Question

A solution contains naphthalene (c10h8) dissolved in hexane (c6h14) at a concentration of 10.00 % naphthalene by mass. part a calculate the vapor pressure at 25 ∘c of hexane above the solution. the vapor pressure of pure hexane at 25 ∘c is 151 torr.

Answer 1

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

$\large {\boxed {\bold {Xa = \frac {na} {na + nb}}}$

• 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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Answer 2

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 :

$P_{i}=P_{i}^{*}\times x_{i}$      ..............(1)

Where,

$P_{i}$ = vapor pressure of component i

$P_{i}^{*}$ = vapor pressure of pure component i

$x_{i}$ = 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 = $\frac{\text{ Given mass}}{\text{ Molar mass}}$

Moles of Naphthalene = $\frac{10g}{128g/mole}$ = 0.0781 moles

Moles of Hexane = $\frac{90g}{86g/mole}$ = 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 = $\frac{\text{ Moles of Hexane}}{\text{ Total moles}}$ = $\frac{1.0465}{1.1246}$ = 0.9305

step 4 : Now, find the vapor pressure of Hexane by using above formula (1).

$P_{i}=P_{i}^{*}\times x_{i}$  

Now put all the values in this formula, we get

Vapor pressure of Hexane = Vapor pressure of pure Hexane × Mole fraction of Hexane

$P_{i}$ = 151 torr × 0.9305 = 140.5055 torr