Calculate the concentration of that solution of sugar which has osmotic pressure 2.46 atmosphere at `27^(@)C`.

Explanation

To calculate the concentration of a sugar solution 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 mol/L)
- \(R\) = ideal gas constant (0.0821 L·atm/(K·mol))
- \(T\) = temperature (in Kelvin)

### Step-by-Step Solution:

1. **Convert Temperature to Kelvin**:
The temperature is given as \(27^\circ C\). To convert this to Kelvin, we use the formula:
\[ T(K) = T(°C) + 273.15 \]
\[ T = 27 + 273.15 = 300.15 \, K \approx 300 \, K \]

2. **Identify Given Values**:
- Osmotic pressure, \(\Pi = 2.46 \, atm\)
- Ideal gas constant, \(R = 0.0821 \, L·atm/(K·mol)\)
- Temperature, \(T = 300 \, K\)

3. **Rearrange the Osmotic Pressure Formula**:
We need to find the concentration \(C\). Rearranging the formula gives:
\[ C = \frac{\Pi}{RT} \]

4. **Substitute the Values**:
Now, substituting the known values into the rearranged formula:
\[ C = \frac{2.46}{0.0821 \times 300} \]

5. **Calculate the Denominator**:
First, calculate \(R \times T\):
\[ R \times T = 0.0821 \times 300 = 24.63 \]

6. **Calculate Concentration**:
Now substitute this value back into the equation for \(C\):
\[ C = \frac{2.46}{24.63} \approx 0.0999 \, mol/L \]

7. **Convert to grams per liter**:
To convert moles per liter to grams per liter, we need the molar mass of sugar (sucrose, C12H22O11), which is approximately \(342.3 \, g/mol\):
\[ \text{Concentration in g/L} = C \times \text{Molar Mass} \]
\[ \text{Concentration in g/L} = 0.0999 \, mol/L \times 342.3 \, g/mol \approx 34.2 \, g/L \]

### Final Answer:
The concentration of the sugar solution is approximately **34.2 g/L**.