Which statements (s) is/are correct about osmotic pressure (P), volume (V) and temperature (T) ?

Options

A. `P prop 1//V` if T is constant
B. `P propT` If V is constant
C. `P prop V` if T is constant
D. `PV` is constant if T is constant

Explanation

To determine which statements about osmotic pressure (P), volume (V), and temperature (T) are correct, we can analyze the relationships among these variables using the formula for osmotic pressure.

### Step-by-Step Solution:

1. **Understanding the Formula**:
The osmotic pressure (P) can be expressed using the formula:
\[ P = \frac{n}{V}RT \]
where:
- \( n \) = number of moles of solute
- \( V \) = volume of the solution
- \( R \) = universal gas constant
- \( T \) = temperature in Kelvin

2. **Analyzing the First Statement**:
The first statement claims that \( P \) is inversely proportional to \( V \) if \( T \) is constant.
- If \( T \) is constant, and since \( n \) and \( R \) are also constants, we can simplify the equation to:
\[ P \propto \frac{1}{V} \]
- This means that as volume increases, osmotic pressure decreases, confirming that the first statement is **correct**.

3. **Analyzing the Second Statement**:
The second statement claims that \( P \) is directly proportional to \( T \) when \( V \) is constant.
- If \( V \) is constant, we can rewrite the equation as:
\[ P \propto T \]
- This indicates that as temperature increases, osmotic pressure also increases, confirming that the second statement is **correct**.

4. **Analyzing the Third Statement**:
The third statement claims that \( P \) is directly proportional to \( V \) if \( T \) is constant.
- From our earlier analysis, we know that if \( T \) is constant, \( P \) is inversely proportional to \( V \):
\[ P \propto \frac{1}{V} \]
- Therefore, this statement is **incorrect**.

5. **Analyzing the Fourth Statement**:
The fourth statement claims that \( PV \) is constant if \( T \) is constant.
- Since we established that \( P \) is inversely proportional to \( V \) when \( T \) is constant, we can express this as:
\[ PV = k \quad (k \text{ is a constant}) \]
- This means that the product of \( P \) and \( V \) remains constant, confirming that the fourth statement is **correct**.

### Conclusion:
Based on the analysis:
- The **correct statements** are:
- First statement: Correct
- Second statement: Correct
- Third statement: Incorrect
- Fourth statement: Correct

Thus, the correct statements are the first, second, and fourth.