The osmotic pressure of 7% solution of urea at 298 K is

Explanation

To find the osmotic pressure of a 7% solution of urea at 298 K, we can use the formula for osmotic pressure given by:

\[ \pi = CRT \]

where:
- \(\pi\) = osmotic pressure
- \(C\) = concentration in moles per liter (mol/L)
- \(R\) = universal gas constant (0.0821 L·atm/(K·mol))
- \(T\) = temperature in Kelvin (K)

### Step 1: Determine the mass of urea in the solution
A 7% solution of urea means there are 7 grams of urea in 100 mL of solution.

### Step 2: Convert the volume of the solution from mL to L
Since osmotic pressure is usually expressed in terms of liters, we need to convert 100 mL to liters:

\[ 100 \, \text{mL} = 0.1 \, \text{L} \]

### Step 3: Calculate the number of moles of urea
To find the concentration, we first need to calculate the number of moles of urea. The molecular weight of urea (NH₂CONH₂) is approximately 60 g/mol.

Using the formula for moles:

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

Substituting the values:

\[ n = \frac{7 \, \text{g}}{60 \, \text{g/mol}} = 0.11667 \, \text{mol} \]

### Step 4: Calculate the concentration (C)
Now, we can calculate the concentration \(C\) in moles per liter:

\[ C = \frac{n}{V} = \frac{0.11667 \, \text{mol}}{0.1 \, \text{L}} = 1.1667 \, \text{mol/L} \]

### Step 5: Substitute values into the osmotic pressure formula
Now we can substitute \(C\), \(R\), and \(T\) into the osmotic pressure formula:

\[ \pi = CRT = (1.1667 \, \text{mol/L}) \times (0.0821 \, \text{L·atm/(K·mol)}) \times (298 \, \text{K}) \]

### Step 6: Calculate the osmotic pressure
Now we perform the multiplication:

\[ \pi = 1.1667 \times 0.0821 \times 298 \approx 28.54 \, \text{atm} \]

Thus, the osmotic pressure of the 7% solution of urea at 298 K is approximately **28.54 atm**.

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