpha \]
where \( n \) is the number of ions formed on dissociation. Here, \( n = 5 \):
\[ I = 1 + (5 - 1) \cdot 0.5 = 1 + 4 \cdot 0.5 = 1 + 2 = 3 \]

5. **Use the Osmotic Pressure Formula:**
The osmotic pressure (π) is given by the formula:
\[ \pi = I \cdot C \cdot R \cdot T \]
where:
- \( C = 0.1 \, \text{mol/L} \) (molarity)
- \( R = 0.0821 \, \text{L atm K}^{-1} \text{mol}^{-1} \) (gas constant)
- \( T = 300 \, \text{K} \) (temperature)

6. **Substitute the Values:**
Now, substituting the values into the osmotic pressure formula:
\[ \pi = 3 \cdot 0.1 \cdot 0.0821 \cdot 300 \]

7. **Calculate the Osmotic Pressure:**
\[ \pi = 3 \cdot 0.1 \cdot 0.0821 \cdot 300 = 7.389 \, \text{atm} \]

### Final Answer:
The osmotic pressure of the solution is approximately **7.389 atm**.

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