The relationshp between the values of osmotic pressure of 0.1 M solution of `KNO_3(P_1) and CH_3COOH(P_2)` is :

Options

A. `P_1/(P_1+P_2) = P_2/(P_1+P_2)`
B. `P_1 gt P_2`
C. `P_2 gt P_1 `
D. `P_1 = P_2`

Explanation

To solve the question regarding the relationship between the osmotic pressures of a 0.1 M solution of KNO₃ (P₁) and CH₃COOH (P₂), we can follow these steps:

### Step 1: Understand the formula for osmotic pressure
The osmotic pressure (π) of a solution can be calculated using the formula:
\[ \pi = iCRT \]
where:
- \( \pi \) = osmotic pressure
- \( i \) = van 't Hoff factor (number of particles the solute dissociates into)
- \( C \) = molarity of the solution
- \( R \) = universal gas constant
- \( T \) = temperature in Kelvin

### Step 2: Identify the van 't Hoff factor for KNO₃
KNO₃ is a strong electrolyte that dissociates completely in solution:
\[ KNO₃ \rightarrow K^+ + NO₃^- \]
This means that 1 mole of KNO₃ produces 2 moles of ions. Thus, the van 't Hoff factor \( i \) for KNO₃ is:
\[ i_{KNO₃} = 2 \]

### Step 3: Identify the van 't Hoff factor for CH₃COOH
CH₃COOH (acetic acid) is a weak electrolyte and does not dissociate completely. It dissociates as follows:
\[ CH₃COOH \rightleftharpoons CH₃COO^- + H^+ \]
Since it does not dissociate completely, the van 't Hoff factor \( i \) for CH₃COOH will be less than 2. For weak acids, \( i \) is typically between 1 and 2. Therefore:
\[ 1 < i_{CH₃COOH} < 2 \]

### Step 4: Compare the osmotic pressures
Since both solutions have the same concentration (0.1 M) and are at the same temperature, we can compare their osmotic pressures based on their van 't Hoff factors:
- For KNO₃:
\[ \pi_{KNO₃} = i_{KNO₃} \cdot C \cdot R \cdot T = 2 \cdot 0.1 \cdot R \cdot T \]
- For CH₃COOH:
\[ \pi_{CH₃COOH} = i_{CH₃COOH} \cdot C \cdot R \cdot T \]
Since \( i_{CH₃COOH} < 2 \), it follows that:
\[ \pi_{CH₃COOH} < \pi_{KNO₃} \]

### Step 5: Conclusion
Thus, we can conclude that:
\[ P_1 > P_2 \]
where \( P_1 \) is the osmotic pressure of the KNO₃ solution and \( P_2 \) is the osmotic pressure of the CH₃COOH solution.

### Final Answer
The relationship between the osmotic pressures is:
\[ P_1 > P_2 \]