Kinetic energy for a mole of a gas discrepancy

[gkangelexa]

Exam krackers says that the average kinetic energy for a mole of a gas is K.E._avg = 3/2 RT

but my chemistry book says that the total kinetic energy for a mole of gas is = 3/2 RT
meaning that
N_A (average K.E. of one molecule) = 3/2 RT


These 2 statements are different, for the bottom one says that the total K.E. for a mole of gas is = 3/2 RT, yet the top one says that the average K.E. for a mole is =3/2RT

Which is correct?

 

[Ygggdrasil]

What units does the expression 3/2 RT have?

 

[gkangelexa]

R = 8.314 J/(K x mol)

so 3/2 RT units are J/ mol


Average kinetic energy for one molecule is: 1/2 m (mean square speed)...
so the units for that are: (kg m²) / (s² molecule)

so this means my chemistry book is correct because

(average kinetic energy for one molecule) (N_A) works because the units work:

since N_A = molecules/ mol... the multiplication equals 1 J/mol...


right??

So then why does my Exam Krackers book say that the average kinetic energy for a mole of gas = 3/2 RT...?

 

[Ygggdrasil]

You are correct that (3/2)RT gives the total energy per mole of a monatomic ideal gas. The average kinetic energy of a molecule of that gas is given by a very similar formula, (3/2)k_BT, where k_B is the Boltzman constant. As you can probably guess, k_B = R/N_A.

I'm not sure why your other book says that (3/2)RT is the average kinetic energy for a mole of gas.

 

[LudusRex]

Both statements are correct, but they are expressing different concepts. The first statement, from Exam Krackers, is referring to the average kinetic energy of a single molecule in a mole of gas. This is calculated by taking the total kinetic energy of all the molecules in the mole and dividing it by the number of molecules in the mole, which is Avogadro's number (NA). This is represented by the equation K.E.avg = 3/2 RT.

The second statement, from your chemistry book, is referring to the total kinetic energy of all the molecules in a mole of gas. This is calculated by multiplying the average kinetic energy of a single molecule (3/2 RT) by the number of molecules in a mole (NA). This is represented by the equation NA (average K.E. of one molecule) = 3/2 RT.

Therefore, both statements are correct and are simply expressing different ways of calculating the kinetic energy of a mole of gas. It is important to understand the difference between average kinetic energy and total kinetic energy in this context.