# gasses pressure/kinetic energy

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#### orangetea

##### Full Member
7+ Year Member
I just wanted to make sure I have this concept correct.

So under the same pressure(identical conditions) all gases have the same kinetic energy right?
So does that mean that they have the same momentum?(a heavier gas would travel slower and vice versa for a lighter gas?

But then I am confused about pressure.. does that mean they exert the same pressure on the walls? How can that be when one gas might be heavier than the other?

Thanks!

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The thing that determines their KE is temperature.

The below is a Pressure Volume graph. Each line represents different isotherm. Everywhere along the blue line is at one temperature. Everything along the black line is at another temperature. And everything at the red line is at a third temperature. Holding pressure constant, you can achieve all of these lines by varying volume.

The thing that determines their KE is temperature.

And that's just the average KE of the particles. They don't all have the same speed. I think they have a Boltzman distribution but I could be wrong.

Okay I think I figured it out.

So temperature determines KE and yes @sillyjoe you are right about it being average!
The momentum is the same but the impulse collision will be different (under identical conditions) due to the different masses of the gases.
and P=F/A was confusing me but assuming identical conditions the Force they exert is different (due to different masses) and it would be on the same area. So that's why pressure is the same for heavier/lighter gases under the same conditions.

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And that's just the average KE of the particles. They don't all have the same speed. I think they have a Boltzman distribution but I could be wrong.

Correct. The velocity of the gas is inversely proportional to the square of the mass. If you increase the mass 4x, the velocity is cut in half.

The thing that determines their KE is temperature.

The below is a Pressure Volume graph. Each line represents different isotherm. Everywhere along the blue line is at one temperature. Everything along the black line is at another temperature. And everything at the red line is at a third temperature. Holding pressure constant, you can achieve all of these lines by varying volume.

I was just confused about momentum, KE, impulse, and pressure of gases of different masses under the same conditions.

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I was just confused about momentum, KE, impulse, and pressure of gases of different masses under the same conditions.

Page 6 of TBR Gen Chem 2 explains this very well

"If the kinetic energy of the particle increases, the particle's speed increases, so it collides more frequently with the wall. Because it is moving faster, it collides with greater momentum, so impulse increases. The result on the macroscopic level is that the force per unit area exerted against the walls increase, meaning pressure is greater. The kinetic theory of gases explains macroscopic observations using principles derived from a microscopic model.
When there are many gas particles in the container, collisions between particles become more common than collisions with the wall. However, the presence of more particles in the container also results in a greater number of collisions with the walls, so the pressure of the system increases as particles are added to the system. When there are particles of different masses in a mixed gas, heavier particles move more slowly, hence they exhibit lower collision frequencies. However, because they have a greater mass and only slightly reduced speed, they collide with greater force (momentum).

As a general rule, lighter gas molecules have greater average speeds (and greater collision frequencies) than heavier ones, but less momentum (and thus less collision force). Because pressure depends on both collision frequency and collision force, gas particles of different masses exert the same pressure. On the macroscopic level, this means that pressure is the same under identical conditions for all ideal gases, independent of their molecular mass. A good example is to compare helium and nitrogen. The reason they have the same pressure at the same temperature is because they have the same kinetic energy (mv2 term). The molecule with greater mass has less speed. The average speed is inversely proportional to the square root of the mass. "

1 users
Page 6 of TBR Gen Chem 2 explains this very well

"If the kinetic energy of the particle increases, the particle's speed increases, so it collides more frequently with the wall. Because it is moving faster, it collides with greater momentum, so impulse increases. The result on the macroscopic level is that the force per unit area exerted against the walls increase, meaning pressure is greater. The kinetic theory of gases explains macroscopic observations using principles derived from a microscopic model.
When there are many gas particles in the container, collisions between particles become more common than collisions with the wall. However, the presence of more particles in the container also results in a greater number of collisions with the walls, so the pressure of the system increases as particles are added to the system. When there are particles of different masses in a mixed gas, heavier particles move more slowly, hence they exhibit lower collision frequencies. However, because they have a greater mass and only slightly reduced speed, they collide with greater force (momentum).

As a general rule, lighter gas molecules have greater average speeds (and greater collision frequencies) than heavier ones, but less momentum (and thus less collision force). Because pressure depends on both collision frequency and collision force, gas particles of different masses exert the same pressure. On the macroscopic level, this means that pressure is the same under identical conditions for all ideal gases, independent of their molecular mass. A good example is to compare helium and nitrogen. The reason they have the same pressure at the same temperature is because they have the same kinetic energy (mv2 term). The molecule with greater mass has less speed. The average speed is inversely proportional to the square root of the mass. "

THIS IS EXACTLY WHAT I WAS LOOKING FOR. you rock.

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