The osmotic pressure of a solution containing 100 ml of 3.4% solution (w/v) of urea (mol mass 60 g/mole) and 50 ml of 1.6% solution (w/v) of cane-sugar (mol mass 342 g/mole) at 27ºC is:

Options

A. 10.56 atm
B. 8.98 atm
C. 17.06 atm
D. 9.70 atm

Answer

To find the osmotic pressure of the solution containing urea and cane sugar, we will follow these steps:

### Step 1: Understand the formula for osmotic pressure
The osmotic pressure (π) is given by the formula:
\[ \pi = C \cdot R \cdot T \]
where:
- \(C\) = concentration in molarity (moles per liter)
- \(R\) = gas constant (0.0821 L·atm/(K·mol))
- \(T\) = temperature in Kelvin

### Step 2: Convert temperature to Kelvin
The temperature is given as 27ºC. To convert this to Kelvin:
\[ T(K) = 27 + 273 = 300 \, K \]

### Step 3: Calculate moles of urea
The urea solution is 3.4% w/v, which means there are 3.4 grams of urea in 100 mL of solution. The molar mass of urea is 60 g/mol.

To find the number of moles of urea:
\[ \text{Moles of urea} = \frac{\text{mass of urea}}{\text{molar mass of urea}} = \frac{3.4 \, g}{60 \, g/mol} = 0.05667 \, mol \]

### Step 4: Calculate moles of cane sugar
The cane sugar solution is 1.6% w/v, meaning there are 1.6 grams of cane sugar in 100 mL of solution. Since we have 50 mL, the mass of cane sugar in 50 mL is:
\[ \text{Mass of cane sugar} = \frac{1.6 \, g}{100 \, mL} \times 50 \, mL = 0.8 \, g \]
The molar mass of cane sugar is 342 g/mol.

To find the number of moles of cane sugar:
\[ \text{Moles of cane sugar} = \frac{0.8 \, g}{342 \, g/mol} = 0.00234 \, mol \]

### Step 5: Calculate total moles
Now, we can find the total number of moles in the solution:
\[ \text{Total moles} = \text{Moles of urea} + \text{Moles of cane sugar} = 0.05667 + 0.00234 = 0.05899 \, mol \]

### Step 6: Calculate total volume in liters
The total volume of the solution is:
\[ \text{Total volume} = 100 \, mL + 50 \, mL = 150 \, mL = 0.150 \, L \]

### Step 7: Calculate molarity
Molarity (C) is calculated as:
\[ C = \frac{\text{Total moles}}{\text{Total volume in L}} = \frac{0.05899 \, mol}{0.150 \, L} = 0.3933 \, mol/L \]

### Step 8: Calculate osmotic pressure
Now we can calculate the osmotic pressure using the formula:
\[ \pi = C \cdot R \cdot T = 0.3933 \, mol/L \cdot 0.0821 \, L \cdot atm/(K \cdot mol) \cdot 300 \, K \]
Calculating this gives:
\[ \pi = 9.65 \, atm \]

### Step 9: Round the answer
Rounding off gives:
\[ \pi \approx 9.70 \, atm \]

### Final Answer
The osmotic pressure of the solution is approximately **9.70 atm**.