Question

What is the root mean square speed of an As4 particle as it is sublimed? (Assume at high temperatures arsenic acts like an ideal gas; the Boltzmann constant, kB, can be approximated as 1.4 x 10-23 J∙K-1) and the kinetic energy of the gas is equal to 3/2kB T

Answer 1

Answer: $v_{rms} =$ 273m/s

Explanation: Root Mean Square Speed of an atom or molecule is the speed of a particle in a gas. It is the average speed a particle in a gas can have.

It can be calculated:

$\frac{1}{2}mv^{2} = \frac{3}{2} k_{B}T$

$v^{2} = \frac{3k_{B}T}{m}$

$v = \sqrt{\frac{3k_{B}T}{m}}$

m is mass of one atom or molecule in kg.

An atom of Arsenic sublimes at 614°C. Converting to Kelvin:

T = 614 + 273 = 887K

Molecular mass of As4 is approximately 0.3kg.

$m = \frac{0.3}{6.10^{23}}$

$m=5.10^{-25}$kg

Calculating Root mean square speed :

$v = \sqrt{\frac{3*1.4.10^{-23}*887}{5.10^{-25}}$

$v = \sqrt{745.08.10^{2}$

v = 273m/s

The root mean square speed of As4 is approximately 273m/s.