Ratio of atomic masses of two ideal gases

AI Thread Summary
The discussion centers on the ratio of atomic masses of two ideal gases, concluding with a ratio of 1:10. Participants clarify that while the molar mass ratio can be derived, the wording of the problem may be misleading. There is a connection made between internal energy and molar mass, suggesting that internal energy is proportional to mass. Additionally, Avogadro's number is defined as the number of molecules per mole, with suggestions for clearer notation. The conversation highlights the importance of precise language in scientific problems and the relationship between atomic and molar mass.
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Homework Statement
Please see below
Relevant Equations
Please see below
For part(b)
1680232199273.png

The solution is, ##1:10##, however, is the wording correct? I don't see how to find the ratio of atomic mass, however, I can solve for the ratio of the molar mass.

##n_A = n_B## from part(a) by setting the internal energy equation for each ideal gas equal
##\frac{M_A}{m_A} = \frac{M_B}{m_B}##
##1000M_A = 10000M_B##
##M_A = 10M_B##

Is the reason they said that is because ##u ∝ M##. Is there a equation that proves that?

Many thanks!
 
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What is the definition of Avagadro's number?
 
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hutchphd said:
What is the definition of Avagadro's number?
Thank you for your reply @hutchphd!

It is the number of molecules per 1 mol. So has units ##\frac{1}{mol}##

Many thanks!
 
I think there is also a spelling error in part(b) it should be ratio not ration
 
hutchphd said:
What is the definition of Avagadro's number?
Do you please know whether my answer was correct @hutchphd ?

Many thanks!
 
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It might be better to write it as ##\frac {number~ of~ molecules}{mole}## in this circumstance
 
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hutchphd said:
It might be better to write it as ##\frac {number~ of~ molecules}{mole}## in this circumstance
Thank you for your reply @hutchphd! I agree that is a much better way to write it. However, is the wording to this problem in post #1 wrong? Or dose Avagadro's number relate to this in some way.

Many thanks!
 
I found from dimensional analysis that the I can get correct units for a mass of one atom (atomic mass):## \frac{M_A}{N_A} = 10\frac{M_B}{N_A} ##
## u_A = 10u_B##
 
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