Raoult's Law Problem: Estimate Mole Fractions at 65K

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Discussion Overview

The discussion revolves around a homework problem involving the estimation of mole fractions of nitrogen (N2), oxygen (O2), and argon (Ar) in both liquid and gas phases when 1 mole of air is cooled from 300 K to 65 K at a total pressure of 4 atm. Participants explore the application of Raoult's Law and the Clausius-Clapeyron equation in this context.

Discussion Character

  • Homework-related
  • Technical explanation
  • Exploratory

Main Points Raised

  • One participant calculates the initial vapor pressures of N2, O2, and Ar based on their mole fractions and atmospheric pressure.
  • Another participant emphasizes the need to clarify the initial total pressure, which is stated to be 4 atm.
  • There are inquiries about the Antoine equations for the three gases, suggesting their relevance for solving the problem.
  • Some participants express uncertainty about the appropriate enthalpy of vaporization to use with the Clausius-Clapeyron equation.
  • One participant suggests that using the Antoine equation parameters could simplify the problem without needing to integrate the Clausius-Clapeyron equation.
  • A later reply proposes a collaborative approach to set up the necessary equations, highlighting the challenge of determining the fractional split of liquid and vapor and the final pressure.

Areas of Agreement / Disagreement

Participants generally agree on the need for specific equations and parameters to solve the problem, but there is no consensus on the best approach or the specific values to use, indicating multiple competing views and uncertainty in the methodology.

Contextual Notes

Participants mention the need for boiling points and enthalpies of vaporization, but these values are not provided. The discussion also reflects uncertainty regarding the application of the Clausius-Clapeyron equation and the use of Antoine equations.

Samuel1321
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Homework Statement


Consider air to be made up of only N2 (78 mole %), O2 (21%) and Ar (1%)
Estimate the mole fractions of each in both the liquid and gas phases if 1 mole of air at 300 K and 4 atm. total pressure were cooled to 65 K in the same volume

Homework Equations


Raoult's law Pi = Pi* xi

The Attempt at a Solution



So I know that the atmospheric pressure is 760 torr. So before they are cooled

vapor pressure of N2 would be (0.78)(760) torr

Vapor Pressure of O2 would be (0.21)(760) torr

Vapor Pressure of Ar would be (0.01)(760) Torr

I'm not sure how should I proceed. Maybe I should use the Clausius Clapeyron equation to find the final pressure after cooling it down? But what delta H value should I use?
 
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Look at the question again; what is the initial total pressure?
You need to know the boiling points and enthalpies of vaporisation of the gases, but these should be easy to look up.
 
What are the Antoine equations for these three substances?
 
mjc123 said:
Look at the question again; what is the initial total pressure?
You need to know the boiling points and enthalpies of vaporisation of the gases, but these should be easy to look up.

The initial total pressure is 4 atm.

Should I just find the final total pressure first using the clasius clapeyron equation? The problem is if I use the CC equation, which enthalpy of vaporization should I use?
 
Chestermiller said:
What are the Antoine equations for these three substances?

I have not learned that equation yet, is there another way to solve this problem?
 
Samuel1321 said:
I have not learned that equation yet, is there another way to solve this problem?
The Antoine equation is an 3-parameter very accurate fit to the integrated Clausius-Clapeyron equation. The parameters are available for common substances like oxygen, nitrogen, and argon, so you don't have to integrate the CC equation to describe the VLE behavior of the pure species. Google it, and get the Antoine equation parameters for your 3 species. This way, you don't need to know the boiling point, and the heat capacities of the vapor and liquid as functions of temperature, and you don't need to integrate the CC equation.

Of course, to solve your problem, the VLE behavior of the pure species is only the first step. Given the overall mole fractions of the 3 species, you need to determine the split of liquid and vapor, and the mole fractions of the 3 species in the liquid and in the vapor.
 
@Samuel1321 Do you have any idea how to go about setting up the equations for this problem? It is pretty challenging. There will be two main unknowns: the fractional split of liquid and vapor and the final pressure. I can lead you through how to set up the two key equations, if you are willing to work with me. Any interest?
 

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