Ideal gas - percentage of fraction of molecules

In summary, the conversation is about a problem involving the Maxwell-Boltzmann distribution and the use of equations and integrals to solve it. The person asking for help is unsure about how to use the equation given in their textbook and is seeking clarification on the limits and values to use. They receive guidance from the expert and proceed with their calculations.
  • #1
Jahnavi
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Homework Statement


gas_percentage.jpg


Homework Equations

The Attempt at a Solution



Honestly speaking , I have absolutely no idea about this problem .This doesn't happen often .In the KTG chapter , only definition and formula of Average , RMS and Most probable speeds is given .

This question is for an entrance exam which requires minimum application of calculus . So I am guessing there is a formula for this problem which I am unaware of .

Please help me solve this problem in a simple way .
 

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  • #2
Does your text not cover the Maxwell-Boltzmann distribution? Likely the Average , RMS and Most probable speed were derived using it.
 
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  • #3
Jahnavi said:
Honestly speaking , I have absolutely no idea about this problem
You should know this does not count as an attempt -- so we're not allowed to help :rolleyes: .

Could it be you don't know what distribution you need for this ? i doubt that ...
 
  • #4
Thanks @gneill for replying .

gneill said:
Does your text not cover the Maxwell-Boltzmann distribution? Likely the Average , RMS and Most probable speed were derived using it.

Please see the attached image from the textbook .As you can see nothing is derived .Only definitions and formula are given .
 

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  • #5
Jahnavi said:
Please see the attached image from the textbook .As you can see nothing is derived .Only definitions and formula are given .
What about equation 24.13 at the bottom of the page?
 
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  • #6
gneill said:
What about equation 24.13 at the bottom of the page?

OK . But I don't understand how to use this equation .

Do I need to find dN/N ? Or do I need to integrate this equation ? What will be the limits of N and v ?
 
  • #7
Jahnavi said:
OK . But I don't understand how to use this equation .

Do I need to find dN/N ? Or do I need to integrate this equation ? What will be the limits of N and v ?

Yes, dN/N would be the fraction of molecules with speeds between v and v+dv. Since the range of speeds given is pretty narrow, you should be able to get a pretty good approximation using dv ≅ Δv . Integration would give you an exact result, but the integral might be a bit tricky.
 
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  • #8
Should I go ahead with v = 323 and ∆v = 3 or v = 324 and ∆v = 2 ?
 
  • #9
Jahnavi said:
Should I go ahead with v = 323 and ∆v = 3 or v = 324 and ∆v = 2 ?
The latter.
 
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  • #10
Thank you gneill !
 

1. What is an ideal gas?

An ideal gas is a theoretical gas composed of molecules that have no volume and do not interact with each other. It follows the kinetic theory of gases, which assumes that the molecules are in constant, random motion.

2. What is the percentage of ideal gas in a mixture of gases?

The percentage of ideal gas in a mixture of gases is determined by dividing the number of moles of the ideal gas by the total number of moles in the mixture. This will give you the mole fraction, which can then be converted to a percentage.

3. How is the fraction of molecules calculated in an ideal gas?

The fraction of molecules in an ideal gas can be calculated by using the ideal gas law, which states that the number of moles of a gas is directly proportional to its pressure, volume, and temperature. By knowing the values of these variables, the fraction of molecules can be determined.

4. Can the fraction of molecules in an ideal gas change?

Yes, the fraction of molecules in an ideal gas can change depending on the conditions of the gas. Factors such as temperature, pressure, and volume can affect the number of molecules present in a given volume of the gas.

5. How does the fraction of molecules in an ideal gas affect its properties?

The fraction of molecules in an ideal gas does not directly affect its properties. However, it is used to calculate other important properties such as pressure, volume, and temperature through the ideal gas law. It can also be used to determine the behavior of the gas under different conditions.

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