Kinetic Theory of Gases

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Question:

A cylinder contains a mixture of He and Ar gas in equilibrium at 150 °C.(a)What is the average kinetic energy (K.E) for each type of gas molecule? (b) What is the root-mean-square speed of each type of molecule.

Average Kinetic Energy Data
Boltzmann Constant, k_B = 1.38 x 10^-23 J/K

Atomic Mass of He, m_He = g

Atomic Mass of Ar, m_Ar = g

Temperature, T = °C

or, T = K

Enter the values to calculate for different mixture and temperature

\(\overline {K.E} \) =
1 / 2
mv²_rms =
3 / 2
k_BT

\(\overline {K.E} \) =
3 / 2
k_BT

=
3 / 2
x 1.38 x 10^-23 x 423 J

= 8.76 x 10^-21 J

1 / 2
mv²_rms = 8.76 x 10^-21 J

v²_rms =
2 x 8.76 x 10^-21 / m

where m is the mass of the gas particles.

For He atom, m_He = M_He / N_A = / 6.022 x 10²³ g/atom = 6.64 x 10^-27 kg/atom For He, v²_rms = 1.752 x 10^-20 / v_rms = m/s For Ar atom, m_Ar = M_Ar / N_A = / 6.022 x 10²³ g/atom = 6.63 x 10^-26 kg/atom v²_rms = 1.752 x 10^-21 / v_rms = m/s