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 Boltzmann 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.