Final answer:
To find the vapor pressure of the solution, calculate the mole fraction of water using the masses of urea, sucrose, and water converted to moles. Then, apply Raoult's law multiplying this mole fraction with the given vapor pressure of pure water to obtain the vapor pressure of the solution.
Step-by-step explanation:
To calculate the vapor pressure of a solution after dissolving nonvolatile solutes such as urea and sucrose, we can use Raoult's law. This law states that the vapor pressure of a solvent in an ideal solution is directly proportional to the mole fraction of the solvent.
Since both urea and sucrose are nonvolatile, they will not contribute to the vapor pressure but will instead lower the vapor pressure of the water due to the reduction in mole fraction of the water.
We start by assuming that urea and sucrose do not ionize or react with the solvent and that they produce an ideal solution. Thus, the mole fraction of the solvent (water) times the vapor pressure of the pure solvent (water) will equal the vapor pressure of the solution. The formula for this calculation can be written as:
Psolution = Xwater × Pwater0
Where:
- Psolution is the vapor pressure of the solution
- Xwater is the mole fraction of water in the solution
- Pwater0 is the vapor pressure of pure water
To find the mole fraction of water, we will first convert the given masses of urea, sucrose, and water to moles. Then we will calculate the total moles in the solution to finally find the mole fraction of water (Xwater).
After obtaining this value, we can then use it to calculate the vapor pressure of the solution using the given vapor pressure of pure water at the same temperature.