The osmotic pressure of a dilute solution is given by

Options

A. `P=P_(0)xxN_(1)`
B. `piV=nRT`
C. `DeltaP=P_(0)N_(2)`
D. `(DeltaP)/(P^(@))=(P^(@)-P_(s))/P^(@)`

Explanation

To solve the question regarding the osmotic pressure of a dilute solution, we will follow these steps:

### Step 1: Understand the Concept of Osmotic Pressure
Osmotic pressure (π) is a property of solutions that is related to the concentration of solute particles in a solution. It is the pressure required to stop the flow of solvent into the solution through a semipermeable membrane.

### Step 2: Write the Formula for Osmotic Pressure
The osmotic pressure of a dilute solution is given by the formula:
\[ \pi = CRT \]
where:
- \( \pi \) = osmotic pressure
- \( C \) = concentration of the solution (in moles per liter)
- \( R \) = universal gas constant (0.0821 L·atm/(K·mol))
- \( T \) = absolute temperature (in Kelvin)

### Step 3: Rearranging the Formula
We can rearrange this formula to express it in terms of volume (V) and number of moles (n):
\[ \pi V = nRT \]
This equation shows the relationship between osmotic pressure, volume of the solution, number of moles of solute, and temperature.

### Step 4: Analyze the Options
From the problem statement, we need to identify which option corresponds to the derived equation. The correct expression for osmotic pressure in terms of volume and moles is:
\[ \pi V = nRT \]
This matches with option B.

### Step 5: Eliminate Incorrect Options
- Option A and C do not represent valid expressions related to colligative properties.
- Option D represents the relative lowering of vapor pressure, which is not related to osmotic pressure.

### Conclusion
The correct answer is option B: \( \pi V = nRT \).

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