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The massof anoxgyenmolecule differsfromthat ofa nitrogenmolecule. Dothe oxygenmoleculesand thenitrogenmoleculesin airhavethe samermsspeedv_(rms) ? |
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Answer» SOLUTION :weknow that ` V_(rms)`isrelated toKavgbyequation. ` K_(AVG)= 1/2mv_(rms )^(2)` Although thetwotypesof moleculeshavethe same`K_(Avg) `they havedifferentmassesm andthustheirrmsspeedsmustdiffer. the findtheir rmsspeeds , wesolveEq. 20-15for ` v_(rms ) `andthensubstitutefor molecularmassm withequation`M = m N_A`becausemolarmassesM canbefoundinappendixF.weobtain ` V_(rms) = sqrt((2K _(avg) N_A)/(M ))` Calculations:INTHE airthatwebreatheoxygenandnitrogenare diatomicmolecules`(O_2and N_2)`-eachmolecule consistsof twoatoms. themolarmass`M_(O_2)` ofdiatomicoxygenis 1( 15.9994g / mol ) `~~= 0.0320` Kg/ moland themolarmass`M_(N_2)`of diatomicnitrogenis `2 ( 14.0067g // mol ) ~~ 0.0280kg // mol ` NowwecansubstituteknowndataintoEq 20-27foroxygenwefind ` V_(rms ) =sqrt((2 ( 6.21 xx 10^(-21)J)(6.02 xx 10^(23) mol ^(-1)))/( 0.0320kg // mol ))` `=483m//s ` Similarly,fornitrogenwefind ` V_(rms )= 517m//s ` the nitrogenwe find ` V_(rms )= 517m//s` Thenitrogenmolecules, withtheirsmaller MASS( ANDTHE sameaveragekineticenergy) , havethegreaterrmsspeed . |
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