chemistry question for chem wez!

[Smooth Operater]

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two identical tanks are filled with gas at 20 Celsius. Both gases are at 1 atm. If one tank contains helium and the other contains neon, then...

the correct answer is "both tanks contain the same number of gas atoms"

how come "the average kinetic energry of the neon atoms is greater than that of the helium" is not the correct answer also? I though for KE=1/2mv^2, the bigger the value of m is, the higher the kinetic energy is. In this case, neon has higher mass and thus has higher kinetic energy.


Thanks!!

 

[armorshell]

Because the KE of gas molecules is a function of temperature only. It's true the neon has a higher mass then helium, but it will also have a slower velocity.

 

[mo magic carpet]

I know that at STP, Equal volumes of gases have the same number of gas molecules. That is a rule by the wat.

In this case, the pressure is 1atm, and the volume and temp are constant therefore they must have the same number ofmolecules.

 

[grapeflavorsoda]

two identical tanks are filled with gas at 20 Celsius. Both gases are at 1 atm. If one tank contains helium and the other contains neon, then...

the correct answer is "both tanks contain the same number of gas atoms"

how come "the average kinetic energry of the neon atoms is greater than that of the helium" is not the correct answer also? I though for KE=1/2mv^2, the bigger the value of m is, the higher the kinetic energy is. In this case, neon has higher mass and thus has higher kinetic energy.


Thanks!!

ideal gas law: PV=nRT => n=(PV)/(RT). since the containers are identical, volumes must be same. the question stem also states that T and P are identical. thus "n" must be same.

average kinetic energy is sum of kinetic energy of each molecules in the system divided by the total number of molecules. you must remeber that the molecules within a system have various velocity(if you see a proper derivation of the ideal gas, it does not assume that all the molecules in a given temperature have uniform velocity, but it is assumed that molecules within a system in a given temperature have distribution of velocity that is independent of the spatial coordinates).

So each different homogenous gas system at given temperature will have different velocity distribution and this distribution is dependent on the mass of the molecule in that homogenous gas system. This distribution function was first derived by Maxwell, and later confirmed by Boltzmann. Anyway, as you can imagine given the same n, P, and V(thus T), the velocity distribution function gives lower value for average velocity square(which is the sum of the different velocity of the molecules squared, divided by the total number of molecules). This average velocity square value is multiplied by mass of the molecule and again multiplied by 1/2, to give average kinetic energy. But it turns out(mathematically), this average square value is reduced(for heavier molecules) in manner that it exactly compensates the increased mass, thus conserving the average kinetic energy of an ideal homogeneous gas system when n,T, and P are constant.

The above argument is not usually given in introductory chem class since to derive both maxwell and is ideal gas is mathetically rigorous and tedious. But you probably have heard the statement "the average kinetic energy of the ideal gas depends on the temperature; K.E. = (3RT)/2.

 

[Smooth Operater]

thank guys, all the memories of advanced physical chemistry are coming back now 😛