Osmotic pressure of a solution at a given temperature

Options

A. increases with concentration
B. decreases with concentration
C. remains same
D. initially increases and then decreases

Explanation

To solve the problem regarding the osmotic pressure of a solution at a given temperature, we will analyze the relationship between osmotic pressure and concentration based on the formula provided in the video transcript.

### Step-by-Step Solution:

1. **Understanding Osmotic Pressure**:
- Osmotic pressure (π) is defined by the formula:
\[ \pi = iCRT \]
where:
- \( i \) = van 't Hoff factor (number of particles the solute dissociates into)
- \( C \) = concentration of the solution (in mol/L)
- \( R \) = universal gas constant (0.0821 L·atm/(K·mol))
- \( T \) = absolute temperature (in Kelvin)

2. **Given Conditions**:
- The problem states that we are considering osmotic pressure at a "given temperature." This implies that \( T \) is constant.
- Since \( R \) is also a constant, we can simplify our analysis.

3. **Analyzing the Variables**:
- Since \( T \) and \( R \) are constants, the osmotic pressure (π) will depend on the product of \( i \) and \( C \).
- Therefore, we can express the relationship as:
\[ \pi \propto i \cdot C \]

4. **Effect of Concentration on Osmotic Pressure**:
- If the concentration \( C \) increases, and assuming \( i \) remains constant (as we do not have information about it), the osmotic pressure \( \pi \) will increase.
- Thus, we can conclude that osmotic pressure increases with an increase in concentration.

5. **Conclusion**:
- The correct interpretation of the effect of concentration on osmotic pressure is that as the concentration of the solution increases, the osmotic pressure also increases.

### Final Answer:
Osmotic pressure increases with concentration at a given temperature.