Colligative Properties

The osmotic pressure is given by the formula: Where: - = number of moles of urea,
- = gas constant = 0.082 L atm K mol ,
- = temperature in Kelvin = 300 K,
- = volume of solution in liters = 500 mL = 0.5 L.
First, calculate the number of moles of urea: Now, calculate the osmotic pressure:

Step 1: The depression in freezing point ( ) is related to the molality ( ) of the solution by the formula: where: - is the depression in freezing point, - is the cryoscopic constant for benzene, - is the molality of the solution. The molality is defined as: In this case, we are given: - Molar mass of benzoic acid = 122 g/mol, - Mass of solvent (benzene) = 49 g = 0.049 kg, - Degree of association . For benzoic acid, it undergoes dimerization, meaning 2 moles of benzoic acid combine to form a dimer. So, the number of moles of benzoic acid is reduced by the factor .
Step 2: We can now write the molality as: Substitute the known values: Simplifying further:
Step 3: Now we use the depression in freezing point equation: Substitute the known values: Solving for : So, the value of is 11.36g