The Internal Energy of Neon Gas

[PrideofPhilly]

Homework Statement

The internal energy of a monoatomic ideal gas such as neon is simply the total kinetic energy of all its atoms.

What is the internal energy of 2 liters of neon at a temperature of 200 K and pressure of 0.7 atm?

Homework Equations

PV = nRT
KE(ave) = 3/2kT
U = 3/2nRT

The Attempt at a Solution

KE = 1/2mv^2

From a previous problem, I figured out that v(rms) = 499.227 m/s.

And, 2 liters of neon X 0.9002 g/L (density of neon) = 0.0018004 kg

KE = 1/2(0.0018004 kg)(499.227 m/s) = 224.3546833 J (wrong answer)

I feel like I am approaching this problem in the wrong manner. Please help!

 

[LowlyPion]

That's the density of Ne at STP. What is the density at 200K and .7 atm?

 

[PrideofPhilly]

So, d = P X MM/RT

d = (0.7 atm)(20 g/mol)/(8.31 J/mol*K)(200 K)
d= 0.008423586

2 L * 0.008423586 = 1.684717208E-5 kg

KE = 1/2(1.68E-5)(499.227 m/s)^2 = 2.09 J (WRONG ANSWER)

AM I USING THE WRONG UNITS OR DID I DO A MATH ERROR?

 

[LowlyPion]

So, d = P X MM/RT

d = (0.7 atm)(20 g/mol)/(8.31 J/mol*K)(200 K)
d= 0.008423586

2 L * 0.008423586 = 1.684717208E-5 kg

KE = 1/2(1.68E-5)(499.227 m/s)^2 = 2.09 J (WRONG ANSWER)

AM I USING THE WRONG UNITS OR DID I DO A MATH ERROR?

I'd say your numbers are wrong, because without even looking you had .0018 kg using STP. I wouldn't expect such a small number after accounting for the 200/273 ratio and the .7 ratio.

Won't the approach work out to be more like (P1/T1)/(P2/T2) = d1/d2 ?

 

[RTW69]

I may be missing something but it looks from the revelant equations that
U=1.5*(R/M)*T where R is the universal gas constant, M is the molecular weight of neon and T is temperature in deg K. Am I over simplifing this?

 

[ideasrule]

The solution to the problem is startlingly simple; you were less than a hair away from getting it. You wrote, as a relevant equation, U = 3/2nRT. You also wrote PV = nRT. So if U=(3/2)PV, and you have both P and V.

Remember this neat result: the internal energy of an ideal gas depends only on its pressure and volume.