What Is the Change in Entropy When Mixing N2 and O2 Gases?

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Discussion Overview

The discussion revolves around the change in entropy when mixing nitrogen (N2) and oxygen (O2) gases in a thermodynamic context. Participants explore the relevant equations and concepts related to entropy change during isothermal mixing, including the application of specific formulas and the underlying principles of ideal gases.

Discussion Character

  • Homework-related
  • Technical explanation
  • Conceptual clarification
  • Debate/contested

Main Points Raised

  • One participant presents the problem statement and relevant equations for calculating entropy change, expressing confusion about the second equation involving mole fractions.
  • Another participant identifies the universal gas constant (R) and questions the meaning of N in the context of the equations.
  • Discussion includes a reference to the entropy formula for ideal gases, relating it to multiplicity and suggesting that the entropy change can be derived from the properties of individual species in a mixture.
  • Participants inquire about the proof of the entropy change equation for mixing ideal gases and whether it involves complex derivations.
  • There is a mention of the need for a better understanding of entropy before deriving the ideal gas entropy of mixing, with one participant offering to share a write-up on thermodynamic laws.

Areas of Agreement / Disagreement

Participants express varying levels of understanding regarding the equations and concepts of entropy. There is no consensus on the derivation of the entropy change equation, and some participants seek clarification on foundational concepts.

Contextual Notes

Participants reference different aspects of thermodynamics, including the properties of ideal gases and the implications of mixing gases at constant pressure. The discussion highlights the complexity of entropy and the need for a solid grasp of thermodynamic principles to engage with the topic effectively.

mooncrater
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Homework Statement


The question is says:
Two vessels divided by a partition contain 1 mol of N2 and 2 mol of O2 gas. If the partition is removed and gases ate mixed isothermally, then find the change in entropy due to mixing assuming initial and final pressure are same .

Homework Equations


ΔS=qrev/T [the one I know]
ΔSsys=-RΣniln xi
Where ni = number of moles of gas.
xi= mole fraction of gas.[ the foreigner equation]

The Attempt at a Solution


As written here in the relevant equations part, the second equation is the one which is new to me. I don't know how it works, what it does and from where it came from. It looks like boltzmann's entropy formula but I don't think that both of them are same. The question can be easily solved by this equation, but this equation is the one creating problem.
 
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What is R?
 
Also, this at least looks related to the formula for change in entropy of an ideal gas.

That is, taking the entropy of each which I believe, in general, is ##S= Nk[\log(Ω)]## where Ω is multiplicity. So taking the difference of two entropies gives you a ration of multiplicities inside the log. I don't know what formulas you have for multiplicity, but it seems like this may be where your equation comes from. Though, someone else can likely explain it better, or correct me.
 
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R is the universal gas constant.
What is N here?
 
mooncrater said:
R is the universal gas constant.
What is N here?
Number of atoms.
 
Smith and van Ness, Introduction to Chemical Engineering Thermodynamics, page 300:

A ideal gas is a model gas comprised of imaginary molecules of zero volume that do not interact. Each chemical species in an ideal gas mixture therefore has its own private properties, uninfluenced by the presence of other species. This is the basis of Gibb's theorem:

A total thermodynamic property (U, H, S, A, G) of an ideal gas mixture is the sum of the total properties of the individual species, each evaluated at the mixture temperature but at is own partial pressure.

Chet
 
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ΔSsys=-RΣniln xi
Where ni = number of moles of gas.
xi= mole fraction of gas.

What would be the proof for this?
Is it a complicated one involving partial derivatives?
 
Raghav Gupta said:
ΔSsys=-RΣniln xi
Where ni = number of moles of gas.
xi= mole fraction of gas.

What would be the proof for this?
Is it a complicated one involving partial derivatives?
No. From the information I gave in my previous post, you should be able to derive the equation for the entropy change for mixing ideal gases, going from the pure components at pressure P to the mixture at the same pressure P.

Chet
 
Chestermiller said:
A total thermodynamic property (U, H, S, A, G) of an ideal gas mixture is the sum of the total properties of the individual species, each evaluated at the mixture temperature but at is own partial pressure.

Chet
So S = V + P + T ?
ΔS= ΔV + ΔP + ΔT ?
 
  • #10
Raghav Gupta said:
So S = V + P + T ?
ΔS= ΔV + ΔP + ΔT ?
Do you know how to determine the change in entropy of a pure species ideal gas if its pressure changes at constant temperature?
 
  • #11
No,
Actually entropy is to me degree of randomness and also have formula,
ΔS = Δq/T
 
  • #12
Raghav Gupta said:
No,
Actually entropy is to me degree of randomness and also have formula,
ΔS = Δq/T
OK. Before you can do the derivation of the ideal gas entropy of mixing, you need to develop some background understanding of entropy. Did I send you my write up on the first and second laws of thermo?

Chet
 
  • #13
No, you till now have not send it. Why that question?
I think you may be thinking that we had a discussion in some other thread about it?
Or are you asking can I send you the write - up?
 
  • #14
Raghav Gupta said:
No, you till now have not send it. Why that question?
I think you may be thinking that we had a discussion in some other thread about it?
Or are you asking can I send you the write - up?
No. I'll send you a link to it. It is for students who are struggling with some of the concepts because the concepts are presented so poorly in textbooks.
 
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