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 find the concentration of the sugar solution in moles per liter given its osmotic pressure, we can use the formula for osmotic pressure:

\[ \pi = cRT \]

where:
- \(\pi\) = osmotic pressure (in atm)
- \(c\) = concentration of the solution (in moles per liter)
- \(R\) = ideal gas constant = \(0.0821 \, \text{L atm K}^{-1} \text{mol}^{-1}\)
- \(T\) = temperature (in Kelvin)

### Step-by-Step Solution:

1. **Convert the temperature from Celsius to Kelvin**:
\[ T = 24^\circ C + 273.15 = 297.15 \, K \quad (\text{approximately } 297 \, K) \]

2. **Substitute the known values into the osmotic pressure formula**:
Given:
- \(\pi = 2.5 \, \text{atm}\)
- \(R = 0.0821 \, \text{L atm K}^{-1} \text{mol}^{-1}\)
- \(T = 297 \, K\)

The formula becomes:
\[ 2.5 = c \times 0.0821 \times 297 \]

3. **Rearrange the formula to solve for concentration \(c\)**:
\[ c = \frac{\pi}{RT} \]

4. **Substitute the values into the rearranged formula**:
\[ c = \frac{2.5}{0.0821 \times 297} \]

5. **Calculate the denominator**:
\[ 0.0821 \times 297 \approx 24.4857 \]

6. **Calculate the concentration**:
\[ c = \frac{2.5}{24.4857} \approx 0.1025 \, \text{mol/L} \]

### Final Answer:
The concentration of the sugar solution is approximately \(0.1025 \, \text{mol/L}\).

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