Respuesta :
Answer : The vapor pressure of hexane = 140.5055 torr
Solution : Given,
Concentration of Naphthalene by mass = 10 %
Vapor pressure of pure Hexane = 151 torr
From the periodic table, the molar masses of Naphthalene and Hexane are:
Molar mass of Naphthalene = 128 g/mole
Molar mass of Hexane = 86 g/mole
From the Raoult's law, the vapor pressure of the component is equal to the vapor pressure of the pure component multiplied by its mole fraction.
Formula used :
[tex]P_{i}=P_{i}^{*}\times x_{i}[/tex] ..............(1)
Where,
[tex]P_{i}[/tex] = vapor pressure of component i
[tex]P_{i}^{*}[/tex] = vapor pressure of pure component i
[tex]x_{i}[/tex] = mole fraction of of component i in the solution
For this problem, few steps are involved:
step 1 : concentration of 10% naphthalene by mass means 10 g of naphthalene present in 100 g of solution.
This means,
The mass of naphthalene = 10 g
The mass of hexane = 100 - 10 = 90 g
step 2 : find the number of moles of naphthalene and hexane.
Formula used :
Number of moles = [tex]\frac{\text{ Given mass}}{\text{ Molar mass}}[/tex]
Moles of Naphthalene = [tex]\frac{10g}{128g/mole}[/tex] = 0.0781 moles
Moles of Hexane = [tex]\frac{90g}{86g/mole}[/tex] = 1.0465 moles
Total moles = Moles of Naphthalene + Moles of Hexane
= 0.0781 + 1.0465 = 1.1246 moles
step 3 : Now, calculate mole fraction of Hexane
Mole fraction of Hexane = [tex]\frac{\text{ Moles of Hexane}}{\text{ Total moles}}[/tex] = [tex]\frac{1.0465}{1.1246}[/tex] = 0.9305
step 4 : Now, find the vapor pressure of Hexane by using above formula (1).
[tex]P_{i}=P_{i}^{*}\times x_{i}[/tex]
Now put all the values in this formula, we get
Vapor pressure of Hexane = Vapor pressure of pure Hexane × Mole fraction of Hexane
[tex]P_{i}[/tex] = 151 torr × 0.9305 = 140.5055 torr
The vapor pressure at 25°C of hexane : 140.52 torr
Further explanation
Solution properties are the properties of a solution that don't depend on the type of solute but only on the concentration of the solute.
Solution properties of electrolyte solutions differ from non-electrolyte solutions because electrolyte solutions contain a greater number of particles because electrolytes break down into ions. So the Solution properties of electrolytes is greater than non-electrolytes.
The term is used in the Solution properties
- 1. mole fraction
the ratio of the number of moles of solute to the mole of solution
[tex] \large {\boxed {\bold {Xa = \frac {na} {na + nb}}} [/tex]
- 2. Vapor pressure
Vapor pressure depends on the mole fraction of the components in the solution
P = Xs. P °
P = vapor pressure solution
P ° = pure vapor pressure of the solvent
Xs = mole fraction solvent
ΔP = P ° - P where
ΔP = change in vapor pressure
We determine the mole fraction of hexane (we consider a 100 g solution)
mass of naphthalene (C₁₀H₈) = 105 = 10 g
molar mass: 128 g/mole
mole: 10: 128 = 0.078
mass of hexane (C₆H₁₄) = 90 g
molar mass: 86 g/mole
mol = 90: 86 = 1.0465
Total mole = 1.0465 + 0.078 = 1.1245
Hexane mole fraction = 1.0465: 1.1245 = 0.9306
vapor pressure hexane = hexane mole fraction. vapor pressure of pure hexane
Phexane = 0.9306 x 151
Phexane = 140.52 torr
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