The osmotic pressure of a sugar solution at `24^(@)C` is `2.5 atm`. The concentration of the solution in mole per litre is

Options

A. 10.25
B. 1.025
C. 1025
D. 0.1025

Explanation

To solve the problem of finding the concentration of a sugar solution given its osmotic pressure, we can use the formula for osmotic pressure:

\[ \pi = i \cdot C \cdot R \cdot T \]

Where:
- \(\pi\) = osmotic pressure (in atm)
- \(i\) = Van't Hoff factor
- \(C\) = concentration (in moles per liter)
- \(R\) = ideal gas constant (0.0821 L·atm/(K·mol))
- \(T\) = temperature (in Kelvin)

### Step-by-Step Solution:

**Step 1: Identify the given values.**
- Osmotic pressure (\(\pi\)) = 2.5 atm
- Temperature = 24°C

**Step 2: Convert temperature from Celsius to Kelvin.**
\[ T(K) = 24 + 273 = 297 \text{ K} \]

**Step 3: Determine the Van't Hoff factor (\(i\)).**
For sugar (like glucose), the Van't Hoff factor (\(i\)) is 1 because it does not dissociate into ions in solution.

**Step 4: Substitute the known values into the osmotic pressure equation.**
\[ \pi = i \cdot C \cdot R \cdot T \]
Substituting the values:
\[ 2.5 = 1 \cdot C \cdot 0.0821 \cdot 297 \]

**Step 5: Rearrange the equation to solve for concentration (\(C\)).**
\[ C = \frac{\pi}{R \cdot T} \]
Substituting the known values:
\[ C = \frac{2.5}{0.0821 \cdot 297} \]

**Step 6: Calculate the denominator.**
\[ 0.0821 \cdot 297 = 24.4857 \]

**Step 7: Calculate the concentration (\(C\)).**
\[ C = \frac{2.5}{24.4857} \approx 0.1025 \text{ moles per liter} \]

### Final Answer:
The concentration of the sugar solution is approximately **0.1025 moles per liter**.