Which statement are true about osmotic pressure `(pi)`, volume (V) and temperature (T)?
`{:("Solution (A)","Solution (B)"),(FeCl_(3),K_(4)Fe(CN)_(6)):}`

Options

A. `pi prop(1)/(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 statements are true about osmotic pressure (π), volume (V), and temperature (T), we can start with the formula for osmotic pressure:

### Step 1: Understand the Formula
The formula for osmotic pressure is given by:
\[ \pi = CRT \]
Where:
- \(\pi\) = osmotic pressure
- \(C\) = concentration of the solution (moles of solute per volume of solution)
- \(R\) = gas constant
- \(T\) = temperature in Kelvin

### Step 2: Express Concentration in Terms of Volume
We can express concentration \(C\) as:
\[ C = \frac{n}{V} \]
Where:
- \(n\) = number of moles of solute
- \(V\) = volume of the solution

Substituting this into the osmotic pressure formula gives:
\[ \pi = \frac{n}{V}RT \]

### Step 3: Analyze the Relationship Between π and V
From the equation \(\pi = \frac{nRT}{V}\), we can see that:
- If \(n\) and \(T\) are constant, then \(\pi\) is inversely proportional to \(V\):
\[ \pi \propto \frac{1}{V} \]
This means that as the volume increases, the osmotic pressure decreases if the number of moles and temperature remain constant.

### Step 4: Analyze the Relationship Between π and T
From the same equation, if \(V\) and \(n\) are constant, then:
\[ \pi \propto T \]
This means that osmotic pressure is directly proportional to temperature. As temperature increases, osmotic pressure also increases.

### Step 5: Evaluate the Given Statements
Now, let's evaluate the statements provided in the question:

1. **Option 1**: π is directly proportional to \( \frac{1}{V} \) (True if T is constant)
- This statement is **true**.

2. **Option 2**: π is directly proportional to T if V is constant (True)
- This statement is **true**.

3. **Option 3**: π is directly proportional to V if T is constant (False)
- This statement is **false** because π is inversely proportional to V.

4. **Option 4**: πV is constant if T is constant (False)
- This statement is **false** because π is inversely proportional to V, so πV is not constant.

### Conclusion
The true statements about osmotic pressure (π), volume (V), and temperature (T) are:
- **Option 1**: True
- **Option 2**: True
- **Option 3**: False
- **Option 4**: False