The relationship between the values of osmotic pressures of`0.1M`solutionsof`KNO_(3)(P_(1))`and`CH_(3)COOH(P_(2))`is

Options

A. `P_1 gt P_2`
B. `P_2 gt P_1`
C. `P_1=P_2`
D. `P_1/(P_1+P_2)= P_2/(P_1+2P_2)`

Answer

To determine the relationship between the osmotic pressures of 0.1 M solutions of KNO₃ (P₁) and CH₃COOH (P₂), we can follow these steps:

### Step 1: Understand the Concept of Osmotic Pressure
Osmotic pressure (π) is given by the formula:
\[ \pi = CRTI \]
where:
- \( C \) = concentration of the solution (in molarity)
- \( R \) = universal gas constant
- \( T \) = absolute temperature (in Kelvin)
- \( I \) = van 't Hoff factor, which accounts for the number of particles the solute dissociates into in solution.

### Step 2: Analyze KNO₃
KNO₃ is an ionic compound that completely dissociates in solution. The dissociation can be represented as:
\[ \text{KNO}_3 \rightarrow \text{K}^+ + \text{NO}_3^- \]
This means that one formula unit of KNO₃ produces two ions (K⁺ and NO₃⁻) in solution.

- For KNO₃:
- Concentration (C) = 0.1 M
- van 't Hoff factor (I) = number of particles produced = 2 (since it dissociates into 2 ions)

Thus, the osmotic pressure for KNO₃ (P₁) is:
\[ P_1 = CRT \times I = 0.1 \times R \times T \times 2 = 0.2CRT \]

### Step 3: Analyze CH₃COOH
CH₃COOH (acetic acid) is a weak acid and does not completely dissociate in solution. It partially dissociates as follows:
\[ \text{CH}_3\text{COOH} \rightleftharpoons \text{CH}_3\text{COO}^- + \text{H}^+ \]
The extent of dissociation (α) is less than 1, and for weak acids, we generally consider the van 't Hoff factor (I) to be approximately 1 because it does not dissociate completely.

- For CH₃COOH:
- Concentration (C) = 0.1 M
- van 't Hoff factor (I) ≈ 1 (due to partial dissociation)

Thus, the osmotic pressure for CH₃COOH (P₂) is:
\[ P_2 = CRT \times I = 0.1 \times R \times T \times 1 = 0.1CRT \]

### Step 4: Compare the Osmotic Pressures
Now we can compare the two osmotic pressures:
- \( P_1 = 0.2CRT \)
- \( P_2 = 0.1CRT \)

From this, we can conclude that:
\[ P_1 > P_2 \]

### Final Conclusion
The relationship between the osmotic pressures of the two solutions is:
\[ P_1 > P_2 \]
This means that the osmotic pressure of the KNO₃ solution is greater than that of the CH₃COOH solution.