lighter gas particles travel faster than heavier ones

[csx]

When there are a mixture of particles of different masses the heavier
particles move more slower and dont collide as frequently with the container walls.
Although they have a greater mass and a reduced speed why do they collide with greater force (momentum)?

Momentum=m*v

shouldn't they collide with equal momentum?

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[Chrisz]

First we have to consider kinetic energy.
0.5mv^2=KE=3RT/2
so v=sqroot(3RT/m)
Now you calculate the momentum
mv=m[sqroot(3RT/m)]=sqroot(3RTm)
Now you see for momentum mv=sqroot(3RTm)
as m increases, momentum increases as well at a constant temperature (which means constant KE)

 

[premed1001]

When there are a mixture of particles of different masses the heavier
particles move more slower and dont collide as frequently with the container walls.
Although they have a greater mass and a reduced speed why do they collide with greater force (momentum)?

Momentum=m*v

shouldn't they collide with equal momentum?

force and momentum are not the same thing?

if m increases then force should increase (ma)

First we have to consider kinetic energy.
0.5mv^2=KE=3RT/2
so v=sqroot(3RT/m)
Now you calculate the momentum
mv=m[sqroot(3RT/m)]=sqroot(3RTm)
Now you see for momentum mv=sqroot(3RTm)
as m increases, momentum increases as well at a constant temperature (which means constant KE)

if m increases, wouldnt v decreases, keeping it constant?

 

[Czarcasm]

When there are a mixture of particles of different masses the heavier
particles move more slower and dont collide as frequently with the container walls.
Although they have a greater mass and a reduced speed why do they collide with greater force (momentum)?

Momentum=m*v

shouldn't they collide with equal momentum?

Just an example, consider H2 and O2 gas diffusing in space at a given temperature. While their average kinetic energies are the same, their velocities are very different. If you recall the equation for Graham's Law of Effusion (also applies to diffusion or movement of gases in a container), H2 gas will travel 4 times faster than O2. However, it is 1/16 as massive as O2. Therefore, their momentum would also differ. Momentum is mass x velocity. If we have 1/16 the mass of O2 but 4 times the velocity, then the overall momentum with respect to H2 is 1/4 that of O2.

 

[Chrisz]

force and momentum are not the same thing?

if m increases then force should increase (ma)


if m increases, wouldnt v decreases, keeping it constant?

First, you have to understand why a gas molecule have a speed in the first place. The gas molecule have a speed because they have a kinetic energy. For a gas molecule, its kinetic energy is proportional to temperature, which is KE=0.5mv^2=3RT/2
At a constant temperature, KE is constant for gas molecules of any molecular mass(kinetic theory; ideal behavior).
From this equation, 0.5mv^2=3RT/2 we can find speed v=sqroot(3RT/m).
v=sqroot(3RT/m) tells us that as molecular mass increases, speed decreases at a constant temperature.
Now we have to find momentum. mv=m[sqroot(3RT/m)]=sqroot(m)sqroot(3RT)
From here, we can tell as mass increase, momentum increases.
Summary:
At a constant temp, as mass increases, speed decreases, but the momentum increases. The reason for it is that the decrease in speed and increase in mass is not by a same factor. In other words, the increase in mass has larger effect on momentum while the decrease in speed has a smaller effect; therefore, an overall increase in momentum. when we calculate speed, we have to take a sqroot. See the difference.
Everything is in the derivation already. You have to understand why it is derived in such way and give it a reasonable verbal interpretation. Otherwise, you will not notice the fact that increase in mass would not lead to a same degree decrease in speed.

 

[premed1001]

Wow thank you for this!