Gas laws, rms and kinetic energy

Question

What is the average K.E of a hydrogen molecule at 27 oC in joules and in electron volts?. What is the rms speed?

Answer 1

V_rms \(=\sqrt{\frac{3RT}{M}}\) (where R = 8.315, T = 300, M = 2)

\(=\sqrt{\frac{3\times8.315\times300}{2\times10^{-3}}}\)

\(=\sqrt{\frac{7483.5}{2\times10^{-3}}}\)

\(=\sqrt{\frac{74835\times10^{3-1}}{2}}\)

\(=\sqrt{37417.5\times10^2}\)

= 193.4 x 10

V_rms = 1934 m/s

Average Kinetic energy E_k = 3/2 K_BT x N_A

= 3/2 R/N_A x T x N_A

= 3/2 x 8.315 x 300

= E_k = 3741.3 J

Average Kinetic energy in eV

E_k \(=\frac{3741.3}{1.6\times10^{-19}}\)

E_k = 2338.31 x 10⁺¹⁹ eV