The osmotic pressure and vapor pressure of a 0.6% aqueous solution of urea at 25°C can be calculated using the ideal gas law and the concept of Raoult's law.

Osmotic Pressure:

The osmotic pressure of a solution is the pressure required to prevent the flow of solvent molecules into the solution through a semipermeable membrane. It is directly related to the concentration of the solute.

To calculate the osmotic pressure of the 0.6% urea solution, we can use the formula:

Osmotic pressure = n/VRT

Where n is the number of moles of solute (urea), V is the volume of the solution, R is the ideal gas constant, and T is the temperature in Kelvin.

1. Calculate the number of moles of urea:
Since the concentration is given as 0.6%, we can assume 100g of the solution. Therefore, the mass of urea in the solution is 0.6g (0.6% of 100g).

The molar mass of urea (NH2CONH2) is (14.01 * 2) + 12.01 + (16.00 * 2) + 14.01 + 1.01 + (14.01 * 2) = 60.06 g/mol.

The number of moles of urea can be calculated as:
moles = mass/molar mass = 0.6g / 60.06 g/mol = 0.00999 mol (approximately 0.01 mol)

2. Calculate the osmotic pressure:
Assuming a volume of 1 liter (V = 1 L), the ideal gas constant (R) is 0.0821 L·atm/(mol·K), and the temperature (T) is 25°C = 298 K.

Using the formula:
Osmotic pressure = (0.01 mol) / (1 L) * (0.0821 L·atm/(mol·K)) * (298 K) = 2.43 atm

Therefore, the osmotic pressure of the 0.6% urea solution is 2.43 atm.

Vapor Pressure:

Vapor pressure is the pressure exerted by the vapor of a liquid in equilibrium with its liquid phase at a given temperature. According to Raoult's law, the vapor pressure of a solvent in a solution is proportional to the mole fraction of the solvent in the solution.

To calculate the vapor pressure of the 0.6% urea solution, we can use the formula:

Vapor pressure = mole fraction of solvent * vapor pressure of pure solvent

1. Calculate the mole fraction of water:
Since urea is a non-volatile solute, it does not contribute to the vapor pressure. Therefore, the mole fraction of water is 1.

2. Calculate the vapor pressure:
Given that the vapor pressure of pure water at 25°C is 24 mm Hg, the vapor pressure of the 0.6% urea solution is:
Vapor pressure = (1) * (24 mm Hg) = 24 mm Hg

Therefore, the vapor pressure of the 0.6% urea solution is 24 mm Hg.

Summary:
- The osm