calculating atmospheric surface density

[Calsir]

Thanks for the backchecking. So the overall formula is allright now, that's good. I didn't know that there are different gas-constants for each gas... ah well. ANOTHER update on the chem-table...

Yep, it's due to the fact that different pure gases have different molar masses;

R_mg = R / W

where

R is the perfect molar gas constant [R=8.3145 J / (mol K)]

W is the molar mass of the gas, or its atomic weight in grams (for instance 16e-3 kg/mol for Oxygen (O_2) or 2e-3 kg/mol for Hydrogen (H_2))

R_mg is in J / (kg K). (beware of the conversion ratio g/kg = 1e-3 that I implicitly used)

For any gas mixture, its gas constant can be written as

R_mg = R * sum_i (Y_i / W_i)

where Y_i is the mass fraction (concentration in mass) of each species "i". sum_i denotes the summation operator.

 

[jedidia]

Thanks a lot for the reply, I've been gone for the better part of two weeks, so I couldn't take a look at it earlier.

I am a bit confused: You say that the specific gas constant is the perfect molar gas constant divided by the molar mass.

However, this division seems allready implied in the formula I'm using:

(M is the molar mass), so shouldn't this formula work for any gas?

 

[ex-orbinaut]

I am a bit confused: You say that the specific gas constant is the perfect molar gas constant divided by the molar mass.

However, this division seems allready implied in the formula I'm using:

Yes, you are right. It is. Note that in the testing of the formula, I just used the "precooked" gas constant for Earth's dry air. It is technically the same forumla...

 

[jedidia]

Great. So I'm all set. thanks everyone.

 

[Calsir]

I am a bit confused: You say that the specific gas constant is the perfect molar gas constant divided by the molar mass.

However, this division seems allready implied in the formula I'm using:

(M is the molar mass), so shouldn't this formula work for any gas?

Yes, as it has been said before, it is correct. The issue is about the value of the molar mass M, which has to take into account that you are dealing with a gas mix. I was just using a different terminology, and I apologize for that. In your equation you can use this relation:

1/M = sum_i (Y_i/M_i)

where M is the molar mass of the gas mix, which is determined by the mass fractions Y_i and the molar masses M_i for each species i.

Confusion may also arise since the letter R is used for both the perfect gas constant (given in J/(mol K)) and the specific gas constant (given in J/(kg K)).

 

[jedidia]

where M is the molar mass of the gas mix, which is determined by the mass fractions Y_i and the molar masses M_i for each species i.

You're talking a bit too mathematical here for me to follow...

I calculate the molar mass by adding the molar mass of each gas times the percentage of its occurence in the atmosphere. Is that what you're saying above?

 

[Calsir]

You're talking a bit too mathematical here for me to follow...

I calculate the molar mass by adding the molar mass of each gas times the percentage of its occurence in the atmosphere. Is that what you're saying above?

Exactly. Sorry about the confusion. One more thing, the percentage of its occurrence (concentration) must be in mass, not in volume. One question, were the equations that I wrote clear or was the notation ("sum_i", etc) that confused you?

EDIT: I forgot that, for ideal gases, the volume concentration and the mass concentration are the same, duh.

 

[jedidia]

were the equations that I wrote clear or was the notation ("sum_i", etc) that confused you?

I could make sense of them, which is why I had the impression that the operation was allready included in my formula.

EDIT: I forgot that, for ideal gases, the volume concentration and the mass concentration are the same, duh.

Hmmm... I think that should be exact enough then for my practical purposes. Thanks for your input!