Chapter 10.7, Problem 10.12CYU

### 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

# A sample of methane. CH4, is found to effuse through a porous barrier in 1.50 minutes. Under the same conditions, an equal number of molecules of an unknown gas effuses through the barrier in 4.73 minutes. What is the molar mass of the unknown gas?

Interpretation Introduction

Interpretation:

Molar mass of the unknown gas has to be calculated from the given data.

Concept Introduction:

Effusion: Movement of gas through tiny pore in a container into another having low pressure.

Comparing rate of effusion of two gases:

Rateofeffusionofgas1Rateofeffusionofgas2=molarmassofgas2molarmassofgas1

The amount of gas moving from one place to another and square root of its molar mass are inversely proportional.

Explanation

The molar mass of the unknown gas using the relationship between rate of effusion and molar mass.

Given:

â€‚Â Rateâ€‰ofâ€‰effusionâ€‰ofâ€‰CH4â€‰â€‰â€‰â€‰â€‰â€‰â€‰â€‰â€‰â€‰â€‰â€‰â€‰â€‰â€‰â€‰â€‰=â€‰â€‰1.50â€‰minRateâ€‰ofâ€‰effusionâ€‰ofâ€‰unknownâ€‰â€‰â€‰â€‰â€‰â€‰â€‰â€‰=â€‰4.73â€‰minMolarâ€‰massâ€‰ofâ€‰CH4â€‰â€‰â€‰â€‰â€‰â€‰â€‰â€‰â€‰â€‰â€‰â€‰â€‰â€‰â€‰â€‰â€‰â€‰â€‰â€‰â€‰â€‰â€‰â€‰â€‰=â€‰16g/mol

â€‚Â Rateâ€‰ofâ€‰effusionâ€‰ofâ€‰gasâ€‰1â€‰Rateâ€‰ofâ€‰effusionâ€‰ofâ€‰gasâ€‰2â€‰â€‰â€‰â€‰=â€‰molarâ€‰massâ€‰ofâ€‰gasâ€‰2molarâ€‰massâ€‰ofâ€‰gasâ€‰1

â€‚Â â€‰Rateâ€‰ofâ€‰effusionâ€‰ofâ€‰CH4Rateâ€‰ofâ€‰effusionâ€‰ofâ€‰unknownâ€‰â€‰â€‰â€‰=â€‰molarâ€‰massâ€‰ofâ€‰unknownmolarÂ massÂ ofÂ CH4

â€‚Â nÂ molecules1.50â€‰minnâ€‰molecules4

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