Chapter 10, Problem 114SCQ

### Chemistry & Chemical Reactivity

10th Edition
John C. Kotz + 3 others
ISBN: 9781337399074

Chapter
Section

### Chemistry & Chemical Reactivity

10th Edition
John C. Kotz + 3 others
ISBN: 9781337399074
Textbook Problem

# The sodium azide required for automobile air bags is made by the reaction of sodium metal with dinitrogen monoxide in liquid ammonia:3 N2O(g) + 4 Na(s) + NH3(ℓ) → NaN3(s) + 3 NaOH(s) + 2 N2(g) (a) You have 65.0 g of sodium, a 35.0-L flask containing N2O gas with a pressure of 2.12 atm at 23 °C, and excess ammonia. What is the theoretical yield (in grams) of NaN3? (b) Draw a Lewis structure for the azide ion. Include all possible resonance structures. Which resonance structure is most likely? (c) What is the shape of the azide ion?

(a)

Interpretation Introduction

Interpretation:

For the given reaction the under given conditions the theoretical yield for NaN3 , the Lewis, resonance structure and the shape of the azide ion should be determined.

Concept Introduction:

Any gas is described by using four terms namely pressure, volume, temperature and the amount of gas. Thus combining three laws namely Boyle’s, Charles’s Law and Avogadro’s Hypothesis the following equation could be obtained. It is referred as ideal gas equation.

nTPV = RnTPPV = nRTwhere,n = moles of gasP = pressureT = temperatureR = gas constant

Under some conditions gases don not behave like ideal gas that is they deviate from their ideal gas properties. At lower temperature and at high pressures the gas tends to deviate and behave like real gases.

Boyle’s Law:

At given constant temperature conditions the mass of given ideal gas in inversely proportional to its volume.

Charles’s Law:

At given constant pressure conditions the volume of ideal gas is directly proportional to the absolute temperature.

Two equal volumes of gases with same temperature and pressure conditions tend to have same number of molecules with it.

The relationship between partial pressure and Ptotal is

Pi=χiPtotalwhere,Pi=partial pressureχi=molefractionPtotal=Totalpressure

Explanation

Given:

â€‚Â MassÂ ofÂ NaÂ =Â 65gPNO2â€Šâ€Š=â€Šâ€Š2.12Â mmÂ HgÂ =Â 2.12760â€Šâ€Š=â€Šâ€Š2.79Ã—10âˆ’3atmâ€Šâ€Šâ€Šâ€Šâ€Šâ€Šâ€Šâ€Šâ€Šâ€ŠVâ€Šâ€Šâ€Š=â€Šâ€Šâ€Š35Lâ€Šâ€Šâ€Šâ€Šâ€Šâ€Šâ€Šâ€Šâ€Šâ€Šâ€ŠTÂ =Â 23oCÂ =Â 273.15+23Â =Â 296.15K

First the given mass of sodium is converted into moles as follows,

â€‚Â molesÂ =massmolarÂ massâ€Šâ€Šâ€Šâ€Šâ€Šâ€Šâ€Šâ€Šâ€Šâ€Šâ€Šâ€Šâ€Šâ€Šâ€Šâ€Šâ€Šâ€Šâ€Šâ€Šâ€Šâ€Šâ€Šâ€Šâ€Šâ€Šâ€Šâ€Šâ€Šâ€Š=â€Šâ€Š65Â g22.99Â g/molâ€Šâ€Šâ€Šâ€Šâ€Šâ€Šâ€Šâ€Šâ€Šâ€Šâ€Šâ€Šâ€Šâ€Šâ€Šâ€Šâ€Šâ€Šâ€Šâ€Šâ€Šâ€Šâ€Šâ€Šâ€Šâ€Šâ€Šâ€Šâ€Šâ€Š=â€Šâ€Š2.83moles

There are about 2.83moles of sodium present in the given amount.

Then, the amount of N2O formed is calculated as follows,

â€‚Â PVÂ =Â nRTnÂ =Â PVRT=â€Šâ€Š2.12â€Šâ€ŠatmÃ—35L0.0821Ã—296.15K=3.052moles

Now, analyzing the given chemical equation it is evident that four moles of sodium requires 3 moles of N2O hence one mole of sodium need 34â€Šâ€Šmolesâ€Šâ€ŠofÂ N2O

(b)

Interpretation Introduction

Concept introduction:

• Sometimes the chemical bonding of a molecule cannot be represented using a single Lewis structure. In these cases, the chemical bonding are described by delocalization of electrons and is known as resonance.
• All the possible resonance structures are imaginary whereas the resonance hybrid is real.
• These structures will differ only in the arrangement of the electrons not in the relative position of the atomic nuclei.

(c)

Interpretation Introduction

Concept introduction:

• Sometimes the chemical bonding of a molecule cannot be represented using a single Lewis structure. In these cases, the chemical bonding are described by delocalization of electrons and is known as resonance.
• All the possible resonance structures are imaginary whereas the resonance hybrid is real.
• These structures will differ only in the arrangement of the electrons not in the relative position of the atomic nuclei.

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