The pH of a 0.1 M solution of a weak acid HA is found to be 2 at a temperature T. The osmotic pressure of the acid solution would be equal to

Options

A. 0.11 RT
B. 0.22 RT
C. 2 RT
D. RT

Answer

To solve the problem, we need to determine the osmotic pressure of a 0.1 M solution of a weak acid HA, given that its pH is 2. Here’s a step-by-step breakdown of the solution:

### Step 1: Determine the concentration of hydrogen ions [H⁺]
The pH of the solution is given as 2. We can calculate the concentration of hydrogen ions using the formula:

\[ [H^+] = 10^{-\text{pH}} = 10^{-2} = 0.01 \, \text{M} \]

### Step 2: Determine the degree of ionization of the weak acid
The initial concentration of the weak acid HA is 0.1 M. Since the concentration of hydrogen ions [H⁺] is 0.01 M, we can determine the amount of HA that has ionized:

\[ \text{Ionized HA} = [H^+] = 0.01 \, \text{M} \]

### Step 3: Calculate the concentration of undissociated acid
The concentration of undissociated acid HA after ionization can be calculated as follows:

\[ [\text{HA}] = 0.1 \, \text{M} - 0.01 \, \text{M} = 0.09 \, \text{M} \]

### Step 4: Determine the total concentration of particles in solution
When HA ionizes, it produces one hydrogen ion [H⁺] and one conjugate base [A⁻]. Therefore, the total concentration of particles in the solution (I) can be calculated as:

\[ I = [\text{HA}] + [H^+] + [A^-] = 0.09 \, \text{M} + 0.01 \, \text{M} + 0.01 \, \text{M} = 0.11 \, \text{M} \]

### Step 5: Calculate the osmotic pressure
The osmotic pressure (π) can be calculated using the formula:

\[ \pi = I \cdot R \cdot T \]

Where:
- \(I\) is the total concentration of particles (0.11 M),
- \(R\) is the ideal gas constant (0.0821 L·atm/(K·mol)),
- \(T\) is the temperature in Kelvin (which we will keep as T for now).

Substituting the values, we get:

\[ \pi = 0.11 \cdot 0.0821 \cdot T = 0.009051 \cdot T \]

### Final Answer
Thus, the osmotic pressure of the acid solution is:

\[ \pi = 0.11 RT \]