Which statement is incorrect about osmotic pressure`(pi)`, volume `(V)`, and temperature `(T)`?

Options

A. `pi prop1/V`,if T is constant.
B. `pi prop T`,if `V` is constant.
C. `pi prop V`,if `T` is constant.
D. `pi V` is constant,if `T` is constant.

Explanation

To determine which statement is incorrect about osmotic pressure (π), volume (V), and temperature (T), we can analyze the relationships between these variables using the formula for osmotic pressure.

### Step-by-Step Solution:

1. **Understand the Formula for Osmotic Pressure**:
The osmotic pressure (π) is given by the equation:
\[ \pi = CRT \]
where:
- \(C\) = concentration of the solution (in moles per liter)
- \(R\) = universal gas constant
- \(T\) = absolute temperature (in Kelvin)

2. **Analyze the Relationship Between π and V**:
The concentration \(C\) can be expressed as:
\[ C = \frac{n}{V} \]
where \(n\) is the number of moles and \(V\) is the volume. Substituting this into the osmotic pressure equation gives:
\[ \pi = \frac{nRT}{V} \]
From this equation, we can see that if \(T\) is constant, then:
\[ \pi \propto \frac{1}{V} \]
This means that osmotic pressure is inversely proportional to volume at constant temperature.

3. **Evaluate the Statements**:
- **Statement A**: Osmotic pressure is inversely proportional to volume if temperature is constant. **(True)**
- **Statement B**: If the volume is constant, osmotic pressure is directly proportional to temperature. **(True)**
- **Statement C**: Osmotic pressure is directly proportional to volume if temperature is constant. **(Incorrect)**
- **Statement D**: The product of osmotic pressure and volume is constant if temperature is constant. **(True)**

4. **Identify the Incorrect Statement**:
The incorrect statement is **Statement C**: "Osmotic pressure is directly proportional to volume if temperature is constant." This contradicts the established relationship that osmotic pressure is inversely proportional to volume at constant temperature.

### Conclusion:
The incorrect statement about osmotic pressure, volume, and temperature is **Statement C**.

---