How Do You Calculate Molar Masses from Diffusion Rates and Density?

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SUMMARY

The discussion focuses on calculating the molar masses of two gases in a mixture, given their diffusion rates and the mixture's density. The mixture has a density of 1.47 g/L at 1.00 atm and 298 K, with one gas diffusing 1.25 times faster than the other. The relationship derived is 1.5625 = M_B / M_A, where M_B and M_A are the molar masses of gases B and A, respectively. The ideal gas law is essential for further calculations, specifically in determining the molar masses from the density and diffusion rates.

PREREQUISITES
  • Understanding of Graham's Law of Effusion
  • Familiarity with the Ideal Gas Law (PV = nRT)
  • Knowledge of gas density calculations
  • Basic principles of molar mass determination
NEXT STEPS
  • Study Graham's Law of Effusion for gas diffusion calculations
  • Learn how to apply the Ideal Gas Law to gas mixtures
  • Research methods for calculating molar mass from density
  • Explore the relationship between diffusion rates and molar mass
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Chemistry students, particularly those studying gas laws and molar mass calculations, as well as educators seeking to clarify concepts related to gas mixtures and diffusion.

Canuck156
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Hi, this is the question I'm having trouble with:

A gas mixture is known to contain equal numbers of moles of two gases. The mixture has a density of 1.47g/L at 1.00 atm and 298K. In a diffusion experiment, one of the gases was found to diffuse 1.25 times faster than the other under the same conditions. What are the respective molar mases of the two gases?

I've found that 1.25=\sqrt{\frac{M_B}{M_A}} Therefore 1.5625=\frac{M_B}{M_A}, where M_B is the molar mass of gas B. However, from there I have no idea where to go next. I think I'm supposed to use the ideal gas law, but I'm not sure how to apply it when there's a mixture of gases. Any help is appreciated! Thanks!
 
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Nobody knows how to do this? Come on, surely someone must be able to help? :smile:
 
does the ideal gas law depend on
what those 10^23 objects are?
(an ideal gas = atoms don't interact)

so find (n_moles/V)(m/mole).
 
Oh... OK, I get it now. Thanks lightgrav. I didn't realize that that was one of the properties of an ideal gas... Maybe I shouldn't be doing University Chem without having done High School Chem first... :rolleyes:
 

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