Ideal Gas Mixture Composition Calculation

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Discussion Overview

The discussion revolves around calculating the composition of an ideal gas mixture consisting of methane and ethane within a rigid cylinder. Participants are addressing specific homework problems related to estimating the average molar mass, mole fraction, and mass fraction of the gas mixture at given conditions of temperature and pressure.

Discussion Character

  • Homework-related
  • Mathematical reasoning
  • Technical explanation

Main Points Raised

  • One participant calculated the average molar mass of the gas mixture to be 25.85 kg/kmol but expressed difficulty in proceeding with subsequent parts of the problem.
  • Another participant suggested expressing the mass of the sample in terms of the number of moles of each gas.
  • One participant reported calculating the moles of ethane as 0.14 and moles of methane as 0.26 but questioned the correctness of their mole fraction calculation.
  • Several participants requested clarification on how to calculate the total number of moles of both gases using the ideal gas equation.
  • One participant emphasized that the total mass of the gases cannot equal the mass of each gas added together, indicating a misunderstanding in mass distribution among the gases.
  • Another participant mentioned the relationship between mass, molar mass, and the number of moles as a potential approach to the problem.

Areas of Agreement / Disagreement

Participants appear to disagree on the correct approach to calculating the mole fractions and the total number of moles of the gases. There is no consensus on how to proceed with the calculations, and multiple viewpoints are presented regarding the methodology.

Contextual Notes

Participants have not fully resolved the assumptions regarding the mass distribution of the gas mixture and the application of the ideal gas law. There are also unresolved mathematical steps related to the calculations of moles and fractions.

Who May Find This Useful

Students or individuals interested in gas laws, stoichiometry, and the calculations involved in gas mixtures may find this discussion relevant.

Oblivion77
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Homework Statement



A rigid cylinder of 1000cm cubed contains 4.168grams of an ideal gas mixture. The gas mixture consists of methane and ethane at a temperature of 100C and a pressure of 500kPa

a) Estimate the average molar mass of the mixure
b) Calculate the composition of the mixture on a mole fraction basis
c) Express the mixture composition on a mass fraction basis

Homework Equations



PV=nRT

The Attempt at a Solution



I calculated part a) already and found that to be 25.85kg/kmol. I am stuck on part b and c.
Thanks for any help.
 
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Express mass of the sample in terms of numbers of moles of each gas.
 
Borek said:
Express mass of the sample in terms of numbers of moles of each gas.
Ok

I got mols of ethane to be 0.14 and mols of methane to be 0.26. Now what? I tried doing
0.14 / (0.14 + 0.26) to get the fraction of ethane but it is wrong.
 
Show how you calculated total number of moles of both gases.
 
Borek said:
Show how you calculated total number of moles of both gases.

For methane: CH4 molar mass is 16.04g/mol. We have 4.168g so M= m/n, n = m/M therefore
n = 4.168 / 16.04 = 0.259 ~ 0.26mols of methane

same thing for ethane.
 
No. You can't have 4.168g of methane plus 4.168g of ethane and 4.168g in total.

Use ideal gas equation to calculate total numebr of moles of gases.

Do you know Avogadro's hypothesis?
 
Borek said:
No. You can't have 4.168g of methane plus 4.168g of ethane and 4.168g in total.

Use ideal gas equation to calculate total numebr of moles of gases.

Do you know Avogadro's hypothesis?

Ok, so how would I calculate how much of each compound by just knowing the molar mass?

V/n = constant?
 
Mass is molar mass times number of moles.
 

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