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:

`(1)/(2)mv^(2) = (3)/(2) k_(B)T`

`v^(2) = (3k_(B)T)/(m)`

`v = \sqrt{(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 = (0.3)/(6.10^(23))`

`m=5.10^(-25)`kg

Calculating Root mean square speed :

`v = \sqrt{(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.