Anonymous

# Very hard physics problem....HELP!?

Find the total kinetic energy content of 1.31 moles of an ideal gas at temperature 435 K.

I am supposed to use the equation...KE=(3/2)*k*T but I have no clue how to apply it.

Relevance

For any ideal gas, the KE of each molecule is...

3/2(kb)T = KE of each molecule,

where kb = Boltzmann's constant = 1.381 x 10^-23 J/K

T = absolute temperature = 435K (given)

3/2(1.381 x 10^-23)(435) = KE of each molecule

9.01 x 10^-21 J = KE of each molecule

NA = Avogadro's number = 6.023 x 10^23 particles/kmoles

No. of molecules = 1.31 kmoles x 6.023 x 10^23/kmoles

No. of molecules = 7.89 x 10^23

Total KE = KE of each molecule x No. of molecules

Total KE = (9.01 x 10^-21)(7.89 x 10^23)

Total KE = 7108.89 Joules or 7.1kJ

teddy boy

• K is the Boltzmann Constant, which is the universal gas constant R = 8.314 divided by Avagadro's number. Therefore k has a value of 1.380*10^-23 J K ^-1

Ek would then be 1.5* 1.380*10^-23* 435 J

= 9.00 * 10^-21J per molecule.

For 1 mol, multiply by Avagadro's number. But this is just going around in circles because above we divided by Avagadro's number to get the Boltzmann constant.

It is there fore much simpler to say that the kinetic energy of 1 mol ideal gas is given by the equation:

Ek = 3/2 RT where R is the universal gas constant and T is temperature in K . For 1.31 mol multiply again by 1.31.

I leave it to you to do the arithmetic.

• k = 1.381 x 10^-23 J/K

Look under "Cruft".

KE is the average kinetic energy of a molecule at the temperature K.

Multiply out the temperature, the k, the number of molecules in tn a mole and the number of moles to get total KE.

P.S. I get 7110 Joules (3 sig figs) It is convenient that the 10^23 and the 10^-23 cancel out.

• Anonymous