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The average kinetic energy of the molecules in a gas sample depends only on the temperature, T. But given the same kinetic energies, a lighter molecule will move faster than a heavier molecule. 3RT where R-8.314 J/(mol K) and. is molar mass in kilograms per mole. Note that a joule is the same as a kg m2ls2. rms speed4 What is the rms speed of O2 molecules at 375 K? Number m/s What is the rms speed of He atoms at 375 K? Number m s

Explanation / Answer

1)

M = molar mass of the gas in kg/mol
For O2, M = 32.00 g/mol = 0.032 kg/mol
For He, M = 4.00 g/mol = 0.004 kg/mol

For O2
v = sqrt((3 x 8.314 x 375)/ 0.032 kg/mol) = 540.637 m/s

For He
v = sqrt((3 x 8.314 x 375)/ 0.004 kg/mol) = 1529.154 m/s

2)

The equation you need to use is:

l = k T/(sq root 2)(pi)d^2 p

k = Boltzmann constant
T = Kelvin temperature
d = diameter in m
p = pressure in Pa

2.5 X 10^-6 m = 1.38X10^-23 J/K (293 K)/1.414(3.14)(2.7X10^-10)^2(p)
p = 4.99 X10^3 Pa= 0.049 atm

for 2.5 mm, p=4.99Pa = 0.000049atm

for 2.5m, p=0.00499Pa =0.000000049 atm

3)1 bar = 1 x 10^5 pascal.

5.00 bar x ( 1 x10^5 Pa / 1bar) = 5 x 10^5 Pa

Molar mass of H2 = 2 x 10^-3 kg/mol

Zwall = (P/4KT) [sqrt(8RT/?M)]

= (5 x 10^5 Pa / 4 x 1.38x10^-23 J/K x 294K) [ sqrt(8 x 8.314 J/Kmol x 294K / 3.14 x 2 x 10^-3 kg/mol)]

Zwall = 3.08094x10^25 x 1764.59 = 5.4366x10^28 s^-1 m^-2

1 picometer = 1.0

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