Problem 83 in chapter 5 of Zumdahl/Zumdal\'s Chemistry6th edition textbook: One

Question

Problem 83 in chapter 5 of Zumdahl/Zumdal's Chemistry6th edition textbook: One way of separating oxygen isotopes is by gaseous diffusionof carbon monoxide. The gaseous diffusion process behaves like aneffustion process. Calculate the relative rates of effusion of12C16O, 12C17O, 12C18O. The problem asks for the relative rate of EFFUSION of threecompounds. The solution provided by Cramster takesthe DIFFUSION rate by taking the inverse of the combinedmolar masses. It then takes the square root of the ratio of 12C18Omolar mass divided by the molar mass of all three compounds. Howwould a student know to divide 1 by the molar mass then to compareall three compounds to the mass of the largest one? Problem 83 in chapter 5 of Zumdahl/Zumdal's Chemistry6th edition textbook: One way of separating oxygen isotopes is by gaseous diffusionof carbon monoxide. The gaseous diffusion process behaves like aneffustion process. Calculate the relative rates of effusion of12C16O, 12C17O, 12C18O. The problem asks for the relative rate of EFFUSION of threecompounds. The solution provided by Cramster takesthe DIFFUSION rate by taking the inverse of the combinedmolar masses. It then takes the square root of the ratio of 12C18Omolar mass divided by the molar mass of all three compounds. Howwould a student know to divide 1 by the molar mass then to compareall three compounds to the mass of the largest one?

Explanation / Answer

we knw that rate,r 1 / M Where M = Molar mass of the gas So relative rates of effusion are r 12C16O : r 12C17O : r 12C18O   =(1/ M 12C16O ) : (1/ M 12C17O ): (1/ M 12C18O )                                                                                              = ( 1/ 28) : (1/ 29 ) : (1/ 30)                                                                                              = 0.1889 : 0.1856 : 0.1825                                                                                               =  (0.1889/ 0.1825) : (0.1856/0.1825) : (0.1825/0.1825)                                                                                              = 1.035 : 1.017 : 1

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