What is the vapor pressure of the solvent
in an aqueous solution at 25◦C of 0.29 m (molality) urea(CO(NH2)2), a nonelectrolyte? The vapor pressure of water at 25◦C is 23.76 Torr.
Answer in units of Tor
I want to use the mole fraction and multiply it by VP and add the two VP, but I don't know what to do with the molality so that's its useful..
To find the vapor pressure of the solvent in an aqueous solution, you can use Raoult's law, which states that the vapor pressure of the solvent above the solution is directly proportional to the mole fraction of the solvent in the solution.
Let's break down the steps to solve this problem:
1. Convert molality (m) to mole fraction (X):
Molality (m) is defined as the number of moles of solute per kilogram of solvent. To convert it to mole fraction (X), divide the moles of solute by the total moles in the solution (solute + solvent).
2. Calculate the mole fraction of water:
Since urea is a non-electrolyte, it does not significantly affect the vapor pressure of the solvent. Hence, the mole fraction of the solvent (water) would be approximately 1-X, where X is the mole fraction of urea.
3. Use Raoult's law to find the vapor pressure of the solvent:
Multiply the mole fraction of water by the vapor pressure of pure water at the given temperature (25°C). This will give you the partial pressure of the solvent in the solution.
4. Add the vapor pressure of the solvent to the vapor pressure of the solute:
Since the urea is a nonelectrolyte, its vapor pressure is negligible and can be ignored. Therefore, the vapor pressure of the solvent in the solution will be the same as the partial pressure of the solvent.
Now let's apply these steps to the given problem:
1. Calculate the mole fraction of urea (X):
Since the molality (m) of urea is given as 0.29 m, we need to convert it into moles. Since molality is defined as moles of solute divided by kilograms of solvent, multiply the molality by the mass of the solvent (water) in kilograms.
2. Convert mole fraction of urea to mole fraction of water (1-X):
Since the sum of mole fractions in a solution is always equal to 1, subtract the mole fraction of urea (X) from 1. This will give you the mole fraction of water in the solution.
3. Calculate the partial pressure of the solvent (water) using Raoult's law:
Multiply the mole fraction of water by the vapor pressure of pure water at 25°C (given as 23.76 Torr).
4. The resulting value is the vapor pressure of the solvent in the aqueous solution.