What would be the osmotic pressure at `25^@C` of an aqueous solution containing 1.95 g of sucrose `(C_12 H_22 O_11)` present in 150 ml of solution?

Options

A. 0.81 atm
B. 0.93 atm
C. 0.65 atm
D. 0.76 atm

Answer

To find the osmotic pressure of the solution, we can use the formula for osmotic pressure:

\[ \Pi = iCRT \]

Where:
- \(\Pi\) = osmotic pressure
- \(i\) = van 't Hoff factor (for sucrose, which is a non-electrolyte, \(i = 1\))
- \(C\) = molarity of the solution
- \(R\) = universal gas constant = \(0.0821 \, \text{L atm K}^{-1} \text{mol}^{-1}\)
- \(T\) = temperature in Kelvin

### Step 1: Calculate the molar mass of sucrose (C₁₂H₂₂O₁₁)
The molar mass of sucrose can be calculated as follows:

- Carbon (C): 12 g/mol × 12 = 144 g/mol
- Hydrogen (H): 1 g/mol × 22 = 22 g/mol
- Oxygen (O): 16 g/mol × 11 = 176 g/mol

Adding these together:

\[ \text{Molar mass of sucrose} = 144 + 22 + 176 = 342 \, \text{g/mol} \]

### Step 2: Calculate the number of moles of sucrose
Using the formula:

\[ \text{Number of moles} = \frac{\text{mass (g)}}{\text{molar mass (g/mol)}} \]

Substituting the values:

\[ \text{Number of moles} = \frac{1.95 \, \text{g}}{342 \, \text{g/mol}} \approx 0.0057 \, \text{mol} \]

### Step 3: Calculate the molarity of the solution
Molarity (C) is defined as moles of solute per liter of solution. The volume of the solution is given as 150 mL, which is equivalent to 0.150 L.

\[ C = \frac{\text{Number of moles}}{\text{Volume (L)}} \]

Substituting the values:

\[ C = \frac{0.0057 \, \text{mol}}{0.150 \, \text{L}} \approx 0.038 \, \text{mol/L} \]

### Step 4: Convert the temperature to Kelvin
The temperature in Celsius is given as \(25^\circ C\). To convert to Kelvin:

\[ T = 25 + 273 = 298 \, \text{K} \]

### Step 5: Calculate the osmotic pressure
Now we can substitute the values into the osmotic pressure formula:

\[ \Pi = iCRT \]

Substituting the known values:

\[ \Pi = 1 \times 0.038 \, \text{mol/L} \times 0.0821 \, \text{L atm K}^{-1} \text{mol}^{-1} \times 298 \, \text{K} \]

Calculating this gives:

\[ \Pi \approx 0.93 \, \text{atm} \]

### Final Answer:
The osmotic pressure at \(25^\circ C\) of the aqueous solution is approximately **0.93 atm**.

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