Osmotic pressure of a solution is

Options

A. Directly proportional to the molar concentration of the solution.
B. Inversely proportional to the molecular weight of the solue.
C. Inversely proportional to the temperature.
D. Directly proportional to the volume of the solution.

Explanation

To solve the question regarding the osmotic pressure of a solution, we will use the formula for osmotic pressure and analyze the relationships involved.

### Step-by-Step Solution:

1. **Understand the Formula for Osmotic Pressure**:
The osmotic pressure (π) of a solution is given by the equation:
\[ \pi = CRT \]
where:
- \( \pi \) = osmotic pressure
- \( C \) = concentration of the solution (in mol/L)
- \( R \) = universal gas constant (0.0821 L·atm/(K·mol))
- \( T \) = temperature in Kelvin

2. **Analyze the Relationship with Concentration**:
From the equation \( \pi = CRT \), we can see that osmotic pressure is directly proportional to the concentration of the solution (C). Therefore, if the concentration increases, the osmotic pressure also increases.

**Hint**: Remember that direct proportionality means if one quantity increases, the other also increases.

3. **Analyze the Relationship with Molar Mass**:
The osmotic pressure can also be expressed in terms of the number of moles (n) of solute:
\[ \pi = \frac{n}{V}RT \]
where \( V \) is the volume of the solution. Since \( n \) can be expressed as:
\[ n = \frac{w}{M} \]
where \( w \) is the weight of the solute and \( M \) is the molar mass of the solute, we can rewrite the osmotic pressure as:
\[ \pi = \frac{w}{MV}RT \]
This shows that osmotic pressure is inversely proportional to the molar mass (M) of the solute. If the molar mass increases, the osmotic pressure decreases.

**Hint**: Inverse proportionality means that if one quantity increases, the other decreases.

4. **Analyze the Relationship with Temperature**:
From the original formula \( \pi = CRT \), we can see that osmotic pressure is directly proportional to temperature (T). If the temperature increases, the osmotic pressure also increases.

**Hint**: Direct proportionality with temperature means that higher temperatures lead to higher osmotic pressures.

5. **Analyze the Relationship with Volume**:
From the equation \( \pi = \frac{n}{V}RT \), we can see that osmotic pressure is inversely proportional to the volume (V) of the solution. If the volume increases, the osmotic pressure decreases.

**Hint**: Again, inverse proportionality means that increasing the volume will decrease the osmotic pressure.

### Conclusion:
Based on the analysis, we can summarize the relationships:
- Osmotic pressure is **directly proportional** to the concentration of the solution (C).
- Osmotic pressure is **inversely proportional** to the molar mass of the solute (M).
- Osmotic pressure is **directly proportional** to the temperature (T).
- Osmotic pressure is **inversely proportional** to the volume of the solution (V).

Thus, the correct statements regarding osmotic pressure are:
- It is directly proportional to the molar concentration of the solution.
- It is inversely proportional to the molecular weight of the solute.
- It is directly proportional to the temperature.
- It is inversely proportional to the volume of the solution.

### Final Answer:
The correct options are:
- Directly proportional to the molar concentration of the solution.
- Inversely proportional to the molecular weight of the solute.