Mu(rms) and KE of gases

[dougkaye]

Quick questions about these kinetic-molecular equations.

1) Mu(rms) = sqrt(3RT/M)

and

2) KE = (3/2)RT

For equation 1: is this just the average speed of gas molecules for a MOLE of gas at given temperature?

Equation 2: Is this the total KE of mole of any gas at given temp?

My main confusion was whether this was for a SINGLE molecule, or a mole.

Thanks!

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[ilovemcat]

Quick questions about these kinetic-molecular equations.

1) Mu(rms) = sqrt(3RT/M)

and

2) KE = (3/2)RT

For equation 1: is this just the average speed of gas molecules for a MOLE of gas at given temperature?

Equation 2: Is this the total KE of mole of any gas at given temp?

My main confusion was whether this was for a SINGLE molecule, or a mole.

Thanks!

A container of various gases held at some temperature will have the same average kinetic energy, regardless of the number of moles you have of each gas you have. What equation 2 basically tells you is that the average KE of each gas molecule is proportional to temperature. Notice the word average. There's actually a distribution curve of the gases. Some gases move slower, some move really fast but on average, the bell curve is shifted to where most molecules are moving faster.

The equation isn't so important as the relationship - temperature is proportional to average kinetic energy. I'm not sure I understand your first equation but for any given temperature, molecules with a smaller mass on average will move faster than molecules with a larger mass because even though they have the same average kinetic energy (and therefore momentum), KEavg = 1/2mv^2 = sqrt(2 x KE) = momentum = mv. The larger the mass, the lower the velocity and vice versa.

 

[Mcat35]

Quick questions about these kinetic-molecular equations.

1) Mu(rms) = sqrt(3RT/M)

and

2) KE = (3/2)RT

For equation 1: is this just the average speed of gas molecules for a MOLE of gas at given temperature?

Equation 2: Is this the total KE of mole of any gas at given temp?

My main confusion was whether this was for a SINGLE molecule, or a mole.

Thanks!

those are for Moles since you are using the ideal gas constant

look at the units 0.086 L atm/Kelvin Mole...

If you are doing it for a molecule than you would use the Boltzmann constant

1.3806503 × 10-23 m2 kg s-2 K-1

but ya u don't need to know that specific for the MCAT.. Just know you can set the kinetic energy of mole of gas or molecule of gas directly to Kinetic energy equation 1/2 mv ^2 and solve for w/e they ask you to. Usually a proportionality or equation manipulation problem.