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Chapter 1 • Introduction

1.1 A gas ał 20°C inay be rarefied if il conlains less thun K)¹* molecules per min'. If A\ogadro’s number is 6j023E23 molecules |ier mole. wliat air pressure does ihis represeni?

Soliition: Hic mass of one n>olecule of air inay be oomputed as

m

_ Molecular weighi __28.97 mol

Avogadro’s number 6.023E23 molecule s/g-mol

= 4.81E-23 g

Tlien thedensiiy of air coniaining 10 molecules per min' is. in SI miils.

=(

I0¹³

molecules V

4.8IE-23

A

;ule )

molecule

-4.8IE-I1

-1--4.8IE-5

mm    m

Finał ly. from ilie perfect gas law. Eq. (1.13). ai 20°C - 293 K. we obiain ilie pressure: p = /?RT -1 4.8IE-5    |! 287    |<293 K)= 4.0 Pa Ans.

1.2 The eanh’s aimospłiere can ł>e modeled as a uniform layer of air of ihickness 20 km and averagedeihiiy 0.6 kg/m' (see TaWe A-6). Use ihese values toesiimaie ilie loial mass and total number of molecules of air in ihe eniire ulinosphere of Ute earth.

Solulioii:    Lei R* Iie ilie earih‘s radius « 6377 km. Hien ihe loial mass of air in ilie

almosphere is

m, - J />dVol-/>_Ji#(Air Vol)» /?_44<,4^R³(Air ihickness)

-(0.6 kg/m' i4^(6.377E6 m)²(20E3 m) “ 6.1 LIS kg Am.

I)i\ kling by lite mass of one molecule •* 4.8E-23 g (see Prób. 1.1 above). we obiain ilie uwal number of molecules in ilie earth’s atmosphere:

N,

m( aimospłiere)___6.1E2I grams

m(one molecule) 4.8E-23 gm/molecule

1.3 E44 nrolce ul CS Ans.