   Chapter 13, Problem 118IP

Chapter
Section
Textbook Problem

# The hydrocarbon naphthalene was frequently used in mothballs until recently, when it was discovered that human inhalation of naphthalene vapors can lead to hemolytic anemia. Naphthalene is 93.71% carbon by mass, and a 0.256-mole sample of naphthalene has a mass of 32.8 g. What is the molecular formula of naphthalene? This compound works as a pesticide in mothballs by. sublimation of the .solid so that it fumigates enclosed spaces with its vapors according to the equation Naphthalene ( s ) ⇌ naphthalene ( g )     K = 4.29 × 10 − 6 ( at   298   K ) If 3.00 g solid naphthalene is placed into an enclosed space with a volume of 5.00 L at 25°C, what percentage of the naphthalene will have sublimed once equilibrium bas been established?

Interpretation Introduction

Interpretation: The molecular formula of Naphthalene is to be calculated. After the equilibrium establishment the percentage of sublimed Naphthalene is to be calculated.

Concept introduction: The equilibrium constant K describes the ratio of the reactant to the product on the equilibrium conditions in terms of molar concentration.

The equilibrium constant depends upon temperature.

At equilibrium sum of all the partial pressure is equal to the total pressure.

Law of mass action is applicable on the equilibrium reactions.

The Le Chatelier’s principle states that the addition of the reactants shifts the equilibrium to the right while the addition of product shifts the equilibrium to the left at constant temperature.

Sublimation is the process in which solid species directly converts to the gaseous state.

To determine: The molecular formula of Naphthalene; the percentage of sublimed Naphthalene after the establishment of equilibrium.

Explanation

Explanation

The molecular formula of Naphthalene is C10H8_ .

Given

The reaction is given as,

Naphthalene(s)Naphthalene(g)

At temperature 298K the equilibrium constant is 4.29×106 .

Mass of the 0.256moles of naphthalene is 32.8g .

Mass percent of Carbon is 93.71% .

The molar mass of Naphthalene is calculated by the formula,

Molarmass=mn

Where,

• m is the given mass.
• n is the number of moles.

Substitute the values of moles and mass in the above formula.

Molarmass=mn=32.8g0.256mol=128.13g/mol

The mass of Carbon is calculated as,

MassofC=MasspercentofC×Samplemass

Substitute the values of sample mass and mass percent of Carbon in the above equation.

MassofC=MasspercentofC×Samplemass=93.71100×32.8g=30.74g

The moles of carbon is calculated as,

MolesofC=30.74g12.01gmol1=2.56moles

The moles of Hydrogen is calculated as,

MolesofHydrogen=(Samplemass-Carbonmass)MolarmassofHydrogen

Substitute the molar mass and mass of Hydrogen in the above equation.

MolesofHydrogen=(Samplemass-Carbonmass)MolarmassofHydrogen=(32.830.74)g1.008g=2.05moles

Divide each component by lowest number of moles.

For Carbon,

2.562.05=1.25

For Hydrogen,

2.052.05=1

Therefore, the lowest whole number molecular formula is C1

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