A solution is made by dissolving 22.9 g urea (), a nonelectrolyte, in 302 g water. (The vapor pressure of pure water is 23.8 torr at 25°C and 71.9 torr at 45°C.)
Calculate the vapor pressure of this solution at 25°C.
Vapor pressure =
torr
Calculate the vapor pressure of this solution at 45°C.
Vapor pressure =
torr
To calculate the vapor pressure of the solution, we need to use Raoult's law. According to Raoult's law, the vapor pressure of a solution is equal to the mole fraction of the solvent times the vapor pressure of the pure solvent.
First, we need to calculate the mole fraction of water (solvent) in the solution. We can calculate the mole fraction by dividing the moles of water by the total number of moles in the solution.
To find the moles of water, we need to use the given mass (302 g) and the molar mass of water (18 g/mol). We divide the mass by the molar mass to get moles:
moles of water = mass of water / molar mass of water
moles of water = 302 g / 18 g/mol
moles of water = 16.78 mol
Similarly, we can calculate the moles of urea using the given mass (22.9 g) and the molar mass of urea (60 g/mol):
moles of urea = mass of urea / molar mass of urea
moles of urea = 22.9 g / 60 g/mol
moles of urea = 0.382 mol
Next, we calculate the mole fraction of water:
mole fraction of water = moles of water / total moles
mole fraction of water = 16.78 mol / (16.78 mol + 0.382 mol)
mole fraction of water = 0.977
Now, we can calculate the vapor pressure of the solution at 25°C using Raoult's law:
vapor pressure = mole fraction of water * vapor pressure of pure water at 25°C
vapor pressure = 0.977 * 23.8 torr
vapor pressure = 23.2676 torr
Therefore, the vapor pressure of the solution at 25°C is approximately 23.3 torr.
To calculate the vapor pressure at 45°C, we follow the same steps but use the vapor pressure of pure water at 45°C, which is 71.9 torr.
Calculating the mole fraction of water and using Raoult's law:
mole fraction of water = 0.977 (as calculated above)
vapor pressure = 0.977 * 71.9 torr
vapor pressure = 70.167 torr
Therefore, the vapor pressure of the solution at 45°C is approximately 70.2 torr.