A 1% (mass/vol) KCl solution is ionised to the extent of 80%. The osmotic pressure at `27^(@)`C of the solution will be :

Options

A. 6.95 atm
B. 5.94 atm
C. 2.71 atm
D. 3.30 atm

Answer

To find the osmotic pressure of a 1% (mass/volume) KCl solution that is ionized to the extent of 80% at 27°C, we can follow these steps:

### Step 1: Calculate the mass of KCl in the solution
Given that the solution is 1% (mass/volume), this means that in 100 mL of solution, there is 1 gram of KCl.

### Step 2: Calculate the molar mass of KCl
The molar mass of KCl (Potassium Chloride) is approximately 74.5 g/mol.

### Step 3: Calculate the number of moles of KCl
To find the number of moles of KCl in 1 gram:
\[ \text{Number of moles} = \frac{\text{mass}}{\text{molar mass}} = \frac{1 \text{ g}}{74.5 \text{ g/mol}} \approx 0.0134 \text{ mol} \]

### Step 4: Convert the volume of the solution to liters
Since we have 100 mL of solution, we convert it to liters:
\[ \text{Volume in liters} = \frac{100 \text{ mL}}{1000} = 0.1 \text{ L} \]

### Step 5: Calculate the molarity (C) of the KCl solution
Molarity (C) is defined as the number of moles of solute per liter of solution:
\[ C = \frac{\text{Number of moles}}{\text{Volume in liters}} = \frac{0.0134 \text{ mol}}{0.1 \text{ L}} = 0.134 \text{ M} \]

### Step 6: Determine the van 't Hoff factor (i)
KCl dissociates into two ions: K\(^+\) and Cl\(^-\). Therefore, the number of particles (N) is 2. The ionization extent (α) is given as 80%, or 0.8. The formula for the van 't Hoff factor (i) is:
\[ i = N - 1 + \alpha = 2 - 1 + 0.8 = 1.8 \]

### Step 7: Calculate the osmotic pressure (π)
The formula for osmotic pressure is given by:
\[ \pi = i \cdot C \cdot R \cdot T \]
Where:
- \(R\) (the gas constant) = 0.0821 L·atm/(K·mol)
- \(T\) (temperature in Kelvin) = 27°C + 273 = 300 K

Substituting the values:
\[ \pi = 1.8 \cdot 0.134 \cdot 0.0821 \cdot 300 \]

### Step 8: Perform the calculation
Calculating the above expression:
\[ \pi \approx 1.8 \cdot 0.134 \cdot 0.0821 \cdot 300 \approx 5.948 \text{ atm} \]

### Final Answer
The osmotic pressure of the solution is approximately **5.948 atm**.

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