Ideal Gas Mixture Composition Calculation

In summary, we have a problem involving a rigid cylinder containing an ideal gas mixture of methane and ethane at a temperature of 100C and a pressure of 500kPa. Part a) asks us to estimate the average molar mass of the mixture, which was found to be 25.85kg/kmol. Parts b) and c) ask us to calculate the composition of the mixture on a mole fraction and mass fraction basis, respectively. To do this, we first need to calculate the total number of moles of both gases using the ideal gas equation. Then, we can use the molar mass of each compound to determine the number of moles of each in the mixture. Finally, we can express the composition of
  • #1
Oblivion77
113
0

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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  • #2
Express mass of the sample in terms of numbers of moles of each gas.
 
  • #3
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.
 
  • #4
Show how you calculated total number of moles of both gases.
 
  • #5
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.
 
  • #6
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?
 
  • #7
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?
 
  • #8
Mass is molar mass times number of moles.
 

Related to Ideal Gas Mixture Composition Calculation

1. What is the Ideal Gas Law?

The Ideal Gas Law is a mathematical equation that describes the relationship between the pressure, volume, temperature, and number of moles of an ideal gas. It is expressed as PV = nRT, where P is pressure, V is volume, n is the number of moles, R is the universal gas constant, and T is temperature in Kelvin.

2. What is an ideal gas?

An ideal gas is a theoretical gas that follows the Kinetic Molecular Theory, which assumes that the gas particles have no volume and do not interact with each other. It also assumes that the gas particles are in constant, random motion.

3. How does the Ideal Gas Law relate to composition?

The Ideal Gas Law does not directly relate to composition. However, the composition of a gas can affect its properties such as molar mass and the specific gas constant, which are both used in the Ideal Gas Law equation.

4. What are the units of the Ideal Gas Law?

The units of the Ideal Gas Law depend on the units used for pressure, volume, temperature, and the gas constant. However, the most commonly used units are atmospheres (for pressure), liters (for volume), Kelvin (for temperature), and joules per mole-kelvin (for the gas constant).

5. How is the Ideal Gas Law used in real-world applications?

The Ideal Gas Law is used in various industries, such as chemistry, physics, and engineering, to calculate the behavior of gases. It is also used in everyday applications, such as in gas laws, weather predictions, and gas storage and transportation. It is a fundamental law in understanding the behavior of gases in different conditions.

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