Kinetic theory of gases theory question

In summary, the discussion focuses on the comparison between the average speed and kinetic energy of an oxygen molecule and a hydrogen molecule in a mixture at room temperature. It is determined that the oxygen molecule has a smaller average speed due to its heavier mass, resulting in a lower average velocity. However, both molecules have the same average internal energy, which is kinetic energy. The concept of "average" is mentioned, but its significance is minimal in this case due to the significant difference in mass between the two molecules.
  • #1
Mandavi
21
0

Homework Statement


Consider a mixture of oxygen and hydrogen kept at room temperature.As compared to a hydrogen molecule an oxygen molecule hits the wall-
(a) with greater average speed
(b)with smaller average speed
(c)with greater average kinetic energy
(d)with smaller average kinetic energy

Homework Equations


We have to consider both the gases as ideal to get the answer.
Now, for a mixture vrms=(3RT/M)^1/2
where M is average mass of the gases in the mixture and is
M=(n1M1+n2M2)/n1+n2
n denote the number of moles of gases and M their respective molecular masses.
Average kinetic energy for a gas molecule=3/2kT
k=boltzmann constant
T=absolute temperature

The Attempt at a Solution


The answer given is (b)with smaller average speed.Someone please explain the reason for this.
 
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  • #2
If I understood it right :
both molecules have the same average internal energy, which is kinetic energy
now,the oxygen molecule is heavier than the hydrogen molecule , thus the velocity of the oxygen molecule should be smaller.
mv^2/2 = E
V=(3RT/M)^1/2 when the mass is higher . velocity is lower...
 
  • #3
Dweirdo said:
If I understood it right :
both molecules have the same average internal energy, which is kinetic energy
now,the oxygen molecule is heavier than the hydrogen molecule , thus the velocity of the oxygen molecule should be smaller.
mv^2/2 = E
V=(3RT/M)^1/2 when the mass is higher . velocity is lower...

Right,but doesn't the word "average" has any significance here?
 
  • #4
I would rather say Energy per molecule.
the "Average" thing is here because this measures the average velocity ,but it has (if it has) a little effect on the answer. the difference between 2 different types of molecules in this case is big, so you can drop that word.
 
  • #5
Dweirdo said:
I would rather say Energy per molecule.
the "Average" thing is here because this measures the average velocity ,but it has (if it has) a little effect on the answer. the difference between 2 different types of molecules in this case is big, so you can drop that word.

Okay!Thank you very much!:smile:
 

1. What is the Kinetic Theory of Gases?

The Kinetic Theory of Gases is a scientific theory that explains the behavior of gases in terms of the motion of their individual particles. It states that gas particles are in constant random motion and that their kinetic energy is directly proportional to their temperature.

2. What are the main assumptions of the Kinetic Theory of Gases?

The main assumptions of the Kinetic Theory of Gases are that gas particles are in constant, random motion; that the particles are very small compared to the distance between them; that there is no force of attraction or repulsion between particles; and that collisions between particles and with the walls of the container are perfectly elastic.

3. How does the Kinetic Theory of Gases explain gas pressure?

The Kinetic Theory of Gases explains gas pressure as the result of the constant collisions between gas particles and the walls of the container. As the particles move around, they exert a force on the walls, which creates pressure.

4. What is the relationship between temperature and kinetic energy in the Kinetic Theory of Gases?

According to the Kinetic Theory of Gases, the temperature of a gas is directly proportional to the average kinetic energy of its particles. This means that as the temperature increases, the particles move faster and have more kinetic energy.

5. How does the Kinetic Theory of Gases explain the properties of gases?

The Kinetic Theory of Gases explains the properties of gases such as their compressibility, expansion, and diffusion, by considering the behavior of individual gas particles. For example, the theory explains that gases can be easily compressed because the particles are far apart and can be pushed closer together. It also explains how gases can fill the entire volume of a container because the particles are constantly moving and spreading out to fill the available space.

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