Ratio of atomic masses of two ideal gases

[ChiralSuperfields]

Homework Statement

Please see below

Relevant Equations

Please see below

For part(b)

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!

 

[hutchphd]

What is the definition of Avagadro's number?

 

[ChiralSuperfields]

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!

 

[ChiralSuperfields]

I think there is also a spelling error in part(b) it should be ratio not ration

 

[ChiralSuperfields]

What is the definition of Avagadro's number?

Do you please know whether my answer was correct @hutchphd ?

Many thanks!

 

[hutchphd]

It might be better to write it as $\frac {number~ of~ molecules}{mole}$ in this circumstance

 

[ChiralSuperfields]

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!

 

[ChiralSuperfields]

I found from dimensional analysis that the I can get correct units for a mass of one atom (atomic mass):


$\frac{M_A}{N_A} = 10\frac{M_B}{N_A}$
$u_A = 10u_B$