What will be the osmotic pressure of 5%(w/v) aqueous solution of
urea at `17^(@)`C ?

Options

A. 19.84 atm
B. 1.16 atm
C. 1.984 atm
D. 6.61 atm

Explanation

To find the osmotic pressure of a 5% (w/v) aqueous solution of urea at 17°C, we can follow these steps:

### Step 1: Understand the formula for osmotic pressure
The osmotic pressure (π) can be calculated using the formula:
\[ \pi = CRT \]
where:
- \(C\) = concentration of the solution in moles per liter (mol/L)
- \(R\) = ideal gas constant = 0.0821 L·atm/(K·mol)
- \(T\) = temperature in Kelvin

### Step 2: Calculate the mass of solute
Given that the solution is 5% (w/v), this means there are 5 grams of urea in 100 mL of solution.

### Step 3: Determine the molecular weight of urea
The molecular weight of urea (NH₂CONH₂) is given as 60 g/mol.

### Step 4: Convert the volume of the solution to liters
Since osmotic pressure is typically expressed in terms of liters, convert 100 mL to liters:
\[ 100 \, \text{mL} = 0.1 \, \text{L} \]

### Step 5: Calculate the number of moles of urea
Using the formula:
\[ \text{Number of moles} = \frac{\text{mass}}{\text{molecular weight}} = \frac{5 \, \text{g}}{60 \, \text{g/mol}} = \frac{1}{12} \, \text{mol} \approx 0.0833 \, \text{mol} \]

### Step 6: Calculate the concentration (C)
Now, we can find the concentration \(C\) in moles per liter:
\[ C = \frac{\text{Number of moles}}{\text{Volume in L}} = \frac{0.0833 \, \text{mol}}{0.1 \, \text{L}} = 0.833 \, \text{mol/L} \]

### Step 7: Convert temperature to Kelvin
Convert the temperature from Celsius to Kelvin:
\[ T = 17 + 273 = 290 \, \text{K} \]

### Step 8: Substitute values into the osmotic pressure formula
Now, substitute the values into the osmotic pressure formula:
\[ \pi = CRT = (0.833 \, \text{mol/L}) \times (0.0821 \, \text{L·atm/(K·mol)}) \times (290 \, \text{K}) \]

### Step 9: Calculate the osmotic pressure
Calculating the above expression:
\[ \pi = 0.833 \times 0.0821 \times 290 \approx 19.84 \, \text{atm} \]

### Final Answer
The osmotic pressure of the 5% (w/v) aqueous solution of urea at 17°C is approximately **19.84 atm**.

---