[kissoftalons]

The question is as follows:

You are given two flasks of equal volume, one containing CO at 2 atm and 25 C and the other containing CO2 at 1 atm and 25 C.
a) compare average kinetic energy of the molecules in the 2 flasks
b) compare average speed of the molecules in the two flasks
c) compare number of molecules in the 2 flasks

For a and b. I wanted to check my answer. My reasoning was the since the CO has two as much pressure exerted its particles would be more tightly packed and its kinetic energy would decrease, so the CO would have less average kinetic energy than the CO2 (with only 1 atm of pressure exerted).

The speed of the molecules in the CO would also be slower (more pressure)

Is this right? or do i have this completely backwards?

For c) I'm not very sure if the CO would have twice as many molecules...since it occupies the same volume as the CO2 but its got twice as much pressure on it...

[Donaldson Tan]

You are given two flasks of equal volume, one containing CO at 2 atm and 25 C and the other containing CO2 at 1 atm and 25 C.
a) compare average kinetic energy of the molecules in the 2 flasks
b) compare average speed of the molecules in the two flasks
c) compare number of molecules in the 2 flasks

pressure is due to collision of the particles on the walls. since pressure is directly proportional to concentration at fixed temperature, then the second flask (25C, 2atm) has twice as much particles as the first flask (25C, 1atm).

kinetic energy of the particle is dependent on temperature. since both flasks are of the same temperature, then the particles in both flask exhibit the same kinetic energy. since they exhibit the same average kinetic energy, then they have the average speed. however, the the second flask will have a smaller mean free path.

[Yggdrasil]

since they exhibit the same average kinetic energy, then they have the average speed.

This is only true if the molecules have the same mass [edit: used to say speed].  Since CO is less massive than CO₂, the CO molecules must have a higher average speed than the CO₂ to have the same average kinetic energy.

[Donaldson Tan]

Since CO is less massive than CO₂, the CO molecules must have a higher average speed than the CO₂ to have the same average kinetic energy.

oh.. one is CO and the other CO2? LOL. I thought both flasks contain CO2.

Yggdrasil is right  :thmbup:

[kissoftalons]

Is kinetic energy solely dependent on temperature? My thinking was that the CO with twice as much pressure on it in the same given volume...would have particles that were moving much quicker..and colliding with each other more often. Would this not create more kinetic energy?

[paperclip]

Well for speed: how about 1.4 km per second. That's around the mean speed of helium at 20 degrees celcius. That's about 2250 miles per hour. Gases do indeed speed about. I hope my statistics are correct, seems to be done by Maxwell and Boltzmann.

[Borek]

Is kinetic energy solely dependent on temperature?

If I recall correctly... mean kinetic energy of gas particle is kT/2 - where k is a Boltzman constant (k=R/N - gas constant/Avogadro number), T is absolute tempearture. So kinetic energy depends ONLY on temperature.

Note that to get higher pressure in smaller volume you don't have to change kinetic energy of particles - if volume is smaller, distance between particles is smaller and they collide with the flask walls more often. That's where the higher pressure comes from.

[sdekivit]

kinetic energy = 1/2 * m * <v>^2 = 3kT/2 (recall that molecules move in 3 dimensions. Acoording to the equipartition theorem the average energy of each individual degree of freedom is kT/2 per particle. Thus in 3 dimensions the mean energy is given by 3kT/2.)

[Borek]

3kT/2

Thanks, my mistake. I have spent last 20 years forgetting details

[kissoftalons]

Would the two flasks have the same amount of molecules? Because if the CO particles are moving faster...to create the same amount of kinetic energy, wouldn't that mean that there are the same amount of particles compared to CO2.

For example. If there were more molecules of CO than CO2, couldn't the particles move at the same rate as those in CO2 to obtain the same kinetic energy?

Does this make sense!?

[Donaldson Tan]

from the perfect gas equation, P = (n/V)RT

in both flasks, the volume of the system & temperature  is the same.

this only means n_CO is twice of n_CO2

[Yggdrasil]

Would the two flasks have the same amount of molecules? Because if the CO particles are moving faster...to create the same amount of kinetic energy, wouldn't that mean that there are the same amount of particles compared to CO2.

For example. If there were more molecules of CO than CO2, couldn't the particles move at the same rate as those in CO2 to obtain the same kinetic energy?

Does this make sense!?

Temperature is proportional to the average kinetic energy of the molecules, not the total kinetic energy of the molecules.  So, having twice as many molecules would not double the temperature.  Although the total kinetic energy of the system doubles, the average kinetic energy of the system would remain the same.