Question

Two gas cylinders are identical. One contains the monatomic gas neon (Ne), and the other contains an equal mass of the monatomic gas krypton (Kr). The pressures in the cylinders are the same, but the temperatures are different. Determine the ratio KEAvg,krypton / KEAvg,neon of the average kinetic energy of a krypton atom to the average kinetic energy of a neon atom. KEAvg,krypton / KEAvg,neon =

Need equation with numerical answer!! Thanks

Answer 1

if we assume ideal behavior
.. PV = nRT

so that
.. (PV) = nRT.. Kr
.. (PV) = nRT..Ne

dividing
.. (PKr / PNe) x (VNe / VNe) = (nKr / n..Ne) x (R/R) x (TKr / TNe)

and we know
.. VKr = VNe ===> (VKr / VNe) = 1 and cancels out
.. PKr = Per ===> (PKr / PNe) = 1 and cancels out
.. R/R cancels out

leaving
.. 1 = (nKr / nNe) x (TKr / TNe)

rearranging
.. (TKr / TNe) = (nNe / nKr)

and since moles = mass / molar mass
.. (TKr / TNe) = (mass Ne / mw Ne) x (mass Kr / mw Kr)

and we know that mass NE = mass Kr so that
.. (TKr / TNe) = (mw Kr / mw Ne)

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...

we know that
.. v = sqrt (3 x kb x T / m)... with v in m/s.. m is molar mass in kg/mol

rearranging
.. v² = 3000 x kb x T / m

rearranging
.. m x v² = 3000 x kb x T

and since KE = 1/2 mv²
.. KE = 1500 x kb x T... where KE is kinetic energy per MOLE of gas molecules

we can get rid of the mole if you like by dividing both sides by Avogadro's number
but that's what the kb is for..

anyway
.. KE Kr = 1500 x kb x T KE
.. KE Ne = 1500 x kb x T Ne

dividing
.. KE Kr / KE Ne = T KE / T Ne

and from above
.. KE Kr / KE Ne = mw Kr / mw Ne

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