Respuesta :
Answer:
- 22.0 mmHg
Explanation:
The vapor pressure of a solution is a colligative property, which means that it is determined by the number of particles (molecules or ions) of solute present in a solution.
Raoult's law permits the calculations of the change of the vapor pressure of a solvent when a solute is added.
The equation is:
- P solvent - P solution = ΔP = X solute × P solven
Where:
- P solvent = vapor pressure of the pure solvent.
- P solution = vapor pressure of the solution
- X solute = molar fraction of the solute
In the case of ionic solutes, you must take into account the number of ions that result from the ionization.
Calculating the molar fraction:
- number of moles = mass in grams / molar mass
- number of moles of KCl: 40.0 g / 74.5513 g/mol = 0.567 mol
- moles of ions = 2× number of moles of KCl = 1.134 mol
- moles of water: 250.0g / 18.015 g/mol = 13.877 mol
- total moles = 1.134 mol + 13.877 mol = 15.011 mol
- X solute = moles of ions / total moles = 1.134 mol / 15.011 mol = 0.0755
Calculating the change in the vapor pressure of the solution:
- ΔP = X solute × P solvent = 0.0755 × 23.76 mmHg = 1.78 mmHg
Vapor pressure of the solution:
- P solution = P solvent + ΔP = 23.76 mmHg - 1.79 mm Hg = 21.97mmHg
Rounding to three significant figures (because 40.0g has three significant figures): 22.0 mmHg ← answer.
Raoult's law states that for a given solution, the partial pressure of each component is equal to the mole fraction in that solution. The vapor pressure of the solution is 22 mmHg.
The vapor pressure is defined as the force exerted by the vapors in the walls of a container. It is a colligative property, such that the amount of substance increased or decreased is dependent on the amount of solute present.
The equation can be represented as:
- P[tex]_{\text{solvent}}[/tex] - P[tex]_{\text{solution}}[/tex] = [tex]\Delta[/tex] P = X [tex]_{\text{solute}}[/tex] x P[tex]_{\text{solvent}}[/tex]
where,
- P[tex]_{\text{solvent}}[/tex] = vapor pressure of the pure solvent
- P[tex]_{\text{solution}}[/tex] = vapor pressure of the solution
- X[tex]_{\text{solute}}[/tex] = molar fraction of the solute
Now, calculating the mole fraction, where:
- Moles of ions = 2 × number of moles of KCl = 1.134 mol
- Number of moles KCl = [tex]\dfrac{40}{74.55}&= 0.567[/tex] moles
- Total moles are: 1.134 mol + 13.877 mol = 15.011 mol
- X[tex]_{\text{solute}}[/tex] = [tex]\dfrac{1.134}{15.01}&= 0.075[/tex]
Now, the vapor pressure of the solution can be calculated as:
[tex]\Delta[/tex] P = X[tex]_{\text{solute}}[/tex] x P[tex]_{\text{solvent}}[/tex]
[tex]\Delta[/tex] P = 0.0755 × 23.76 mmHg = 1.78 mmHg
Hence, the vapor pressure of the solution:
P[tex]_{\text{solution}}[/tex] = [tex]\Delta[/tex] P + P[tex]_{\text{solvent}}[/tex]
P[tex]_{\text{solution}}[/tex] = 23.76 mmHg - 1.79 mm Hg = 21.97mmHg
Therefore, the vapor pressure of the solution is approximately 22 mmHg.
To know more about vapor pressure, refer to the following link:
https://brainly.com/question/7991371?referrer=searchResults
