Question

The root-mean-square speed (urms ) is the speed of a gas particle possessing the average kinetic energy (KE ), which is mathematically defined by the following two equations:

KE= NA12mu2

KE= 32RT

Given that N_A∙ m = M, where N_A is Avogadro’s number, m is mass, and M is molar mass, use algebra to derive the equation for urms

Answer 1

We know that Kinetic energy is given by below equations;

K.E. = Na * m * v^2 /2  

v is root means square speed.

Na * m = M

M is molar mass.

So, K.E. = M * v^2 / 2 ...(1)

Also,

K.E. = 3RT/2 ....(2)

Equating equation (1) and (2);

M * v^2 / 2 = 3RT/2

v^2 = 3RT/M

v = sqrt (3RT/M) (sqrt means square root)

R is gas constant , T is temperature in K.