Question

Your research director informs you that the molecules of a sample of gas at 333 K have a root-mean-square (rms) speed of 255 m/s and asks you to calculate the most probable speed and the average speed. Also, while you\'re at it and before lunch, you should calculate the mass of a molecule. Please do so here. 1)Most probable speed:___m/s 2) Average speed:__m/s 3) Molecular mass__kg

Answer 1

Here ,

Vrms = 255 m/s

T = 333 K

1)

for the most probable speed

most probable speed = sqrt(2 * R T/m)

most probable speed = sqrt(2/3) * 255

most probable speed = 208.2 m/s

2)

for the average speed =

average speed = sqrt(8 * R T/(pi * m))

average speed = sqrt(8/(pi * 3)) * Vrms

average speed = 0.921 * 255

average speed = 235 m/s

3)

for the molecular mass is m

Vrms = sqrt(3 * R * T/m)

255 = sqrt(3 * 8.314 * 333/m)

solving for m

m = 0.127 Kg/mol

the molecular mass = 0.127/6.022 *10^23

molecular mass = 2.11 *10^-25 Kg