Finding RMS Speed of Gas Atoms: Ideal Gas

In summary, the ideal gas has a density of 2.4 kgm–3 at a pressure of 2.0 × 105 Pa and a temperature of 300 K. To find the root mean square speed of the gas atoms, the formula P= mnvrms2/3V can be used, where N is the total number of atoms, m is the molar mass, and V is the volume. However, in this problem, N is not given, so it can be omitted and the formula can be simplified to P= mv2/3V. This is because N/V represents the number of particles per unit of volume, which is equivalent to the density (mN/V).
  • #1
AllenHe
74
0

Homework Statement


The ideal gas has a density of 2.4 kgm–3 at a pressure of 2.0 × 105 Pa and a
temperature of 300 K.Find the root mean square speed of the gas atoms.


Homework Equations



p=(1/3)*(Nm/V)*v(squared)


The Attempt at a Solution


I tried to make v(squared) the subject, but N(the number of atoms) is not given, and when I looked at the answer, it made v(squared) the subject, and omitted N. I don's understand why do they have to omit N, is it because we are suppose to find the speed for one atom?
Sorry for my bad English.
 
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  • #2
AllenHe said:

Homework Statement


The ideal gas has a density of 2.4 kgm–3 at a pressure of 2.0 × 105 Pa and a
temperature of 300 K.Find the root mean square speed of the gas atoms.


Homework Equations



p=(1/3)*(Nm/V)*v(squared)


The Attempt at a Solution


I tried to make v(squared) the subject, but N(the number of atoms) is not given, and when I looked at the answer, it made v(squared) the subject, and omitted N. I don's understand why do they have to omit N, is it because we are suppose to find the speed for one atom?
Sorry for my bad English.

Well, N/V is the number of particles per unit of volume. If you multiply this by m, the mass per particle, you get the mass per unit volume. What's another name for that?
 
  • #3
Thanks

cepheid said:
Well, N/V is the number of particles per unit of volume. If you multiply this by m, the mass per particle, you get the mass per unit volume. What's another name for that?

Oh, I get it, so you mean the density is mN/v, right?
 
  • #4
AllenHe said:
Oh, I get it, so you mean the density is mN/v, right?

Yes, he means that in,

P= mnvrms2/3V

Density is mn/V

m=molar mass
n=number of moles

But you have written N=avogadro's number
m=mass of one molecule ?

Are you giving this formula for 1 mole of gas ?
 
  • #5
AllenHe said:
Oh, I get it, so you mean the density is mN/v, right?

Yes, that is exactly what I meant :)
 
  • #6
sankalpmittal said:
Yes, he means that in,

P= mnvrms2/3V

Density is mn/V

m=molar mass
n=number of moles

But you have written N=avogadro's number
m=mass of one molecule ?

Are you giving this formula for 1 mole of gas ?

The OP explicitly stated that N was the total number of atoms. So this problem isn't doing anything with moles.
 

1. What is the ideal gas law and how is it related to the RMS speed of gas atoms?

The ideal gas law is a fundamental equation that describes the behavior of an ideal gas. It states that the product of pressure and volume is directly proportional to the product of the number of moles of gas and its temperature. This law is related to the RMS speed of gas atoms because it helps us understand the relationship between the macroscopic properties of a gas (pressure, volume, and temperature) and the microscopic properties (average speed of gas atoms).

2. Why is it important to calculate the RMS speed of gas atoms in ideal gas?

Calculating the RMS speed of gas atoms in an ideal gas is important because it helps us understand the kinetic energy of the gas particles. This information is essential in many fields of science, such as thermodynamics, chemistry, and physics, as it allows us to predict and explain the behavior of gases under different conditions.

3. How do you calculate the RMS speed of gas atoms in an ideal gas?

The RMS speed of gas atoms in an ideal gas can be calculated using the root mean square formula, which is the square root of the average of the squared speeds of the gas particles. This can be expressed as RMS speed = √(3RT/M), where R is the gas constant, T is the temperature, and M is the molar mass of the gas.

4. What factors affect the RMS speed of gas atoms in an ideal gas?

The RMS speed of gas atoms in an ideal gas is affected by temperature, pressure, and molar mass of the gas. As temperature and pressure increase, the RMS speed of gas atoms also increases. On the other hand, as the molar mass of the gas increases, the RMS speed decreases.

5. Can the RMS speed of gas atoms in an ideal gas be greater than the speed of light?

No, the RMS speed of gas atoms in an ideal gas cannot be greater than the speed of light. According to the theory of relativity, the speed of light is the maximum speed at which all energy, matter, and information in the universe can travel. The RMS speed of gas atoms is calculated using classical mechanics, which does not account for relativistic effects and is therefore limited to speeds below the speed of light.

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