Osmotic pressure of a sugar solution at `24^(@)C` is 2.5 atmosphere .Determine the concentration of the solution in gram mole per litre.

Options

A. `0.0821 "moles/litre"`
B. `1.082 "moles/litre"`
C. `0.1025 "moles/litre"`
D. `0.0827 "moles/litre"`

Explanation

To determine the concentration of the sugar solution in gram moles per liter using the given 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 (for sugar, \(i = 1\) since it does not dissociate)
- \(C\) = concentration in moles per liter (mol/L)
- \(R\) = universal gas constant = 0.0821 L·atm/(K·mol)
- \(T\) = temperature in Kelvin

### Step 1: Convert the temperature to Kelvin
The temperature is given as \(24^\circ C\). To convert this to Kelvin, we use the formula:

\[ T(K) = T(°C) + 273 \]

Calculating:

\[ T = 24 + 273 = 297 \, K \]

### Step 2: Rearrange the osmotic pressure formula to find concentration
Since we are looking for concentration \(C\), we can rearrange the formula:

\[ C = \frac{\Pi}{i \cdot R \cdot T} \]

Given that \(i = 1\) for sugar, the formula simplifies to:

\[ C = \frac{\Pi}{R \cdot T} \]

### Step 3: Substitute the known values into the equation
Now we can substitute the known values into the equation:

- \(\Pi = 2.5 \, atm\)
- \(R = 0.0821 \, L \cdot atm/(K \cdot mol)\)
- \(T = 297 \, K\)

Substituting these values:

\[ C = \frac{2.5}{0.0821 \cdot 297} \]

### Step 4: Calculate the concentration
Now, we perform the calculation:

1. Calculate \(R \cdot T\):

\[ R \cdot T = 0.0821 \cdot 297 \approx 24.4857 \]

2. Now, divide \(\Pi\) by \(R \cdot T\):

\[ C = \frac{2.5}{24.4857} \approx 0.1025 \, mol/L \]

### Conclusion
The concentration of the sugar solution is approximately \(0.1025 \, mol/L\).