Molar Mass of a Mixture: Calculating with nN2, nO2, and p=nRT/V

[pressurised]

Homework Statement

Homework Equations

M=m/n
p=nRT/V

The Attempt at a Solution

I am confused on getting the molar mass of the mixture, unless the answer is wrong.
For n_N2 I done 0.79*(3*10^-3) which gave me 2.37*10^-3kmol

For n_O2 I done the same but with 0.21 to get 6.3*10^-4kmol

The n_total of the mixture is 3.5*10^-3kmol

For each pressure I used p=nRT/V with R=8314 to get 174.594kPa for the total pressure, 31.427kPa for the partial pressure of oxygen, and 118.225kPa for nitrogen.
But when working out the partial pressure of CO₂ I got 24.942kPa. In the answers it states it is actually meant to be 29.94kPa but unless this is a mistake, I am not sure why it would be this.

Lastly for the Molar mass, I done (m_O2/n_total)+(m_N2/n_total)+(m_CO2/n_total) to find the total molar mass, and that gave me 14.455kg/kmol, when it should apparently be 31kg/kmol.

I done 1/3*(0.5*10^-3)(16) to find the mass of Carbon and used 2/3 for the mass of Oxygen in the CO₂.

 

[Borek]

31 g/mol is a correct answer.

Molar mass in this case is a weighted average of molar masses of individual gases (weighted by molar fractions).

 

[pressurised]

31 g/mol is a correct answer.

Molar mass in this case is a weighted average of molar masses of individual gases (weighted by molar fractions).

I can't seem to get anywhere close to 31g/mol. I'm not sure how to really do this.

I done (0.21*16)+(0.79+14)+(⅓*12*1/6)+(2/3*16*1/6) and got 16.86g/mol...

 

[Borek]

Start calculating molar fractions of all gases present in the mixture.

 

[pressurised]

Start calculating molar fractions of all gases present in the mixture.

I got 67.7% of the mixture is Nitrogen, 4.8% is Carbon and 27.5% is Oxygen?

 

[Borek]

I said "gases", not "elements".

 

[pressurised]

I said "gases", not "elements".

I'm completely lost with this. But to what you said, is it 85.7% dry air and 14.3% CO₂?

Do you happen to know any text or video that explains this clearly?

 

[pressurised]

I'm really confused as to why, M_mix=Σx_niM_i doesn't work with this?

 

[Borek]

I'm completely lost with this. But to what you said, is it 85.7% dry air and 14.3% CO₂?

Yes, but you have to split dry air further into oxygen and nitrogen (which are both gases and elements, but treat them just as gases).

Do you happen to know any text or video that explains this clearly?

Sorry, no.

I'm really confused as to why, M_mix=Σx_niM_i doesn't work with this?

Definitely works, but you should take care about meaning of the symbols involved.

What are substances denoted by i?

What is x_i?

What is M_i?

 

[pressurised]

Yes, but you have to split dry air further into oxygen and nitrogen (which are both gases and elements, but treat them just as gases).
Sorry, no.
Definitely works, but you should take care about meaning of the symbols involved.

What are substances denoted by i?

What is x_i?

What is M_i?

I should have used M_j and x_j, but the sum of M_i (is the molar mass of each component) multiplied by n_i (the mole fraction).

I actually split up the dry air into oxygen and nitrogen to carry out the calculation but it won't generate the correct answer for me?
So I take it I shouldn't split up the CO₂ into carbon and oxygen but treat it as a gas? If so that's when I got confused as to finding the molar mass of this compound... (sorry Chemistry is not my strong point)

 

[Borek]

I should have used Mj and xj, but the sum of Mi (is the molar mass of each component) multiplied by ni (the mole fraction).

Doesn't matter if you enumerate compounds with i, j or k, or whatever.

I think you are lost about what is a "component" here, especially as

finding the molar mass of this compound

the mixture is not a compound - it is a mixture of compounds. And actually it doesn't have a molar mass, as molar mass is a property of a compound - something with well defined molecular formula. Mixture doesn't have a formula, it contains separate compounds, each one having a separate formula.

However, when we are dealing with gases each mixture of them can be described by an equivalent molar mass. That is, it will behave (not in chemical reactions, but during physical changes - when being heated, compressed and so on) as a gas with such a molar mass. And this equivalent molar mass can be calculated using formula you have listed - but for calculations you need to take into account all mixed gases, in this case N₂, O₂ and CO₂.

Does it clarify things a bit?

 

[pressurised]

Doesn't matter if you enumerate compounds with i, j or k, or whatever.

I think you are lost about what is a "component" here, especially as
the mixture is not a compound - it is a mixture of compounds. And actually it doesn't have a molar mass, as molar mass is a property of a compound - something with well defined molecular formula. Mixture doesn't have a formula, it contains separate compounds, each one having a separate formula.

However, when we are dealing with gases each mixture of them can be described by an equivalent molar mass. That is, it will behave (not in chemical reactions, but during physical changes - when being heated, compressed and so on) as a gas with such a molar mass. And this equivalent molar mass can be calculated using formula you have listed - but for calculations you need to take into account all mixed gases, in this case N₂, O₂ and CO₂.

Does it clarify things a bit?

Thank you I understand now. By compound I meant I was struggling to find the molar mass of the CO₂ (compound) but it was far more straightforward than I initially thought.
Another part I initially messed up on was failing to realize the figures were not for the molecular pairs O and N travel in, I think that's what you were trying to hint to me when saying 'gases' and not 'elements'? :)

 

[Borek]

think that's what you were trying to hint to me when saying 'gases' and not 'elements'? :)

Not exactly, but it looks like there were several levels of misunderstanding and confusion - no sense to straighten that up now.