Calculate the osmotic pressure of a solution containing 17.1 g of cane - sugar (molecular mass 342) in 500 g of water at 300 K (R = 0.082 lit. atm `deg^(-1)mol^(-1)`). Density of the solution of urea. Find the molecular weight of urea.

Explanation

To calculate the osmotic pressure of a solution containing cane sugar, we will follow these steps:

### Step 1: Calculate the number of moles of cane sugar
To find the number of moles of cane sugar, we use the formula:

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

Given:
- Mass of cane sugar = 17.1 g
- Molar mass of cane sugar = 342 g/mol

\[ \text{Number of moles} = \frac{17.1 \, \text{g}}{342 \, \text{g/mol}} = 0.0500 \, \text{mol} \]

### Step 2: Calculate the volume of the solution in liters
We need to convert the mass of water to volume. Since the density of water is approximately 1 g/mL, the volume of 500 g of water is:

\[ \text{Volume of water} = 500 \, \text{g} \approx 500 \, \text{mL} = 0.500 \, \text{L} \]

### Step 3: Calculate the concentration of the solution
The concentration (C) in mol/L is given by:

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

\[ C = \frac{0.0500 \, \text{mol}}{0.500 \, \text{L}} = 0.100 \, \text{mol/L} \]

### Step 4: Calculate the osmotic pressure using the formula
The osmotic pressure (\(\pi\)) can be calculated using the formula:

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

Where:
- \(C\) = concentration in mol/L = 0.100 mol/L
- \(R\) = ideal gas constant = 0.082 L atm K\(^{-1}\) mol\(^{-1}\)
- \(T\) = temperature in Kelvin = 300 K

Substituting the values:

\[ \pi = 0.100 \, \text{mol/L} \cdot 0.082 \, \text{L atm K}^{-1} \text{mol}^{-1} \cdot 300 \, \text{K} \]

\[ \pi = 2.46 \, \text{atm} \]

### Final Answer
The osmotic pressure of the solution is approximately **2.46 atm**.

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