The osmotic pressure of 8% solution of urea at 300 K is

Explanation

To find the osmotic pressure of an 8% solution of urea at 300 K, 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)
- \(R\) = gas constant (0.0821 L·atm/(K·mol))
- \(T\) = temperature in Kelvin

### Step 2: Determine the mass of urea in the solution
An 8% solution means there are 8 grams of urea in 100 mL of solution.

### Step 3: Convert the volume of the solution to liters
Since osmotic pressure is typically expressed in terms of liters, we convert 100 mL to liters:
\[ 100 \text{ mL} = 0.1 \text{ L} \]

### Step 4: Calculate the number of moles of urea
To find the concentration \(C\), we first need to calculate the number of moles of urea. The molecular weight of urea (NH₂CONH₂) is approximately 60 g/mol. The number of moles (\(n\)) can be calculated using the formula:
\[ n = \frac{\text{mass}}{\text{molecular weight}} = \frac{8 \text{ g}}{60 \text{ g/mol}} = \frac{8}{60} \text{ mol} = 0.1333 \text{ mol} \]

### Step 5: Calculate the concentration \(C\)
Now we can find the concentration \(C\) in moles per liter:
\[ C = \frac{n}{V} = \frac{0.1333 \text{ mol}}{0.1 \text{ L}} = 1.333 \text{ mol/L} \]

### Step 6: Substitute the values into the osmotic pressure formula
Now we can substitute \(C\), \(R\), and \(T\) into the osmotic pressure formula:
\[ \pi = C \cdot R \cdot T = 1.333 \text{ mol/L} \cdot 0.0821 \text{ L·atm/(K·mol)} \cdot 300 \text{ K} \]

### Step 7: Calculate the osmotic pressure
Calculating the above expression:
\[ \pi = 1.333 \cdot 0.0821 \cdot 300 \approx 32.84 \text{ atm} \]

### Final Answer
The osmotic pressure of the 8% solution of urea at 300 K is approximately **32.84 atm**.

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